Grade 6 Natural and Whole Numbers

Transcription

1 ID : ww-6-natural-and-whole-numbers [1] Grade 6 Natural and Whole Numbers For more such worksheets visit Answer t he quest ions (1) Two brands of chocolates are available in packs of 72 and 40 respectively. If Sandra wants to buy equal number of chocolates of both brands, what is the least number of boxes of each chocolate brand that she will need to buy? (2) Find the successor of the given number: (3) A set of biology, chemistry and physics books needs to be divided into multiple stacks of same and highest possible height such that each stack contains books of only one subject. The number of biology books is 374, that of chemistry books is 272 and that of physics books is 816. Assuming that the thickness of all books is the same, what will be the number of stacks of chemistry books? (4) Sunerva-Primo is a comet that orbits around the sun once in 49 years, and Wallaby-Grove is a comet that orbits around the sun once in 63 years. The last time they were seen together in the sky was in In which year will they be seen together in the sky next? Choose correct answer(s) f rom given choice (5) Find LCM of 5/2 and 5/3. a. 2/3 b. 5 c. 5/3 d. 5/2 (6) The number 361 can be represented by a 19 x 19 square grid. Out of the f ollowing numbers, which number can not be represented by such a square grid? a. 729 b. 144 c. 560 d. 576 (7) If you write down all the numbers f rom 1 to 195 (including 1 and 195), how many digits would you have written down? a. 475 b. 471 c. 477 d. 478 (8) How many whole numbers are there between 21 and 71? a. 49 b. 50 c. 48 d. 47

2 ID : ww-6-natural-and-whole-numbers [2] (9) In whole numbers, the associative property is satisf ied with the f ollowing operations a. Addition and Subtraction b. Only Division c. Addition and Multiplication d. Only Subtraction Fill in the blanks (10) A rectangular courtyard with length 7 m 20 cm and breadth 4 m 41 cm is to be paved with square stones of the same size. The least number of such stones required are. (11) The product of any two numbers is equal to product of their and. (12) 209 cola cans and 275 f ruit juice cans need to be stacked in a school canteen. If each stack is of the same height and is to contain cans of the same type, the greatest number of cans each stack can have is. Check True/False (13) Between any two whole numbers there is a whole number. True False (14) All whole numbers are natural numbers True False (15) Every whole number has its predecessor. True False 2016 Edugain ( All Rights Reserved Many more such worksheets can be generated at

3 Answers ID : ww-6-natural-and-whole-numbers [3] (1) 5 boxes of f irst brand, 9 boxes of second brand. Sandra wants to buy equal number of chocolates of two brands, but she needs to buy them in multiples of 72 and 40 respectively. Also, she wants to buy the least number of boxes. the number of chocolates of each brand she will need to buy = L.C.M of 72 and 40. L.C.M of 72 and 40 = 360. Number of boxes of the f irst brand Sandra will need to buy = Number of chocolates of the f irst brand he will need to buy Number of chocolates in one box of f irst brand = = 5 Number of boxes of the second brand Sandra will need to buy= Number of chocolates of the second brand he will need to buy Number of chocolates in one box of second brand = = 9 she will need to buy 5 boxes of f irst brand and 9 boxes of second brand. (2) The successor of is =

4 (3) 8 ID : ww-6-natural-and-whole-numbers [4] The number of biology books is 374, the number of chemistry books is 272 and the number of physics books is 816. Since the thickness of all the books is the same and the height of each stack needs to be the same, the number of books each stack should contain would be equal to the HCF of 374, 272 and 816. All prime f actors of 374: is a factor of is a factor of is a factor of = All prime f actors of 272: is a factor of is a factor of is a factor of is a factor of is a factor of = Step 5 All prime f actors of 816: is a factor of is a factor of is a factor of is a factor of is a factor of is a factor of =

5 Step 6 ID : ww-6-natural-and-whole-numbers [5] Hence, the HCF of 374, 272 and 816 is = 2 17 = 34. Step 7 Now we know that each stack of books will contain 34 books. Total number of chemistry books = 272. Theref ore, the number of stacks of chemistry books = = 8.

6 (4) 2442 ID : ww-6-natural-and-whole-numbers [6] We have been told that the comet Sunerva-Primo orbits around the sun once in 49 years, and the comet Wallaby-Grove orbits around the sun once in 63 years. Once the two comets are seen together, the number of years af ter which they will be seen together in the sky is equal to the LCM of 49 and 63. Let us now calculate the LCM of 49 and 63. All prime f actors of 49: is a factor of is a factor of 7 49 = 7 7. All prime f actors of 63: is a factor of is a factor of is a factor of 7 63 = Step 5 the LCM of 49 and 63 is = = 441. Step 6 The year when they were least seen together in the sky = Theref ore, the year in which they will be seen together in the sky next = = 2442.

7 (5) b. 5 ID : ww-6-natural-and-whole-numbers [7] Please have a look at this article on how to f ind LCM of f ractions -f ractions/ From this aritcle we know that, LCM (a/b, c/d) = LCM(a,c)/HCF(b,d) Theref ore, LCM (5/2, 5/3) = LCM(5, 5)/HCF(2, 3) LCM (5/2, 5/3) = 5/1 LCM (5/2, 5/3) = 5 (6) c. 560 A number which is a perf ect square can be represented on a square grid and the number which is not a perf ect square can not be represented on a square grid. A perf ect square is a natural number which is the square of some natural number. In other words, only a natural number whose square root is a natural number is a perf ect square. Now, if we look at all the options caref ully, we notice that only the number 560 is not a perf ect square. All other numbers are perf ect squares (squares of the numbers 19, 24 or 27). Theref ore, we can say that the number 560 can not be represented on a square grid.

8 (7) c. 477 ID : ww-6-natural-and-whole-numbers [8] We need to f ind the total number of digits in all numbers f rom 1 to 195. The range of numbers f rom 1 to 195 can be broken into numbers with 1, 2 and 3 digits respectively: 1-digit numbers: 1 to 9: A total of = 9 numbers. Number of digits = 9 1 = 9 2-digit numbers: 10 to 99: A total of = 90 numbers. Number of digits = 90 2 = digit numbers: 100 to 195: A total of numbers = 96 numbers. Number of digits = 96 3 = 288 Total number of digits = Number of digits f rom 1-digit numbers + Number of digits f rom 2- digit numbers + Number of digits f rom 3-digit numbers = = 477 the number of digits we would have written if we wrote down all the numbers f rom 1 to 195 is 477. (8) a. 49 The dif f erence between two numbers is same as the whole numbers between two numbers plus it also includes one of the number. the total number of whole numbers that are there between 21 and 71 = 71 - (21 + 1) = = 49.

9 (9) c. Addition and Multiplication ID : ww-6-natural-and-whole-numbers [9] T he Associative Property states that if we are adding or multiplying three or more numbers, it does not matter where we put the parenthesis. It is applicable f or addition and multiplication. For example, 3 + (5 + 7) = (3 + 5) + 7, 3 (5 7) = (3 5) 7. Theref ore, we can say that, in whole numbers the associative property is satisf ied with Addition and Multiplication.

10 (10) 3920 ID : ww-6-natural-and-whole-numbers [10] According to the question, the length and breadth of the courtyard is 7 m 20 cm and 4 m 41 cm respectively. Let us f irst convert each dimension into centimeters. Since we know that 1m = 100 cm, the length and breadth of the courtyard in centimeters is 720 