Section 1: Whole Numbers

Transcription

1 Grade 6 Play! Mathematics Answer Book 67 Section : Whole Numbers Question Value and Place Value of 7-digit Numbers TERM 2. Study: a) million A million has 6 zeros. b) million therefore million 00 thousands. 2. Complete: a) million is written b) million c) A million has 6 zeros. d) million 000 thousands e) million is written f) Study: M HTh TTh Th H T U We say, seven million, three hundred and fifteen thousand, six hundred and forty two. 4. Write down the value of each underlined digit. Value is how much a digit in a number is worth. a) b) c) d) e) f) Write down the place value of each underlined digit. Place value is what column (M, HTh, TTh, Th, H, T or U) the digit is in. Think Position a) Th b) M c) H d) U e) TTh f) HTh 6. Use the following digits to make the: Question 2 Writing 7-digit numbers a) biggest number b) smallest odd number (must end on the 5). Complete: a) One million, two hundred and nine thousand and seventy five is written b) Four million, one hundred thousand and seven is written c) One million, six hundred and forty thousand and eighty is written d) Seven million, two hundred and five thousand, one hundred and twelve is written e) Nine million, four hundred and seventy-nine thousand is written f) Eight million and five hundred and sixty-five is written Millions space Thousands space (No thousands ) g) Two million, five hundred thousand, four hundred and thirty six is written Term 2 Section Whole Numbers Copyright Reserved

2 Grade 6 Play! Mathematics Answer Book 68 Question Writing 7-digit numbers in words. Write each of the following numbers in words. a) : One million, four hundred and two thousand, eight hundred and seventeen. b) : Three million, nine hundred and twenty five thousand and sixty two. c) : Five million, three hundred and eighty thousand, four hundred and one. d) : Eight million, eighty thousand and eight. Question 4 Comparing Numbers The crocodile mouth must eat the bigger number.. Insert the symbol >, < or between each pair of numbers. a) < b) < c) > d) e) f) < Question 5 Ascending and Descending Order. Write the following numbers in ascending order of size , , , , , , Write the following numbers in descending order of size. 2 2, 2, 2, 2 2 2, 2 2, 2 2, 2. Question 6 Short Form. Write in short form. a) b) c) d) e)* f)* 4HTh U 6Th 2U 9TTh 7T M g)* Term 2 Section Whole Numbers Copyright Reserved

3 Grade 6 Play! Mathematics Answer Book 69 Question 7 Number Facts. Complete: a) tens 0 b) 4 hundreds 400 c) 5 thousands d) 00 thousands tens hundreds thousands thousands tens hundreds thousands thousands Complete: a) In there are 00 thousands, 000 hundreds or tens. Number Facts pp b) In there are 000 thousands, hundreds or tens. c) In there are 8000 thousands, hundreds or tens. d) In there are 52 thousands, 5 26 hundreds or tens. e) In there are 2 54 thousands, 2 54 hundreds or tens. f) In there are 5 92 thousands, hundreds or tens.. True or False? million 00 thousand. True Question 8 Rounding off to the nearest, 0 or 00. Complete: a) correct to the nearest 00. b) correct to the nearest 00. c) correct to the nearest 00. d) correct to the nearest correct to the nearest. *e) correct to the nearest correct to the nearest. *f) correct to the nearest correct to the nearest. Question 9 Rounding off to the nearest 5. The number line below shows how to round off to the nearest Round each number off to the nearest 5. a) 5 b) c) d) * Term 2 Section Whole Numbers Copyright Reserved

4 Grade 6 Play! Mathematics Answer Book 70 Question Rounding off to the nearest 5,, 0 or 00. Complete: Number Rounded off to the nearest a) b) * c) * d) * Rounding Off pg. 240 Question Mental Maths. Complete:.2 Complete:. Complete: a) a) a) b) b) b) c) c) c) Complete:.5 Complete:.6 Complete: a) a) a) b) b) b) c) c) c) Complete:.8 Complete:.9 Complete: a) a) a) b) b) b) c) c) c) *Question 2 More than and Less Than. The number which is: a)* more than is b) less than is more than is less than is more than is less than is more than is less than is The number which is: a) M more than is HTh more than is H more than is U more than is b) M less than is HTh less than is H less than is T less than is Term 2 Section Whole Numbers Copyright Reserved

5 Grade 6 Play! Mathematics Answer Book 7 Question 8-digit numbers and 9-digit numbers. Study. a) TM M HTh TTh Th H T U We say, thirty eight million, two hundred and nine thousand, four hundred and sixty five. b) HM TM M HTh TTh Th H T U We say, two hundred and fifteen million, four hundred and seventy three thousand, eight hundred and seven. 2. Write down the value of each underlined digit. Value is how much a digit in a number is worth. a) b) c) d) e) f) Write down the place value of each underlined digit. Place value is what column the digit is in. a) Th b) TM c) HTh d) T e) M f) HM 4. Complete: a) Seventeen million, five hundred thousand and twenty one is written b) Fourteen million, one hundred and seven thousand is written c) Sixty five million, two hundred and forty thousand and eighty six is written d) Seven hundred million, two hundred and thirty thousand and fifteen is written e) Three hundred and sixty-five million, nine hundred thousand and two is written f) Four hundred and eight million, nine hundred and seventy three is written Write each of the following numbers in words. Millions space Thousands space a) : Twelve million, eight hundred and seventeen thousand four hundred and two. b) : Three hundred and twenty million, sixty eight thousand, nine hundred and twenty five. Question 4 Comparing Numbers The crocodile mouth must eat the bigger number.. Insert the symbol >, < or between each pair of numbers. a) 8 8 > 8 8 b) > c) > d) < e) < f) < g) < h) Term 2 Section Whole Numbers Copyright Reserved

6 Grade 6 Play! Mathematics Answer Book 72 Question 5 Value Challenge. a) In the number : The value of the digit 4 on the left is 00 times the value of the digit 4 on the right b) In the number 485 5: The value of the digit 5 on the left is 0 times the value of the digit 5 on the right. c) In the number : The value of the digit 9 on the left is 000 times the value of the digit 9 on the right d) In the number : The value of the digit on the left is 00 times the value of the digit on the right In the number : a) The value of the 2 is 20. b) The value of the 5 is c) The value of the 6 plus the value of the is d) The value of the 9 plus the value of the 4 is e) The value of the 4 multiplied the value of the 2 is f) The value of the 7 on the left is 000 times value of the 7 on the right. *Question 6 More than and Less Than. The number which is: 2. The number which is: a) M more than is a) 5 M less than is b) HTh more than is b) HTh less than is 79 8 c) 8 Th more than is c) 8 TTh less than is d) 5 M more than is d) 20 M less than is * e) H more than is * e) H less than is Complete: a) What number is M more than ? b) What number is 20 M more than ? c) What number is 5 M less than ? d) What number is HTh more than ? Term 2 Section Whole Numbers Copyright Reserved

7 Grade 6 Play! Mathematics Answer Book 7 Section 2: Multiplication Question Speed Exercises TERM 2. Complete. This exercise must be done without counting. a) 4 2 b) c) d) Complete. a) 6 8 b) c) 8 24 d) Question 2 Multiples. Study:, 6, 9, 2, 5 are called multiples of. Multiples think multiply : x, 2 x 6, x 9, 4 x 2 etc 2. Complete each table. a) b) c) Multiples of 4 Multiples of 7 Multiples of 2. Complete: a) Write down the first 5 multiples of 6. 6, 2, 8, 24, 0. b) Write down the first 7 multiples of 9. 9, 8, 27, 6, 45, 54, Complete: a) What is the third multiple of 8? 24 ( 8) b) What is the 2 th multiple of 4? 48 (2 4) 5. True or False? 2, 4, 8, 6, 2 are multiples of 2. False Multiples of 2 are 2, 4, 6, 8, etc. 6. Complete: a) Write down the multiples of 5 between and 40. 5, 20, 25, 0, 5. b) Write down the multiples of 8 between 20 and , 2, 40, 48, 56, 64. Term 2 Section 2 Multiplication Copyright Reserved

8 Grade 6 Play! Mathematics Answer Book 74 Question Factors. Study: x x 6 2 x 4 2 factor factor factor factor factor factor, 2,, 4, 6, 2 are the factors of 2. Always write factors in pairs, from the outside in. 2. Write down the missing factor in each of the following number sentences. a) b) c) *d) *e) Complete: a) The factors of 5 are,, 5, 5. b) The factors of 8 are, 2,, 6, 9, 8. c) The factors of 24 are, 2,, 4, 6, 8, 2, 24. d) The factors of 6 are, 2,, 4, 6, 9, 2, 8, 6. Always start with and the number itself and then fill in the rest of the factor partners from the outside in. *e) The factors of 56 are, 2, 4, 7, 8, 4, 28, 56. Question 4 Multiples and Factors. True or False? a) 2 is a factor of all even numbers. True b) 2 is a factor of. False it is a multiple. c) 4 is a factor of 96. True d) 9 is a multiple of 54. False it is a factor. 2. Which numbers below are factors of 42? Which numbers below are multiples of 2? Question 5 Multiplication (2-digit by -digit). Complete Think: a) b) 0 90 c) d) e) f) g) h) Complete. a) T U b) T U c) (2T U) 2 84 (8T 4U) d) ( 4) 6 ( 6) e) (8T 2U) 504 (48T 24U) f) Term 2 Section 2 Multiplication Copyright Reserved

9 Grade 6 Play! Mathematics Answer Book 75 Question 6 Multiplication (2-digit by 2-digit). Complete: Think: 2 26 a) 0 0 b) c) d) Study: a) Think: 9 0 b) Think: Complete: a) b) c) d) e) f) g) h) Complete. a) T U b) T U c) (4T 2U) 47 (4T 7U) d) (2T U) 6 (6T U) e) f) g) h) Question 7 Multiplication (-digit by -digit). Complete: Think: a) b) c) d) Study: a) Think: b) Think: Complete: a) b) c) d) e) f) g) h) Complete: a) 2 4 b) c) d) e) f) g) * h) * Term 2 Section 2 Multiplication Copyright Reserved

10 Grade 6 Play! Mathematics Answer Book 76 Question 8 Multiplication (-digit by 2-digit). True or False? a) 4 means the same as 2. True See pg. 242 Concept b) 6 means the same as 6. False it means the same as 8 c) 4 6 means the same as 24. True 2. Use the factors of the 2-digit number to calculate each answer. a) 26 5 b) 42 2 c) d) e) *f) Steps will vary depending on the factors chosen Study: a) Think: b) Think: Complete: a) b) c) d) Complete using the vertical column method. a) 478 b) 867 c) d) e) f)* g)* Question 9 Problem Solving (Up to -digit numbers multiplied by 2-digit numbers). There are 24 rows of chairs in the school hall with 5 chairs in each row. How many chairs are there in total in the hall? chairs 2. A grocer sells a fruit and veg basket for R25. How much will 0 baskets cost? R25 0 R750. Eggs are packed into containers which hold 2 dozen eggs each. How many eggs can be packed in 65 of these containers? Dozen means 2 2 dozen eggs 4. The distance from Inge s home to work is 65km. She drives to work and back home every day. Return Trip 65km 2 0km 0km 75 How far does Inge travel in 75 working days? 9750 km Term 2 Section 2 Multiplication Copyright Reserved

11 Grade 6 Play! Mathematics Answer Book 77 Question Price per Kilogram We say this: R25 per ONE kg.. Study: If it costs R25 for kg of potatoes, we write this as R25/kg. a) How much do kg of potatoes cost? b) How much do kg of potatoes cost? Answer: R25 R75 Answer: R25 R Complete the table and then answer the questions that follow. a) b) Chicken Lamb Protein Price per kilogram Cost for 2 kg 4 kg 8 kg 2 kg R 75 / kg R50 R00 R600 R900 R 49 / kg R298 R596 R92 R788 Question The Distributive Property of Multiplication. Study: We know that brackets mean do me separately. However, in the examples below, instead of doing the bracket separately, we distribute the multiplication over the addition or the subtraction. Example ) 4 ( 2) (4 ) (4 2) Example 2) 78 (0 ) (78 0) (78 ) Discuss why this is equal to This is an important property to understand as it is used in algebra from Grade 7 onwards. 2. Calculate using the distributive property of multiplication. Answers may vary. 5 ( 2) (5 ) (5 2) a) 5 2 b) Hint: 9 20 c) (20 4) d) (0 ) Hint: 99 0 (25 20) (25 4) (20 ) (245 20) (245 ) (62 0) (62 ) Fill in the missing numbers so that each sentence is correct. a) 89 ( 5) (89 ) (89 5 ) b) 25 (20 8) (25 20 ) (25 8 ) c) 48 ( 7) ( 48 ) ( 48 7) d) 259 (40 ) ( ) ( 259 ) e) a (b c) (a b ) (a c ) f) ( 8) ( ) ( 8 ) 4. Which statement is equal to 25? 5.* Which statement is equal to 85 99? a) 25 ( ) a) (85 0) (85 ) b) 25 ( ) 25 b) (99 ) c) 25 ( ) 25 0 c) (85 0) (85 ) See Multiplication pg Concepts - 2 Term 2 Section 2 Multiplication Copyright Reserved

12 Grade 6 Play! Mathematics Answer Book 78 Question 2 Multiplication (4-digit by -digit). Complete: Think: a) b) c) d) e) f) Complete: a) 2 42 b) c) d) e) f) *g) *h) Question Multiplication (4-digit by 2-digit). Calculate using the distributive property of multiplication. Steps may vary. a) 6 b) d) ( ) c) e) Complete using the vertical column method. a) 4268 b) 867 c) d) e) f)* g)* Question 4 Multiplication (-digit by -digit and 4-digit by -digit). Complete using the vertical column method. a) 627 b) 6428 c) d) e) f) g) h) * Calculate using the distributive property of multiplication. Steps may vary. a) 42 2 b) Hint: (0 2) (42 0) (42 2) (200 ) (44 200) (44 ) Term 2 Section 2 Multiplication Copyright Reserved

13 Grade 6 Play! Mathematics Answer Book 79 Question 5 Multiplication of three numbers. True or False? Three numbers can be grouped and multiplied in any order. True 2. Fill in the missing numbers. a) 7 (5 ) (7 5) b) c) (427 6) (6 87) d) Multiply these numbers in the easiest order. Hint: Multiplying by is the easiest. a) b) c) d) e) f) Multiply these numbers in the easiest order. Hint: Multiplying by multiples of is the easiest. a) b) c) d) e) f) * Complete. a) d) b) e) c) *f) Question 6 Problem Solving. Sally works in a beauty salon. She earns R75 an hour. If she works for 8 hours each day, how much does she earn per week, from Monday to Friday? Monday to Friday 5 days Income per day: R75 8hours R600 Income per week: R600 5days R In a book of 78 pages there are approximately 5 words to a line and 25 lines to a page. a) Approximately how many words are there on a page? b) Approximately how many words are there in the book? A family saves R256 per month. a) How much do they save in one year? R256 2 R5 072 b) How much do they save in a decade? R5 072 R Calculate the product of 6782 and A normal, healthy adult heart beats about 78 beats per minute. h 60min, ½h 0min a) How many times will a heart beat in half an hour? 78 beats/min 0min 240 beats b) How many times will a heart beat in one hour? 78 beats/min 60min 4680 beats 2 c)* How many times will a heart beat in one day? 4680 beats/h 24h 2 20 beat Term 2 Section 2 Multiplication Copyright Reserved

14 Grade 6 Play! Mathematics Answer Book 80 Section : -D Objects Question Identify and Sort -D Objects. Name the -D objects below. A B C D E Not a prism: curved surface TERM 2 Cone (not a pyramid) cube triangular-based pyramid cylinder triangular prism cone F G H I J triangular prism sphere square-based pyramid 2. Choose the correct word to complete each sentence. hexagonal prism rectangular prism flat circle ends curved square a) A cube has six identical square faces. b) The base of a cone is a circle. c) Prisms have two identical ends and flat surfaces. d) A sphere has a curved surface.. Complete: a) Which objects in question are prisms? A, D, F, I and J. NB: Prisms have identical ends and flat surfaces. (A cylinder is NOT a prism) b) Which objects in question are pyramids? B and H. NB: Pyramids end on a vertex and have flat surfaces. (A cone is NOT a pyramid) Question 2 Faces, Edges and Vertices: The Basics. Study: EDGE The line where two faces meet FACE The flat surface. A cube has VERTEX 6 square faces. The point where the edges meet FACE The flat surface. This pyramid has square face (the base) and 4 triangular lateral faces. Lateral means of its sides. Therefore lateral faces are side faces that are not the base. 2. Complete: a) A flat surface of a -D object is a face. b) The line where two faces of a -D object meet is called an edge. c) The point where two or more edges meet is called a vertex. Term 2 Section -D Objects Copyright Reserved

15 Grade 6 Play! Mathematics Answer Book 8 Question Cubes and Rectangular Prisms. Study: 6 faces 2 faces (top and bottom) 2 faces (left and right) 2 faces (front and back) 2 edges 4 edges (around the top) 4 edges (going down) 4 edges (around the bottom) 8 vertices 4 vertices (around the top) 4 vertices (around the bottom) 2. On the cube: a) Mark the 8 vertices with circles. b) Draw lines over the 4 top edges with blue, the 4 bottom edges with green and the 4 lateral (side) edges with yellow.. Study: 6 faces 2 faces (top and bottom) 2 faces (left and right) 2 faces (front and back) 2 edges 4 edges (around the top) 4 edges (going down) 4 edges (around the bottom) 8 vertices 4 vertices (around the top) 4 vertices (around the bottom) 4. On the rectangular prism: a) Mark the 8 vertices with circles. b) Draw lines over the 4 top edges with blue, the 4 bottom edges with green and the 4 lateral edges with yellow. 5. Complete the table below. -D Object Name Number of Faces Edges Vertices a) Cube b) Rectangular prism Write down 2 similarities between a cube and a rectangular prism.. Both are prisms (box shape) 2. Both have 6 faces.. Both have 2 edges. 4. Both have 8 vertices. 7. All rectangular prisms have rectangular and square faces. True False Some only have rectangular faces. 8. Draw a net for a: Answers may vary. a) Cube b) Rectangular prism Term 2 Section -D Objects Copyright Reserved

16 Grade 6 Play! Mathematics Answer Book 82 Question 4 Triangular Prisms. Study: 5 faces 2 faces (front and back) faces (Lateral faces, joining the two s ) 9 edges edges (around the front ) edges (Lateral edges) edges (around the back ) 6 vertices vertices (around the front) vertices (around the back) 2. On the triangular prism:. Draw a net for a triangular prism: a) Mark the 6 vertices with circles. or b) Draw lines over the front edges with blue, the back edges with green and the lateral edges with yellow. Question 5 Pentagonal Prisms. Study: 7 faces 2 faces (front and back) 5 faces (Lateral faces, joining the two s ) FRONT 5 edges 5 edges (around the front ) 5 edges (Lateral edges) 5 edges (around the back ) vertices 5 vertices (around the front) 5 vertices (around the back) 2. On the pentagonal prism: a) Mark the vertices with circles. b) Draw lines over the 5 front edges with blue, the 5 back edges with green and the 5 lateral edges with yellow. Question 6 Mixed Questions. Complete the table below: -D Object Name FRONT Number of Faces Edges Vertices a) Triangular Prism 5 (2 ) 9 ( ) 6 ( ) b) Pentagonal prism 7 (2 5) 5 (5 5 5) (5 5) c)* Hexagonal prism 8 (2 6) 8 (6 6 6) 2 (6 6) 2.* Circle the correct answer A, B, C or D. Which of the following are properties of a pentagonal prism? a) 5 vertices b) vertices c) 5 edges d) 5 faces A: a) and c) B: b) and c) C: a) and b) D: All of the above Term 2 Section -D Objects Copyright Reserved

17 Grade 6 Play! Mathematics Answer Book 8 Question 7 Cylinders and Cones. Which set of shapes (A, B or C) can be used to make a cylinder? B A: B: C: A cylinder consists of 2 circles at each end with a rectangle wrapped around the outside of each. 2. Study: faces 2 faces (top and bottom) face (wrapped around, joining the two s ) 2 edges 2 edges (top and bottom) 0 vertices. True or False? 4. Draw a net for a cylinder: a) A cylinder has vertices. False It has 0 vertices. b) The dotted lines drawn on the cylinder below are edges. False A cylinder only has edges where the 2 circular faces meet the wrapped around rectangle. 5. Study: vertex A cone has 2 faces, a curved shape and a circular face. A cone has edge, where the curved face and the circular face meet. 6. Complete the table below: -D Object Name Number of Faces Edges Vertices a) Cone 2 b) Cylinder A cylinder has edges and faces. a), 2 b) 2, c), 2 d), 0 8. A cone has vertex, faces and edge. a), 2, b) 2,, c) 2, 0, d),, 2 Term 2 Section -D Objects Copyright Reserved

18 Grade 6 Play! Mathematics Answer Book 84 Question 8 Pyramids. Study: 5 faces 4 faces (lateral) face (At the bottom, the base) 8 edges 4 edges (around the base, at the bottom) 4 edges (lateral) 5 vertices vertex (at the top) 4 vertices (around the base) 2. On the square-based pyramid:. Draw a net for a square-based pyramid. a) Mark the 5 vertices with circles. b) Draw lines over the: - 4 edges around the base with blue. - 4 lateral edges with green.. Study: 4 faces faces (lateral) face (At the bottom, the base) 6 edges edges (around the base, at the bottom) edges (lateral) 4 vertices vertex (at the top) vertices (around the base) 4. On the triangular-based pyramid: 5. Draw a net for a -based pyramid. a) Mark the 4 vertices with circles. b) Draw lines over the: - edges around the base with green. - lateral edges with yellow. 6. Study: The 4 triangles used to build the pyramid above are identical. It is therefore also called a tetrahedron. (tetra is from the Greek for four) 7. Complete the table below: -D Object Name Number of Faces Edges Vertices a) square-based pyramid 5 ( 4) 8 (4 4) 5 ( 4) b) triangular-based pyramid or tetrahedron 4 ( ) 6 ( ) 4 ( ) *c) pentagonalbased pyramid 6 ( 5) (5 5) 6 ( 5) Term 2 Section -D Objects Copyright Reserved

19 Grade 6 Play! Mathematics Answer Book 85 Question 9 Mixed Questions. Complete the table below: -D Object Name Number of Faces Edges Vertices a) Cube b) Cylinder 2 0 c) Pentagonal prism 7 (2 5) 5 (5 5 5) (5 5) d) pentagonalbased pyramid 6 ( 5) (5 5) 6 ( 5) e) Hexagonal prism 8 (2 6) 8 (6 6 6) 2 (6 6) 2. Circle the correct answer A, B, C or D. Which of the following -D objects has (or can have) a square as a base? a) tetrahedron b) cube c) pyramid d) cone A: a) and b) B: b) and d) C: a) and c) D: b) and c). Name the -D object that is made with each net. a) b) c) square-based pyramid cylinder hexagonal prism 4. Name two differences between a triangular-based pyramid and a triangular prism.. A triangular-based pyramid ends on a vertex. (4 faces, 4 vertices, 6 edges) 2. A triangular prism has 2 identical ends. (5 faces, 6 vertices, 9 edges) 5. Which -D object has vertex? a) pyramid b) cylinder c) cube d) cone Term 2 Section -D Objects Copyright Reserved

20 Grade 6 Play! Mathematics Answer Book 86 Assessment. Circle the letter of the correct answer.. In the number , is in the millions place value column. A B 6 C 76 D rounded off to the nearest 5 is A B C D A cylinder has faces, edges and vertices. A, 2, B, 2, 0 C 0, 2, D 2,, 99 0 TERM 2.4 Which statement is equal to 65 99? A 65 (90 9) 65 8 B (60 90) (5 9) 50 4 C (65 0) (65 ) The factors of a number are 2 and 42. What is the number? A 4 4 B 2 42 C 26 D Complete: a) One hundred and fifteen million, fifty one thousand, one hundred and five is written b) What number is 5 M less than ? c) What is the largest number that can be made using the digits between 4 and 5, 6, 7, 8, 9 if each digit is used only once? d) Which numbers below will give when rounded off to the nearest 00? e) In the number the sum of the values of the two s is f) Which number is 2 less than the product of 9 and the sum of 5 and? In other words:. Which number is 2 less than the product of 9 and 8? (because 5 8) 2. Which number is 2 less than 72? (because ). Jean-Louise works in a beauty salon. She earns R90 an hour. She works for 6½ hours each day from Monday to Friday. How much does she earn per week? Monday to Friday 5 days Income per day: R90 6½hours R540 R45 R585 Income per week: R858 5days R Complete the table. -D Object Name 9 (5 ) Number of Faces Edges Vertices a) Rectangular prism d) Hexagonal-based pyramid 7 ( 6) 2 (6 6) 7 ( 6) 5. True or False? a) 20 is a factor of 5. False it is a multiple. b) When a whole number is multiplied by 5 the answer always ends in 5. False. e.g Term 2 For more assessments, visit Copyright Reserved

21 Grade 6 Play! Mathematics Answer Book 87 Section 4: Geometric Patterns Question Patterns with a Constant Difference of TERM 2. Study: A constant difference means that the same number of shapes/objects are added to each new figure in a pattern. For these questions, the constant difference is. 2. Consider the pattern and then complete the table. No. is short for number. Figure number No. of hexagons Rule: No. of hexagons Figure number. Draw the 4 th figure in the pattern and then complete the table and the rule. Figure number No. of triangles Rule: No. of triangles Figure number 4. Draw the 5 th figure in the pattern and then complete the table and the rule. Figure number No. of circles Rule: No. of circles Figure number 5. Draw the 5 th figure in the pattern. a) How does this pattern differ from the pattern in question 4? Each figure has circle more. b) Complete the table and the rule: Figure number Number of circles Rule: No. of circles Figure number 6. Study the pattern below and then complete the rule and the table. Rule: No. of cubes Figure number Figure number Number of cubes Term 2 Section 4 Geometric Patterns Copyright Reserved

22 Grade 6 Play! Mathematics Answer Book 88 Question 2 Patterns with a Constant Difference of 2. Draw the missing rd figure in the pattern. a) How many squares are added from figure to figure? 2 squares b) Complete the table and the rule: Figure number No. of squares Rule: No. of squares 2 Figure number multiples of 2 We are working with multiples of 2. Therefore the rule is 2 2. Draw the 4 th figure in the pattern. a) How many squares are added from figure to figure? 2 squares b) How does this pattern differ from the pattern in No.? Each figure has square less. c) Complete the table and the rule: Figure number No. of squares Rule: No. of squares 2 Figure number. Draw the missing rd figure in the pattern. multiples of 2 minus a) How many squares are added from figure to figure? 2 squares b) How does this pattern differ from the pattern in No.? Each figure has square more. c) Complete the table and the rule: Figure number No. of squares Rule: No. of squares 2 Figure number multiples of 2 plus 4. Study: When a pattern has a constant difference of 2, the first part of the rule is to multiply each input value by 2 and then add or subtract a number, to get to the correct output value. Term 2 Section 4 Geometric Patterns Copyright Reserved

23 Grade 6 Play! Mathematics Answer Book 89 Question Patterns with a Constant Difference of. Draw the rd figure in the pattern. a) How many crosses are added from figure to figure? crosses b) Complete the table and the rule: Figure number No. of crosses Rule: No. of crosses Figure number multiples of 2. Draw the rd figure in the pattern. a) How many crosses are added from figure to figure? crosses b) How does this pattern differ from the pattern in No.? Each figure has 2 crosses more. c) Complete the table and the rule: Figure number No. of crosses Rule: No. of crosses Figure number 2 multiples of plus 2.* Study the pattern and then complete the table. Figure number Number of suns Rule: No. of suns Figure number 2 4.* Study the pattern and then complete the table. s Figure Figure 2 Figure Figure number Number of dots Rule: No. of dots Figure number 2 s Term 2 Section 4 Geometric Patterns Copyright Reserved

24 Grade 6 Play! Mathematics Answer Book 90 Question 4 Patterns with a Constant Difference of 4.* Look at the pattern and then complete the table. 4 s Figure Figure 2 Figure Figure 4 Figure number Number of smileys Rule: No. of smileys 4 Figure number 2.* Look at the pattern and then complete the table. Figure Figure 2 Figure 4 dots Figure number Number of dots Rule: No. of dots 4 Figure number Question 5 Mixed Questions. Study the patterns below and then complete each rule and table. a) Rule: No. of bricks 2 Figure number Figure number Number of bricks b) Rule: No. of bricks Figure number 2 Figure number Number of bricks Term 2 Section 4 Geometric Patterns Copyright Reserved

25 Grade 6 Play! Mathematics Answer Book 9 Question 6 Patterns made from Matches. Matches are used to make the pattern below. a) How many matches are added from diagram to diagram? matches (not 4) b) Complete the table and the rule: Number of squares Number of matches Rule: No. of matches Number of squares 2. Matches are used to make the pattern below. a) Draw the next diagram. b) How many matches are added from diagram to diagram? 2 matches (not ) c) Complete the table and the rule: Number of triangles Number of matches Rule: No. of matches 2 Number of triangles. Study the pattern below and then complete the table Diagram number Number of matches Rule: No. of matches 4 Diagram number multiples of 4 4.* Study the pattern made with matches and then complete the table. 7 matches are added from diagram to diagram (not 8) Diagram number No. of matches Rule: No. of matches 7 Diagram number Term 2 Section 4 Geometric Patterns Copyright Reserved

26 Grade 6 Play! Mathematics Answer Book 92 Question 7 Square Numbers. Study the pattern of square numbers Square Numbers There is not a constant difference between the number of dots. 2. Draw the next diagram in the pattern and then complete the table and the rule. Rule: No. of dots Diagram number Diagram number Diagram number Number of dots Study the pattern made by stacking cans and then complete the table. These are Square Numbers. Stack number Number of dots Question 8 Completing Tables (Additional Practice). Complete each table. Note: The inputs are named x and the outputs are named y. a) x b) x y y Input Output Input 5 2 Output c) x d) x y y Input 8 2 Output Input 2 7 Output 2. Complete each table. Hint: First determine the rule between x and y for each. a) x y b) x y c) x y d) x y x y x 4 y x 7 2 y x 9 y Term 2 Section 4 Geometric Patterns Copyright Reserved

27 Grade 6 Play Mathematics Answer Book 9 Section 5: Symmetry Question Lines of Symmetry (Shapes, Letters and Logos). Study: A line of symmetry divides a shape in half so that the one side fits exactly on the other side when folded. TERM 2 Vertical Horizontal Diagonal Note: Since there are an infinite number of lines through the centre, the circle has an infinite number of lines of symmetry. When the circle is folded over a line of symmetry, the parts of the circle on each side of the line match up. 2. Draw the line of symmetry in each of the figures below. Say whether the line is vertical or horizontal. NB: Dotted lines must be drawn. a) b) c) d) e) Vertical Vertical Horizontal Vertical Horizontal. Draw the line(s) of symmetry, if any, in each letter or number. a) b) c) d) e) f) 4. Draw the line(s) of symmetry, if any, in each logo or symbol below. a) b) c) d) e) Question 2 Draw the other half of symmetrical figures. Draw the other part of each shape using the line of symmetry. In other words draw the shape s mirror image or reflection. a) b) c) Term 2 Section 5 Symmetry Copyright Reserved

28 Grade 6 Play Mathematics Answer Book 94 Question Lines of Symmetry in Squares and Rectangles. Draw the lines of symmetry in the square and the rectangle below and then answer the questions. a) A square has 4 lines of symmetry. b) A rectangle has 2 lines of symmetry. A rectangle does not have a diagonal line of symmetry like a square because the sides are not the same length. If you fold this rectangle diagonally so that a corner meets an opposite corner, the sides do not match. Try it with a piece of notebook paper. 2. Explain in your own words why a rectangle does not have diagonal lines of symmetry. A rectangle s sides are not the same length. If you fold a rectangle diagonally so that a corner meets an opposite corner, the sides do not match. Question 4 Lines of Symmetry in Rhombuses and Parallelograms. True or False? The line drawn in each rhombus is a line of symmetry. a) b) c) d) True False True False Remember, a line of symmetry divides a shape in half so that the one side fits exactly on the other side when folded. 2. Draw the line(s) of symmetry in the rhombus: HINT: There are 2 lines of symmetry.. True or False? 4. a) Draw the line(s) of symmetry, if any, The lines drawn in each parallelogram in the parallelogram below: are lines of symmetry. a) b) b) A parallelogram has 0 lines of symmetry. False False Term 2 Section 5 Symmetry Copyright Reserved

29 Grade 6 Play Mathematics Answer Book 95 Question 5 Lines of Symmetry in Triangles. Study: Triangles A, B and C are not the same. Therefore they do not have the same number of lines of symmetry. A B C symmetry lines symmetry line 0 symmetry lines equal sides 2 equal sides 0 equal sides 2. Draw the line(s) of symmetry, if any, in each triangle below: a) b) c) d) Question 6 Lines of Symmetry in Pentagons and Hexagons. Study: A regular pentagon has five lines of symmetry. Each line of symmetry starts at a corner and ends exactly in the middle of the opposite side. 2. Complete: A regular pentagon has five lines of symmetry. Each line of symmetry starts at a corner and ends exactly in the middle of the opposite side.. True or False? The line drawn in each pentagon is a line of symmetry. a) b) c) d) False True False True 4. Study: A regular hexagon has six lines of symmetry. lines of symmetry start at a corner and end at the opposite corner. lines of symmetry start exactly in the middle of one side and end exactly in the middle of the opposite side. All 6 lines of symmetry Term 2 Section 5 Symmetry Copyright Reserved

30 Grade 6 Play Mathematics Answer Book True or False? The line drawn in each hexagon is a line of symmetry. a) b) c) d) True False False True 6. Draw the lines of symmetry in the pentagon and the hexagon below. a) b) Question 7 Lines of Symmetry in Polygons. Complete: a) Name each polygon below. b) Draw the line(s) of symmetry, if any, in each. A B C D Square Triangle Triangle Pentagon E F G H Rhombus Rectangle Parallelogram Hexagon 2. Complete: a) A rectangle has 2 lines of symmetry. b) A regular octagon has 8 lines of symmetry. c) A square has 4 lines of symmetry d) A regular heptagon has 7 lines of symmetry. e) A rhombus has 2 lines of symmetry f) A parallelogram has 0 lines of symmetry.. True or False? a) A triangle which has 2 equal sides has 2 lines of symmetry. False only b) A circle has line of symmetry. False It has an infinite number. Term 2 Section 5 Symmetry Copyright Reserved

31 Grade 6 Play! Mathematics Answer Book 97 Section 6: Division Question Terminology and Speed Exercises ( ) TERM 2. Study: In a division calculation, Quotient - the number being divided is the dividend. - the divisor is the number that you divide by. Dividend Divisor - the answer is the quotient. 2. Complete: a) Consider is the dividend, 6 is the divisor and 7 is the quotient.. Complete: b) The dividend is 24 and the divisor is. What is the quotient? 24 8 c) The quotient is 5 and the dividend is 0. What is the divisor? a) 8 6 b) c) *d) Complete: a) 2 4 b) c) 6 2 d) Complete Think 5T 5T and Think 24H 6 4H a) b) c) d) e) f) g) h) Question 2 Division with Remainders. Study: If one number doesn t divide into another an exact number of times, we get a remainder. Example: 6 5 remainder, because (5 6). or (6 5) 2. Fill in the missing numbers.. Complete by mental calculation: a) because or (6 4) a) 7 5 r r because (4 6) 25 b) 24 7 r r 5 because (4 6) 5 29 c) r 4 b) because or (7 6) d) r r 2 because (6 7) 2 44 e) r r 4 because (6 7) 4 46 f) r 7 4. The largest possible remainder if a number is divided by a) is 2 b) 6 is 5 c) 9 is 8 d) 2 is e) 8 is 7 f) 24 is 2 g) 2 is h) 45 is 44 i) 60 is 59 j) 87 is 86 0 Term 2 Section 6 Division Copyright Reserved

32 Grade 6 Play! Mathematics Answer Book 98 Question Rules of Divisibility. Study: One number is divisible by another number if no remainder is obtained. For example: 2 4 therefore 2 is divisible by. 2. Tick the correct numbers in each. but 4 4 r 2 therefore 4 is not divisible by. a) 2 is divisible by b) 24 is divisible by c) 5 is divisible by d) 40 is divisible by Study the rules of divisibility below. 4. Complete. 2 The last digit must be an even number. The sum of the digits must be divisible by. 4 The last two digits must be divisible by 4. 5 The last digit must be 0 or 5. 6 The number must be divisible by 2 and by. 8 The last three digits must be divisible by 8. 9 The sum of the digits must be divisible by 9. The last digit must be a 0. a) Which numbers below are divisible by 2? b) Which numbers below are divisible by? c) Which numbers below are divisible by 6? d) Which numbers below are divisible by 4? e) Which numbers below are divisible by 9? Question 4 Factors of 2-digit and -digit Numbers. Write down the missing factor in each of the following number sentences. a) b) c) *d) *e) Complete: a) The factors of 24 are, 2,, 4, 6, 8, 2, 24. b) The factors of 6 are, 2,, 4, 6, 9, 2, 8, 6. c) The factors of 42 are, 2,, 6, 7, 4, 2, 42. Always start with and the number itself and then fill in the rest of the factor partners from the outside in. d) The factors of 72 are, 2,, 4, 6, 8, 9, 2, 8, 24, 6, 72. e) The factors of 0 are, 2, 4, 5,, 20, 25, 50, 0. f)* The factors of 20 are, 2,, 4, 5, 6, 8,, 2, 5, 20, 24, 0, 40, 60, 20. g)* The factors of 6 are, 2, 4, 8, 7, 4, 68, 6. Term 2 Section 6 Division Copyright Reserved

33 Grade 6 Play! Mathematics Answer Book 99 Question 5 Short Division and Long Division (-digit by -digit). Study: The long division method is set out in a similar way to short division, however a calculation is written down for each step to determine the remainder. Examples: a) 52 4 Short Division 452 The remainders are easy to calculate mentally. This method is recommended. b) 875 Short Division 2 9 r The remainders are easy to calculate mentally. This method is recommended. 4 2 Long Division H T U H 4 4H T 4 2T U 4 2U Long Division H T U 2 9 r H 6H 9T 27T U U 2 Please Note: The long division method is usually only used when you are dividing very big numbers (for example or etc.) We are however going to practice using the long division method in this question to make it easier later on. 2. Complete using short division. a) b) c) r d) e) r 4 f) r 7 g) 7 7 r 4 NB: the answer is not r 4.. Complete using long division. h) r NB: the answer is not 26 r. i) r NB: the answer is not 29 r. a) b) r c) r 8 4. Complete: a) Consider is the quotient, 9 is the divisor and 8 is the dividend. b) The divisor is and the dividend is 879. What is the quotient? quotient Term 2 Section 6 Division Copyright Reserved

34 Grade 6 Play! Mathematics Answer Book 0 Question 6 The Factor Method of Division. Study: In these examples we use the factors of each divisor to calculate the answer. Examples a) b) Check answers using multiplication: a) b) We could divide by other factor-pairs of 40 (i.e. 2 and 20 or 5 and 8) but dividing by and then 4 is the easiest. We could divide by other factor-pairs of 60 (i.e. 2 and 0 or 5 and 2 etc.) but dividing by and then 6 is the easiest. 2. Complete using the factor-method of division. Check your answers using multiplication. a) (600 ) d) (9000 ) g) ( ) b) (8000 2) e) (2500 5) h) ( ) c) (200 4) f) (4000 8) i) ( ). Complete: a) We could divide by other factor-pairs of 20, but dividing by and then 2 is the easiest. b) d) (480 2) (600 8) f) ( ) c) e) (250 5) (450 5) * g) ( ) 4. True or False? a) False b) False c) True d) True 5. Complete using the factor-method of division a) and 5 is the only factor-pair of 25. b) (456 4 or ) e) ( or 62 6 ) c) (75 5) f) (00 5 5) d) (50 5 5) *g) (552 8 or ) 6. A toy shop must pack 200 marbles into bags of 50 marbles each. How many bags are needed? bags 7. R5000 must be shared equally between 25 waiters. How much must each waiter get? R R R00 5 R How many trays of eggs, each holding a dozen (2) eggs, can be packed from 780 eggs? trays Term 2 Section 6 Division Copyright Reserved

35 Grade 6 Play! Mathematics Answer Book Question 7 Estimation (up to 4-digit numbers divided by -digit numbers). Estimate each quotient by rounding off the dividends to the nearest. a) b) c) d) e) f) Estimate each quotient by rounding off the dividends to the nearest 0 and the divisors to the nearest. a) b) c) d) * e) * f) Estimate each quotient by rounding off the dividends to the nearest 00 and the divisors to the nearest. a) b) c) d) e) f) Why is it important to be able to estimate answers? To have an idea of what the answer should be before actually doing the calculation. Question 8 Short Division and Long Division (-digit by 2-digit). Study the following examples. Examples: a) 68 4 CLUE BOARD: Short Division The remainders are easy to calculate mentally. This method is recommended. Long Division H T U T 4 4T 2U 4 28U b) CLUE BOARD: Short Division 2 4 r The remainders are difficult to calculate mentally. Long division is recommended for this calculation. Long Division H T U 2 4 r T 24 48T 4U 24 96U Term 2 Section 6 Division Copyright Reserved

36 Grade 6 Play! Mathematics Answer Book 2 2. Complete using short division. NB: it is unnecessary to use long division for these calculations a) 2 2 b) 56 2 c) 69 d) r 2 e) f) 57 2 r 5 g) r 8 NB: the answer is not 2 r 8. h) r 9 NB: the answer is not 2 r 9. i) r NB: the answer is not 2 r.. Complete using long division. NB: it is necessary to use long division for these calculations a) 97 2 r b) c) r 2 d) e) r 22 f) r 4 g) h) r i) r 4. What is the quotient when the dividend is 986 and the divisor is 7? _58_ 6 children 5. R76 must be shared equally between 7 girls and 9 boys. How much money must each child receive? R76 6 children R46 per child *6. How many 5 seater busses are required to transport 850 people? 850 people 5 24 r 25 busses are needed. Question 9 Problem Solving: Production Rate. A machine takes hours to produces 24 toys. a) How many toys does the machine produce per hour? 24 toys hours 8 toys / hour b) How many toys does it produce in hours? 8 toys/h h 80 toys c) How long does it take to produce 96 toys? 96 toys 8 toys/h 2 hours *d) How long does it take to produce 200 toys? 200 toys 8 toys/h 25 hours 2. A machine fills 25 water bottles in 5 hours. a) How many bottles does the machine fill per hour? 25 bottles 5 hours 25 bottles/h b) How many bottles are filled in hours? 25 bottles/h h 75 bottles c) How much time is required to fill 250 bottles? 250 bottles 25 bottles/h hours d) How much time is required to fill 00 bottles? 00 bottles 25 bottles/h 40 hours.* It takes 2 hours to package 456 ready-made meals. a) How many meals are packaged per hour? 456 meals 2 hours 8 meals/h b) How long will it take to package 9 meals? 8 meals in one hour 9 meals in 0 min. or 9 meals 8 meals/h 9/8 ½ hour 4. A factory produces 525 pens every 5 minutes. a) How many pens are produced per minute? 525 pens 5 minutes 5 pens/min b) How many pens can be produced in 20 minutes? 5 pens/min 20min 700 pens c) How many pens can be produced in hour? Hint: 5min 4 h 525 pens 4 20 pens OR 5 pens/min 60min 20 pens Term 2 Section 6 Division Copyright Reserved

37 Grade 6 Play! Mathematics Answer Book Question Short Division and Long Division (4-digit by 2-digit). Study the following examples. Examples: a) 85 5 CLUE BOARD: Short Division 2 2 r The remainders are easy to calculate mentally. This is the recommended method as it is unnecessary to do long division for this calculation. Long Division Th H T U 2 2 r H 5 H T 5 5T 2U 5 U 5 b) CLUE BOARD: Short Division Long division is recommended for this calculation. Th H T U 29 Long Division H 2 64H T 2 96T U 2 288U 2. Complete using short division. NB: it is unnecessary to use long division for these calculations a) b) r 9 c) 57 2 d) 24 2 r 4 e) f) r 9 g) r 5 h) r 20 i) r 2 *. Complete using long division. NB: it is necessary to use long division for these calculations a) r 8 b) r c) r 22 d) e) r 5 f) g) r 4 *h) r i) A school buys 28 textbooks for R4060. What is the cost per textbook? R R sweets must be packed into bags containing 8 sweets each. How many bags of sweets can be packed? bags can be packed 6. How many fifteen-seater tables are needed to seat 279 people? r 4 86 tables are needed. Term 2 Section 6 Division Copyright Reserved

38 Grade 6 Play! Mathematics Answer Book 4 Question Rate of Pay for Work (including Ratio). Study: If Suzy is paid R285 for hours of work it means that she is paid R95 for hour of work. This rate is calculated as follows: R285 hours R95/ hour 2. Sally is paid R450 for a three hour shift. a) What is her hourly rate? R450 h R50/ h Emphasize : per ONE hour. b) How much will she earn for 7 hours of work at the same rate? R50/h 7h R50 *. I get paid R700 for 20 hours of work. At this rate, how much will I earn in 8 hours? NB: First work out how much is earned in ONE hour R700 20h R85/ h Amount earned in 8 hours R85/h 8 R Themba is paid R95 per hour of work. How many hours will it take him to earn R9785? R9785 R95/h hours 5. Mr Branson pays ABC Consulting R8750 for 25 hours of contract work done in May. a) What is ABC Consulting s rate per hour? R R50/hour b) Mr Branson contracts ABC Consulting again in July for 7 hours of work (at the same hourly rate as in May). How much does this cost? R50/h 7h R Anna works for hours on a project and Jane works for 2 hours on the same project. They are paid R250 in total. How much should they each get so that the money is divided fairly. Step : Time worked h 2h 5h Step : Anna s pay R50 R50 Step 2: Rate per hour R250 5 R50/h Step 4: Janie s pay R50 2 R0 Totals R James and Simon work in the tuckshop. James works for hours and Simon for 5 hours. They are paid R480 in total. How much should they each get so that the money is divided fairly. Step : Time worked h 5h 8h Step : James pay R60 R80 Step 2: Rate per hour R480 8h R60/h Step 4: Simon s pay R60 5 R00 Totals R Sally and Neo work in the garden. Sally works for 8 hours and Neo for 7 hours. They are paid R275 in total. How much should they each get so that the money is divided fairly. Step : Time worked 8h 7h 5h Step : Sally s pay R85 8 R680 Step 2: Rate per hour R275 5h R85/h Step 4: Neo s pay R85 7 R595 Totals R275 Term 2 Section 6 Division Copyright Reserved

39 Grade 6 Play! Mathematics Answer Book 5 Assessment 2. Circle the letter of the correct answer.. The missing number in the number sequence, 4, 9,, 25, 6 is: A 20 B 6 C 49 D 2.2 A parallelogram has line(s) of symmetry. A 0 B C 2 D A B 0 C 00 D Which capital letters all have 2 lines of symmetry? A A, H and X B B, C and E C H, I and K D H, I and X.5 Which of these numbers are divisible by : 2, 2, 45, 89, 96 TERM 2 A 2, 2, 89 B 2, 45, 96 C 2, 45, 96 D All of them. 2. True or False? a) All triangles have lines of symmetry. False b) The diagonal of a rectangle is a line of symmetry. False e.g. 8 is not divisible by 4. c) All even numbers are divisible by 4. False. Complete a) The divisor is 2 and the dividend is 656. What is the quotient? quotient 75 pencils 5 minutes 25 pencils / min *b) A factory produces 75 pencils in 5 minutes. How many pencils can be produced in 8 minutes? 25 pencils/min 8min 200 pencils c) Draw the lines of symmetry in the pentagon. 4. Anna works for hours in the garden and Jane works for 2 hours in the garden. They are paid R50 in total. How much should they each get so that the money is divided fairly. Step : Time worked h 2h 5h Step : Anna s pay R70 R2 Step 2: Rate per hour R50 5 R70/h Step 4: Janie s pay R70 2 R40 Totals R50 5. Complete the table. x y x 2 y x 2 y 6. Study the pattern below made with matches. 4 7 Rule: a) How many matches will there be in the next diagram? b) How many matches will there be in the th diagram? matches Term 2 For more assessments, visit Copyright Reserved

40 Grade 6 Play! Mathematics Answer Book 6 Section 7: Decimal Fractions Question The Decimal Number System. Study: Up until now we have learnt about whole numbers and common fractions. TERM 2 4 is an example of a whole number. We can count 4 whole pizzas. ½ is an example of a proper fraction. Think: - smaller than a whole or - a part of a whole. ½ is an example of a mixed number. Think: A combination of a whole number and a common fraction. a) We know how to compare and do calculations with whole numbers up to 9-digits! But what about common fractions such as and 50 and 20 and 250? o It is not easy to order or compare these fractions. o It is even more difficult to do calculations like addition (or multiplication) with these fractions. It is for this reason that we must learn about decimal fractions. 25,74 is said twenty five comma seven four three. The decimal comma separates the whole number part from the (decimal) fraction part. Tens Decimal comma Units 2 5, 7 4 st decimal place 2 nd decimal place rd decimal place The digits after the decimal comma are called decimal places. b) As we can see in the example above, we write decimal fractions with a decimal comma and no denominator. This makes it easier to do calculations like addition, multiplication, etc of fractional parts of numbers. (You will see this further on in this section.) c) As illustrated below, as we move from left to right along the place value columns, each place value is ten times smaller than the one before it. After the units we have the decimal comma. Next comes tenths, then hundredths and then thousandths Th H T U, t h th 00 0 thousands hundreds tens units tenths hundredths thousandths decimal places Decimal means based on ten. After thousandths comes ten thousandths and then hundred thousandths. However we are going to focus on tenths, hundredths and thousandths in this section. 2. Complete the table. Place Value Name a) st decimal place tenths b) 2 nd decimal place hundredths c) rd decimal place thousandths. Underline the tenths digit in each number. a),25 b) 85,7 c) 0,9 d) 82,452 e) 29,8 4. Underline the units digit in each number. a) 94, b) 6,8 c) 89 d) 875,0 e) 54,47 Term 2 Section 7 Decimal Fractions Copyright Reserved

41 Grade 6 Play! Mathematics Answer Book 7 5. Underline the hundredths digit in each number. a) 9,27 b) 0,8 c) 5,72 d) 0,05 e) 7,05 f) 654,84 g) 89,7 6. Ring the number which has a/ an a) in the tenths column. 5,72 50,02 50,02 b) 8 in the units column. 84,5 4,85 48,5 c) 6 in the hundredths column. 80,86 600,8 48,68 d) 2 in the thousandths column. 47, ,02 84, ,2 7. Write down the place value of each underlined digit. We use lowercase letters for decimal places. Place value is what column ( Th H T U, t h th ) the digit is in. a) 5, 927 h b) 245,76 H c) 62,08 T d) 98,62 h e) 85,28 th f) 6864,5 Th g) 6,864 U h) 645,68 t i) 726 U j) 0,7 h k) 800,5 t l) 578 H Question 2 Reading and Writing Decimal Fractions. Study: The number to the right is said eight hundred and forty two comma three one five. H T U, t h th 8 4 2, 5 2. Complete: a) Five hundred and eleven comma seven five is written 5,75. b) One hundred and three comma three is written,. c) Six hundred and ninety comma two nine nine is written 690,299. d) Nine thousand two hundred and seventy comma one two is written 9270,2. e) Three thousand and fifty four comma four zero six is written 054,406.. Say each number in words. a) 25,49: Twenty five comma four nine. b) 980,6: Nine hundred and eighty comma six. c) 5,002: Five comma zero zero two. d) 8,702: Eighty three comma seven zero two. 4. Write in decimal (short) form. 5. Write in decimal (short) form. a) units 5 tenths 9 hundredths,59 a) 8 units hundredths 8,0 b) 2 units tenth 6 hundredths 2,6 b) 5 units 7 hundredths 5,07 c) 5 units 7 tenths 5 hundredths 5,75 c) 4 tens 6 hundredths 40,06 d) tens 5 tenths 8 hundredths 0,58 d) 5 tenths 9 hundredths 0,59 e) 4 hundreds 2 units 6 tenths 402,6 * e) 2 tenths hundreds 00,2 * f) 2 units 9 hundredths 4 tenths 2,49 f) units 8 thousandths,008 Term 2 Section 7 Decimal Fractions Copyright Reserved

42 Grade 6 Play! Mathematics Answer Book 8 Question Working with Tenths. Study: a) b) c) (three tenths) is written as 0,. We say this as zero comma three. 7 (seven tenths) is written as 0,7. We say this as zero comma seven. 9 ( whole and nine tenths) is written as,9. We say this as one comma nine. 2. Write each number in decimal form. a) 0, b) 6 0,6 c) 2 0,2 d) 7 0,7 e) 8 0,8 f) 5,5 g) 9,9 h) 2 2, *i) ,8 *j) ,7. Write each decimal fraction as a common fraction in its simplest form. a) 0,7 f) 0,6 7 b) 0, 6 g) 5 0,2 c) 0,9 9 d),7 2 h) 5 0, e) 2, 2 5 i) 0,5 2 j) 4, Write down the fraction of each diagram which is shaded. a) b) c) Common Fraction Decimal Fraction 0, Common Fraction 6 Decimal Fraction 0,6 Common Fraction 9 Decimal Fraction 0,9 5. Study: a) We know that is equal to. Therefore, (eleven tenths) is written as,. b) We know that 27 is equal to 2 7. Therefore, 27 (twenty-seven tenths) is written as 2,7. 6. Write in decimal-notation. Note: By inspection, the last digit of the numerator is written in the tenths place value column. a) 4,4 b) 7,7 c) 2 2, d) 5,5 e) 59 5,9 *7. Insert, > or < between each pair of numbers to make correct statements. a) 0,5 > 0,4 b) 0,6 < 6 c),8 8 d) 2,5 < 20,5 e) 2, >,2 f) 500, > 50, g) 5 < 0,6 h) 78 > 70,8 i), j) 5 7 < 57 k) 0,9 > 0,8 l) 25 > 2,5 Term 2 Section 7 Decimal Fractions Copyright Reserved

43 Grade 6 Play! Mathematics Answer Book 9 8. Write down the decimal fraction represented by A, B and C on each number line. A B C a) 0 0, 0,6 0,9 A B C b),,4,7 2 A B C c) 2 2, 2,5 2,8 Question 4 Working with Hundredths (and Tenths). Study: a) b) c) 2 0 is written as 0,02. We say this as zero comma zero two is written as 2,09. We say this as two comma zero nine is written as,07. This is because 0 is equal to Write each number in decimal form. a) 7 0 0,07 b) 0 0,0 c) 4 0 0,04 d) 9 0,09 e) 0,0 f) ,05 g) 8 0,08 h) ,07 i) ,06 j) 7 0 0,07. Write in decimal (short) form. a) 2 5 0,25 b) 7 0,7 c) ,9 *d) 7 0 9,97 * e) ,8 * f) ,86 4. Study: a) 2 0 is written as 0,2. b) 25 0 is written as 0,25. c) 7 0 is written as 0, , , , 7 By inspection, the last digit of the numerator ends up in the hundredths place value column. 5. Write each number in decimal form. [Mixed Questions] a) 5 0 0,5 b) 8 0 0,8 c) ,67 d) ,75 e) ,2 f) 2 0,2 g) 2 0,2 h) ,25 i) 0, j) 6 0 0,6 k) 7 0 0,07 l) 0 0,0 m) ,0 n) 8 0,08 o) ,0 Term 2 Section 7 Decimal Fractions Copyright Reserved

44 Grade 6 Play! Mathematics Answer Book *6. Insert, > or < between each pair of numbers to make correct statements. a) 0,4 > 0,04 b) 0,25 < 0,52 c),07 7 d) < 2, e) 2,0 < 2, f) 5 0 <,5 g) 0,29 < 0,9 h) 50,6 > 5,06 i) 6,96 > 6,69 j),5 >,5 k) 0,25 < 02,5 l) 86,86 > 86,68 7. Write down the decimal fraction represented by A, B and C on each number line. A B C a) 0 0,0 0,02 0,04 0,05 0,07 0, A B C b) 0, 0, 0, 0,6 0,9 0,20 A B C c)*,5,40,45,60,75,85 A B C d)* 4,40 4,42 4,46 4,48 4,58 4,6 Question 5 Necessary and Unnecessary Zeros. Study: a) b) c) 8 < 8 0 therefore 0,20 0,2 therefore,60,6 therefore 0,08 < 0,8 this zero adds no value this zero adds no value this zero changes the value of the number. From a) and b) we see that a zero after the last decimal place adds no value to a number..2 This is not to be confused with c) where we know that 8 hundredths is less than 8 tenths. 2. Write each number in decimal form. Delete the unnecessary zeros. a) 0 0 0,0 b) ,80 c) ,50 d) 70 0,70 *e) ,20. Write each number in decimal form. Why don t you delete any zeros? They change the value of the number. a) 0 0,0 b) 8 0 0,08 c) 5 0 0,05 d) 7 0,07 *e) ,02 4. True or False? a) 0, 0,0 True b) 0,04 0,4 False 4 hundredths < 4 tenths c) 0,90 0,9 True 5. Consider the following numbers: 5,20 5,02 5,2 50,2 502 a) Circle the two numbers which are equal. b) Which number is the greatest? 502 Term 2 Section 7 Decimal Fractions Copyright Reserved

45 Grade 6 Play! Mathematics Answer Book 6. Consider the following numbers:,5 5,05,50 5,00 5,0 a) Circle the two numbers which are equal. b) Which number is the greatest? 5 *7. Insert, > or < between each pair of numbers to make correct statements. a) 0,5 0,50 b) 0,09 < 0,9 c) 6,00 6 d),50,5 e) 0,8 > 0,08 f) 0,20 0,2 g),50,5 h) 4,09 < 4,9 i),0 <, j) 6,40 6,4 k) 70,9 > 7,09 l) 0,5 < 05 Question 6 Working with Thousandths (and Hundredths / Tenths). Study: a) b) c) 00 is written as 0,00. We say this as zero comma zero zero three is written as,008. We say this as one comma zero zero eight is written as 2,005. This is because 00 is equal to Write each number in decimal form. a) ,007 b) ,004 c) ,008 d) 00,00 e) 04 00,004. Write in decimal form. a) *c) ,85 b) ,576 *d) , ,79 4. Study: a) is written as 0,78. b) 5 00 is written as 0, , , 05 By inspection, the last digit of the numerator ends up in the thousandths place value column. 5. Write in decimal form. Note: The last digit of the numerator is in the thousandths place value column in each. a) ,25 b) ,89 c) ,607 d) ,725 *e) ,02 f) ,072 g) 00 0,0 h) ,095 i) ,044 j) ,08 6. Convert the decimal fractions to common fractions. a) 0,7 7 0 b) 0, 0 c) 0, d),2 2 e) 0 2, f) 0, g) 0, h) 0, i) 4, j) 00 80, Term 2 Section 7 Decimal Fractions Copyright Reserved

46 Grade 6 Play! Mathematics Answer Book 2 Question 7 Necessary and Unnecessary Zeros. Study: a) b) c) 5 > therefore 0,200 0,2 therefore 0,080 0,08 therefore 0,05 > 0,005 these zeros add no value this zero adds no value these zeros change the value of each number. From a) and b) we see that zero(s) after the last decimal place add no value to a number..2 This is not to be confused with c). We know that 5 hundredths is greater than 5 thousandths. 2. Write each number in decimal form. Delete the zeros which are unnecessary. a) ,00 b) ,800 c) ,500 d) ,600 e) ,00 f) ,040 g) ,070 h) 00 0,0 i) 90 00,090 j) 50 00,050. Consider the following numbers: 45,80 45,08 450,80 4, ,00 45,080 a) Delete all unnecessary zeros. b) Circle the two numbers which are equal. Question 8 Equivalent Fractions: Revision. Study: To write equivalent fractions, multiply the top and the bottom by the same number. This is the same as multiplying the fraction by. 2 6 For example: Complete: a) b) We have multiplied by because 2 2. c) d) e) Write equivalent fractions by doing mental calculations. a) 5 2 b) 2 4 c) 5 6 d) e) f) Study: a) therefore b) therefore c) therefore 4 0 and Complete. a) b) c) d) Write equivalent fractions by doing mental calculations. a) 55 b) c) d) e) f) 2 g) h) 2 75 *i) *j) Term 2 Section 7 Decimal Fractions Copyright Reserved

47 Grade 6 Play! Mathematics Answer Book Question 9 Writing Common Fractions as Decimal Fractions. Study: We know that 9 (common fraction) can be written as 0,9 (decimal fraction). This is easy to change into decimal form because the denominator is. However, not all common fractions have denominators of (or 0 or 00). When this is the case, we must first write a common fraction as something out of or something out of 0 or something out of 00 etc before we are able to write it in decimal form. We do this by writing equivalent fractions, as revised in Question 8. Examples: a) , b) , 4 c) , Write each number in decimal form. a) , c) * 5 b) 04, 08, , , 22 0 d) , 02 0, , 25 e) , 75 25, , , 6 0 f) , 48 0, , 05 g) * , 5 0, , 0, 25 75, 75 0, , , * * , 75 * Question Writing Decimal Fractions as Common Fractions. Convert the decimal fractions to common fractions. [Revision] a) 0,7 0,,9 7 b) 0,0 0 c) 0,27 0, , 9 2, , , , 96 0, 85 0, d) 0, *e) 0, , ,27 00, , Study: To simplify a fraction, divide the top and bottom by the biggest number that can divide into both numbers exactly Examples: a) b) c) We have divided by because: * Write each decimal fraction as a common fraction in its simplest form. 6 a) 0,6 b) 5 0, c) ,75 4 d) 0 4 0, , , , , ,5 2 0, , ,95, , , , Term 2 Section 7 Decimal Fractions 0,25 ¼, 0,75 ¾ & 0,5 ½ must be memorized. Copyright Reserved

48 Grade 6 Play! Mathematics Answer Book 4 Question Mixed Questions. Complete the table. *2. Complete the table. Common Fraction (Simplest Form) Decimal Fraction a) 2 0,5 a) Common Fraction Decimal Fraction (Simplest Form) ,95 b) 4 0,25 b) 4,75 c) 7 0,07 c) ,84 d) 5 0,6 d) ,985. Replace the * with >, < or. 4. Fill in >, < or. a) 0,49 * ½ 0,50 < a) 0,75 ¾ <,4 b) ¼ * 0,250 b),25 ¼ c),7 * 20,65 > c) 0,02 < 2 0 0,2 d) 5,0 * 0,5 > d) 0, ,052 Question 2 Rounding off. Study: We have learnt how to round off whole numbers to the nearest, 0 or 00 etc. We are now going to round off decimal fractions to the nearest tenth, hundredth or thousandth. because of this, the number is closer to 2,5 than to 2,6. Examples: a) 2,5 2,5 to the nearest tenth. because of this 9, the number is closer to 8,72 than to 8,7. [or to one decimal place] b) 8,79 8,72 to the nearest hundredth. [or to two decimal places] because of this 5, the number is closer to 48 than to 47. c) 47,52 48 to the nearest whole number/ unit. [zero decimal places] 2. Round each number off to the nearest tenth. a) 0,7 0,7 b) 0,6 0,2 c) 5,27 5, *d),28, *e) 4,08 4,. Round each number off to the nearest hundredth. a) 0,75 0,8 b) 0,89 0,82 c),72,72 d),06,06 *e) 0,984 0,20 *4. Round off 784,89452 to the nearest *5. Round off 0,275 to a) whole number 785 a) decimal place 0, b) tenth 785,9 b) 2 decimal places 0, c) 0 785,89 c) decimal places 0,28 d) thousand 2000 e) thousandth 785,895 Term 2 Section 7 Decimal Fractions Copyright Reserved

49 Grade 6 Play! Mathematics Answer Book 5 Question Addition and Subtraction: Part. Study: a) 0, 0,5 0,8 [ tenths 5 tenths 8 tenths] b) 0,6 0,4,0 [6 tenths 4 tenths tenths whole ] c),0 0, 0,7 [ tenths tenths 7 tenths] 2. Complete. a) 0,6 0,2 0,8 (6 tenths 2 tenths 8 tenths) 0,8 0, 0,5 (8 tenths tenths 5 tenths),2 0,7,9 (2 tenths 7 tenths 9 tenths),4, 2,7 (4 tenths tenths 27 tenths b) 0,2 0,8,0 (2 tenths 8 tenths tenths) 0,5 0,5,0 (5 tenths 5 tenths tenths) 0,8 0,, (8 tenths tenths tenths) 0,7 0,9,6 (7 tenths 9 tenths 6 tenths) c),0 0,4 0,6 ( tenths 4 tenths 6 tenths),0 0,7 0, ( tenths 7 tenths tenths),2 0, 0,9 (2 tenths tenths 9 tenths) 2, 0,4,7 (2 tenths 4 tenths 7 tenths) d)*, 0,7 2,0 ( tenths 7 tenths 20 tenths) 2,5,5,0 (25 tenths 5 tenths 0 tenths) 2,2,5 0,7 (22 tenths 5 tenths 7 tenths),0 2,8 0,4 (0 tenths 28 tenths 2 tenths). Study the number patterns below. a) 0,8 ; 0,9 ;,0 ;, ;,2. b) 0,7 ; 0,9 ;, ;, ;,5. c),0 ; 2,7 ; 2,4 ; 2, ;,8. Adding tenth. Adding 2 tenths. Subtracting tenths. 4. Write the missing numbers in each pattern. a) 0,2 ; 0, ; 0,4 ; 0,5 ; 0,6 ; 0,7. b) 0,9 ; 0,7 ; 0,5 ; 0, ; 0,. c) 0,2 ; 0,4 ; 0,6 ; 0,8 ;,0 ;,2. d), ;,5 ;,7 ;,9 ; 2, ; 2,. e) 0,5 ; ;,5 ; 2,0 ; 2,5 ;,0. f) 2,0 ;,8 ;,6 ;,4 ;,2 ;,0 ; 0,8. g), ;,5 ;,9 ; 2, ; 2,7 ;,. h),2 ; 2,9 ; 2,6 ; 2, ; 2,0 ;,7 ;,4. 5. Study: a) 0,5 0,02 0,7 [5 hundredths 2 hundredths 7 hundredths] 6. Complete. b) 0,45 0,55,00 [45 hundredths 55 hundredths 0 hundredths] c),00 0,25 0,75 [0 hundredths 25 hundredths 75 hundredths] a) 0,2 0,0 0,5 b) 0,75 0,25,00 (75 h 25 h 0 h whole) 0,06 0,22 0,28 0,54 0,46,00 (54 h 46 h 0 h whole) 0,25 0,7 0,08 0,96 0,08,04 (96 h 8 h 4 h),2 0,04,6,98 0,02 4,00 (98 h 2 h 400 h 4 wholes) 2,45,2,,99 0,0 2,02 (99 h h 202 h) 7. Write the missing numbers in each pattern. c),00 0,75 0,25 ( 0 h 75 h 25 h),00 0,85 0,5 (0 h 85 h 5 h),0 0,02 0,99 ( h 2 h 99 h),00 0,05 2,95 ( 00 h 5 h 295 h) 2,04 0,06,98 ( 204 h 6 h 98 h) d)* 0,99 0,0,00 ( 99 h h 0 h whole) 2,00 0,0,97 ( 200 h h 97 h) 2,25 0,75,00 (225 h 75 h 00 h wholes) 0,62 0,5, (62 h 5 h h) 2,05,99 0,06 ( 205 h 99 h 6 h) a) 0,6 ; 0,7 ; 0,8 ; 0,9 ; 0,20 ; 0,2. b) 0,6 ; 0,68 ; 0,7 ; 0,78 ; 0,8 ; 0,88. c) 2,85 ; 2,65 ; 2,45 ; 2,25 ; 2,05 ;,85. d),20 ;,25 ;,0 ;,5 ;,40 ;,45. e) 8,5 ; 8,25 ; 8,5 ; 8,05 ; 7,95 ; 7,85. f) 4,89 ; 4,9 ; 4,97 ; 5,0 ; 5,05 ; 5,09. *g),96 ;,99 ; 2,02 ; 2,05 ; 2,08 ; 2,. *h),94 ;,96 ;,98 ; 4,00 ; 4,02 ; 4,04. Term 2 Section 7 Decimal Fractions Copyright Reserved

50 Grade 6 Play! Mathematics Answer Book 6 Question 4 Addition and Subtraction: Part 2. Complete: Example 24,65 7,56 82,870 Example 2 Example 5,29 25,820 96,05 29,94 62, ,92 a) 5,90 7,8 b) 4,26,47 c) 57,490 2,857 d),52 8,50,28 7,7 70,47 40,062 e) 242,50 5,67 f) 82, ,40 g) 7,09 620,00 *h) 8724,00 96,46 294,7 4909,48 627, ,46 2. Complete: Example 6 2, , 5 9 6, 0 Example 2 Example 5, 2 2 5, , 6 8, 4 6 2, 5 5 0, 4 5 a) 8,56 6,9 b) 4,65,47 c) 5,24,70 d) 24,25,89 2,7,8,54 2,6 e) 82,0 48,5 f) 59,00 48,5 *g) 75,600 9,467 *h) 8724,700 96,462,5,5 66, 8628,28. Complete. a) Sam weighs 45,5 kg. Her brother, Paul, weighs 6,7 kg more than her. What is Paul s mass? 45,5 kg 6,7kg 52,2 kg c) A road race is km. After completing,45 km, how far do I still have to run?,00km,45km 6,55km b) Richard is,6m tall and Jake is 2m tall. What is the difference in height between the two boys? 2,00m,6m 0,7m *d) The sum of two numbers is 2,5. One of the numbers is 7,29. What is the other number? 7,29 2,5 2,500 7,29 5, Complete. a) 0, 2 0, 5 0, 7 2 0, b) 7, 4 2, 0 6, 2 0, c) 7, 0 8 0, , 8 9, d) 6, 4 5, 7 8 0, , 8 9, , , , 0 8 *5. Calculate. a) 0,2 4, ,26 54,507 b) 80,2,00 0, ,06 Term 2 Section 7 Decimal Fractions Copyright Reserved

51 Grade 6 Play! Mathematics Answer Book 7 Question 5 Multiplication (, 0 and 00). Study: Remember, as we move left along our decimal system, each place value is ten times greater than the place value to its right Th H T U, t h th 00 0 thousands hundreds tens units tenths hundredths thousandths When a number is multiplied by, the value of each digit in the number becomes times greater and therefore each digit moves one place value column left. Examples: U, t U a) 0,7 7 U, t h U, t b) 0,05 0,5 U, t h T U, t c),0, 2. Complete: a) 0,9 9 b) 0,07 0,7 c),8 8 d) 0,65 6,5 0,4 4 0,0 0, 2,5 25 0,8,8 e),99 9,9 f) 4,04 40,4 *g) 0,006 0,06 *h) 0,075 0,75,85 8,5 2,09 20,9 7,005 70,05 4,026 40,26. Study: When a number is multiplied by 0, the value of each digit in the number becomes 0 times greater and therefore each digit moves two place value columns left. Examples: T U, t T U a) 0, T U, t h T U b) 0,4 0 4 H T U, t h H T U c) 2, Complete: a) 0, b) 0, c), d) 0, , ,0 0 5, , e) 6, *f) 2, *g) 0, ,5 *h) 5, ,8 4, , , ,7 20, Complete: [Mixed Questions including 00] a) 0, b) 0,06 0,6 c) 0,, d) 4,8 48 0, 0 0 0, , 0 4, , , , 00 4, e),89 8,9 f) 0,045 0,45 *g) 7,048 70,48 *h) 62,04 620,4, , ,5 7, ,8 62, , , , , * Complete: [Mixed Questions] a) 0, b) 0,9,9 c),205 2,05 d) 0, e) 8, f) 2,79 27,9 g) 8, h) 80, Term 2 Section 7 Decimal Fractions Copyright Reserved

52 Grade 6 Play! Mathematics Answer Book 8 Question 6 Division (, 0 and 00). Study: When a number is divided by, the value of each digit in the number becomes times smaller and therefore each digit moves one place value column right. Examples: U, t U, t a) 4 0,4 U, t h U, t h c) 2,5 0,25 T U, t h U, t h c),7,07 2. Complete: a) 7 0,7 b) 0,8 0,08 c) 2,2 d) 0,46 0, ,4 0,2 0,02 8,8 0,58 0,058 e),7 0,7 f) 5, 0,5 g) 4,09 0,409 *h) 9,00 0,900 2,9 0,29,75 0,75 2,04 0,204 0,802 0,0802. Study: When a number is divided by 0, the value of each digit in the number becomes 0 times smaller and therefore each digit moves two place value columns right. Examples: U, t h U, t h a) 4 0 0,04 U, t h th U, t h th b),9 0 0,09 T U, t h th U, t h th c) 0,5 0 0,05 4. Complete: a) 8 0 0,08 b) 0, 0 0,00 c),7 0 0,07 d) 5 0 0, ,09 0,7 0 0,007 2,9 0 0, ,49 d) 25,6 0 0,256 f) ,7 g) 25, 0 2,5 h) ,2 80,9 0 0, ,8 705,9 0 7, ,05 5. Complete: [Mixed Questions including 00] a) 704,8 70,48 b) ,5 c),5,5 704,8 0 7, ,45,5 0 0,5 704,8 00 0, ,545,5 00 0,05 d),6,06 e) 4,8 0,48 *g) 62,04 6,204,6 0 0,6 4,8 0 0,048 62,04 0 0,6204,6 00 0,06 4,8 00 0, , ,06204 Question 7 Mixed Operations [ and ].* Complete: a) 0, b),9 0,9 c) 20,5 205 d) 789,9 0 7,899 e) 8,8 0,88 f) 0, g) 80,76 0 0,8076 h) ,78 i) 0,07 0,7 j) 0,2 0,02 k) 2,05,205 l) 0, m) 8,4 0 0,084 n) 2,79 27,9 o) 87, p) 2,09 20,9 Term 2 Section 7 Decimal Fractions Copyright Reserved

53 Grade 6 Play! Mathematics Answer Book 9 Question 8 Mixed Operations [,, and ]. Complete: [Revision Exercise] a) 5,6 2,4 8,0 b) 8,7 5,5,2 c),5 5 d) 25,7 2,57 9,8,52,2 9,0 4,6 4,4 0,76 7,6 0,9 0,09 2,62 7,94 20,56 2,2 8,7,5 2, ,08 8,62 7,9 46,52 68,8 89,75 279,05 0, , Write a number sentence for each of the following and then find the answer. a) Find the sum of 5,9 and 2,7. 5,9 2,7 9,6 or 2,7 5,9 9,6 *only correct answer b) What is the difference between 5,5 and 20? 20,0 5,5 4,5* c) Calculate the product of and 2,06. 2,06 20,6 or 2,06 20,6 d) What is 82,5 divided by 0? 82,5 0 0,825* e) Calculate the product of 0,085 and 0. 0, ,5 or 0 0,085 8,5 f) What is the difference between 289,6 and 6,789? 289,600 6, ,8* Question 9 Problem Solving. A rope is 4,5m long. It is cut into pieces of equal length. Calulcate the length of each piece, in metres. 4,5m 0,45m 2. There are 0 sachets of sugar weighing 6,5g each. Calculate the total mass of the sugar sachets. 6,5g 0 650g. You pay with a R50 note when purchasing items costing R5,50 and R29,75. How much change do you receive? R50,00 R45,25 R4,75 R5,50 R29,75 R45,25 4. Jane must run 25km over days. How far does must she run each day if she must run equal daily distances? 25km 2,5km each day. *5. Sipho s mass of 45,78kg is 5,9kg more than that of his sister s mass. What is his sister s mass? 45,78kg 5,9kg 9,88kg *6. Complete. a) The sum of two numbers is 2,8. The one number is 2,75. What is the other number? 2,75 2,8 2,80 2,75 20,05 The other number is: 20,05 b) The difference between two numbers is 8,25. The larger number is 5,5. What is the other number? 5,5 8,25 5,50 8,25 7,25 The other number is: 7,25 c) The product of two numbers is 65,2. The one number is. What is the other number? 65,2 65,2 6,52 The other number is: 6,52 e) The product of two numbers is 256,8. The one number is 0. What is the other number? 0 256,8 256,8 0 2,568 The other number is: 2,568 *7. Multiply the difference between,25 and,8 by 0. (,80,25) 0 2, Term 2 Section 7 Decimal Fractions Copyright Reserved

54 Grade 6 Play! Mathematics Answer Book 20 Section 8: Capacity TERM 2 Question Writing measures of capacity in litres. Study: When changing millilitres to litres, divide by 00. Think, A large number of millilitres will give a small number of litres. m 00 00m Examples: Take note, the decimal comma separates the litres from the millilitres. a) 5000 m 5 b) 2578 m 2,578 c) 75 m,075 d) 9002 m 9,002 because because ,578 because 75 00,075 because , Complete: a) 897 m,897 b) 2097 m 2,097 c) 4007 m 4,007 d) 000 m e) 5006 m 5,006 f) 4025 m 4,025 g) 8000 m 8 h) 6698 m 6,698. Study the following examples. Take note of the unnecessary decimal zeros. a) 2500 m 2,500 2,5 because ,5 b) 250 m 2,50 2,5 because ,5 c) 2050 m 2,050 2,05 because ,05 4. Complete: Do not write any unnecessary decimal zeros. a) 700 m,7 b) 600 m,6 c) 2070 m 2,07 d) 500 m,5 e) 4020 m 4,02 f) 5820 m 5,82 g) 800 m 8,0 h) 90 m 9, 5. Study the following examples in which the capacities are less than litre. a) 400 m 0,400 b) 70 m 0,70 c) 57 m 0,057 d) 8 m 0,008 0,4 because ,4 0,7 because ,7 because ,057 because , Complete: Do not write any unnecessary decimal zeros. a) 00 m 0, b) 900 m 0,9 c) 275 m 0,275 d) 50 m 0,50 e) 920 m 0,92 f) 45 m 0,045 g) m 0,00 h) 60 m 0,06 7. Complete: [Mixed Questions] a) 2800 m 2,8 b) 50 m,05 c) 5 m 0,005 d) 80 m 0,8 e) 2 m 0,02 f) 9725 m 9,725 g) 600 m 0,6 h) 75 m, True or False? a) 60 m 0,06 True b) 72 m 7,2 False: 0,72 Term 2 Section 8 Capacity Copyright Reserved

55 Grade 6 Play! Mathematics Answer Book 2 Question 2 Writing measures of capacity in millilitres. Study: When changing litres to millilitres, multiply by 00. Think, A small number of litres will give a large number of millilitres. Examples: 00 m 00m a) 2, m b), m c) 8, m d) 0, m because 2, because, because 8, because 0, Complete: a),5 500 m b) 0,008 8 m c) 5, m d) 0,2 2 m,6 600 m 0,08 80 m 5, m 2,0 20 m 8, m 0,8 800 m * m 0,02 2 m. Complete: [Mixed Questions] a), m b),2 2 m c), m d) m e) 4,0 40 m f) 0,7 7 m g), m h) 0,08 80 m i) 9, m j) 7,8 78 m k) 0,006 6 m l) 7, m Question Working with Fractions. Study the table: 2. Study the table: *. Study the table: a) 250m 4 0,25 a) 0m 0, a) 200m 5 [ 2 ] 0,2 b) 500m 2 0,5 b) 00m 0, b) 600m 5 [ 6 ] 0,6 c) 750m 4 0,75 c) 900m 9 0,9 c) 800m 4 5 [ 8 ] 0,8 4. Complete: 5. Complete: Write your answers in decimal notation. a) m e) m a) 4 0,25 e) 0, b) m f) m b) 2 4 2,25 f) 7 2 2,7 c) m g) 0 m c) 2,5 *g) 5 0,2 d) m h) m d) 4 0,75 *h) 2 5,4 *6. Complete: a) of ½ 5 5 of 500 m 00 m b) of litre of 00ml 600 ml 5 5 c) 4 of 2 4 of 2000ml 500ml,5l d) 4 5 of 2½ 4 5 of 2500ml 2000ml 2l 7. Anna pours ¼ of water from a full,5 litre jug. How much water is left in the jug? 500 m 250 m 250 m or,25 or ¼ Term 2 Section 8 Capacity Copyright Reserved

56 Grade 6 Play! Mathematics Answer Book 22 Question 4 Ordering and Comparing Measures of Capacity. Fill in >, < or to make correct statements. a) 2, m b),5 > 50m c) 620m < 6,2 6200ml d) 200m < ¼ 250ml e) 750ml ¾ > 75m f) 7, 70 m g) 6 5m < 6,5 6l 50ml h) 0,09 90m i) 7809m < 7,89m 7890ml 2. Write the measures of capacity in ascending order of size. Ascending means small to big. a) 40 m,4 40 m ,4 750 m 40 m 400 m 250 m 40 m 750 m 250 m 400 m b) 4 4, m 4, m 400 m 4040 m 4250 m 4400 m 4040 m 4250 m 400 m 4400 m. Write the measures of capacity in descending order of size. Descending means big to small. D for going Down. a) 2, m 2,05 2, m 2 2, m 2500 m 2509 m 2050 m 2590 m 2509 m 2500 m 2050 m b) 7 6 6, m ,4 604m 6700 m 640 m 6750 m 604 m 6750 m 6700 m 640 m 604 m Question 5 Adding and Subtracting Measures of Capacity. Study: When adding or subtracting capacities, first make sure that the units are the same. Examples: a),5 45m b) 2, 5 40m Option : change 45ml to litres * Option 2: change,5l to millilitres Option : change 5l 40ml to litres * 2 Option 2:, m 2,0 200 m change both capacities to millilitres 0,45 45 m 5, m,95 95 m 7, m * Remember to line up the decimal comma Bonga drinks 750m of water at first break and 0,5 at second break. How many millilitres of water did Bonga drink in total? 750ml 500ml 250ml. Three jugs hold,5, 2 0m and 725m of juice. How much juice is there in all three jugs? Give your answer in litres. *4,255 litres,500 2,00 0,725 *4, A tank s capacity is 2,5. How much water is needed to fill the tank if there is already 7 249m of water in the tank? 2,500 7,249 5,25 or 525m Term 2 Section 8 Capacity Copyright Reserved

57 Grade 6 Play! Mathematics Answer Book 2 Question 6 Multiplying Measures of Capacity. Complete: 2. Complete: a),5,5 a), m m b),9 9 b), m m 6 c) 7,54 7,54 c), m m 7 d) 0,25 2,5 d),2 200 m 600 m,6. Miley drinks,25 of water each day. How much water does she drink in days?,25 2,5 4. Mom buys four,5 bottles of Sprite. How much Sprite did she buy in total? 500 m m 6 5. A family drinks,2 of juice every day. How much juice does the family drink in four days?, m 4,8 6. A five minute shower uses approximately 0 litres of water. In a family of 4, each family member showers once every day. Daily use 0l 4 20l How much water does the family use showering each week? Weekly use 20l 7 840l Question 7 Dividing Measures of Capacity. Complete: a) 4 00 m m b) m m 8 00 m 8 25 m m m c),5 500 m 500 m d), m m 2. A Coke must be shared equally between girl and boys. 4 children How much Coke must each child get? 00 m m 2000 ml ml. A 2 bottle of juice is shared equally between 8 workers. Each worker gets 250 m. 4. Five people share 2¼ of water. How much water does each person get? 2250 m m 5. Complete: a) b) c) * d) Hint: e) f) One glass holds 250ml. How many glasses of water can be filled from a: a) -litre bottle? 00ml 250ml 4 glasses b) 2-litre bottle? 2000ml 250ml 8 glasses c),5 bottle? 500ml 250ml 6 glasses d) bottle? 000ml 250ml 2 glasses 7. Three litres of Whizz-Clean must be poured into 750ml bottles. How many bottles can be filled? 000ml 750ml 4 bottles 8. A bottle of champagne is 750ml. How many glasses (25ml) can be poured from: a) bottle? 750ml 25ml 6 glasses b) bottles? 6 glasses from bottle 8 glasses from bottles Term 2 Section 8 Capacity Copyright Reserved

58 Grade 6 Play! Mathematics Answer Book 24 Question 8 Problem Solving [Mixed Questions]. At a party there are bottles of juice each with a capacity of 0,75. How much juice is there in total at the party? 0,75 7,5 5,00 2. How much is 5, more than 9284m? *6,06 litres 9,284. Pamela makes,5 of soup. *6,06 Determine the greatest number of 50m cups of soup she can serve. 500 ml 50ml cups 4. How much coffee is needed to serve eighteen ¼ cups of coffee? 250ml ml 4,5 l 5. A 5-litre tank contains 2 of rainwater. 4 How much rainwater is needed to fill the tank? 5000 m 2750 m 2250 m [or 2,25 or 2¼ ] 6. Which is more? Three 275ml water bottles or One ¾ bottle of water. 275ml 825ml 750ml *7. How many 750 ml glasses can be filled from 6,75 litres of water? 9 glasses can be filled. 6750ml 750ml 675ml 75ml 9 Hint: 75ml 750ml Question 9 Working with Kilolitres. Study: Large capacities are measured in kilolitres. Kilo means thousand therefore kilolitre is 00 litres. 2. Complete: When changing: a) kilolitres to litres, multiply by 00. b) litres to kilolitres, divide by 00. k k a) 000 k b) 500,5 k c) ,725 k d) 840,84 k e) 5 0,05 k f) 80,08 k g) 897 0,897 k h) 6 0,006 k i) 20 0,2 k j) 6 0,06 k k) 06,006 k l) 40 0,04 k. Complete: a),25 k 250 b), k 0 c) 8 k 8000 d) 4,72 k 4720 e) 6,0 k 60 f) 0,557 k 557 g),04 k 040 h) k 000 i) 4,005 k 4005 j),0 k 00 k) 0,00 k l) 0,8 k k k *4. Complete: a) 20 kilolitres litres. 20 k b) litres 50 kilolitres. 20 k c) kilolitre millilitres. 00 m k m Term 2 Section 8 Capacity Copyright Reserved

59 Grade 6 Play! Mathematics Answer Book 25 Question Millilitres, Litres and Kilolitres: Mixed Questions. Complete. a) 400 m 0,4 b) 7 k 7000 c),2 200 m d) 422 0,422 k e) 0,5 k 50 f) 0,08 80 m g) 5,04 k 5040 h) m i) 9 0,009 k j) 50 k k) 0,00 m l) 0,85 k Circle the correct answers. 2. The capacity of a teaspoon is. a) 0,5 b) ½ m c) 5 m d) 25 m k ¼ k a) 5,4 k b) 5250 c) 525 d) ,45. a) 450 m b) 45 m c) 4050 m d) 0,0045 k Question Price per Litre (or per Kilolitre). To work out a price involving capacity we always want to know what litre (or kl) costs. Example: If it costs R75 for 5 litres of juice it means that it costs R5 for litre. This price is calculated as follows: R75 5 R5/ 2. What is the price of each of the following, in R/litre or R/kilolitre? a) 2 litres of mineral water for R24. (R24 2) R 2 / b) R40 for a 5 Oros. (R40 5) R 8 / c) 5 litres of petrol costs R80. (R80 5) R 2 / d) R84 for k of Liquid X. (R84 ) R 28 / k *. A 2 sparkling water costs R6,80. a) What is the cost per litre? R6,80 2l R8,40/l b) How much will you pay for litres? R8,40/l l R25,20 * 4. A 5-litre apple juice costs R65,50. a) What is the cost per litre? R65,50 5l R,/l b) How much will you pay for 7 litres? R,/l 7l R9,70 Question 2 Reading Scales. How much liquid is in each of the following containers? a) litre jug b) 2 litre milk *c),5 litre milk *d) 2,25 litre milk Each interval 500ml 50ml It is half full 2250ml 2 25ml or Each interval 2250ml 225 ml 600 ml 800 ml 600 ml 25 ml Term 2 Section 8 Capacity Copyright Reserved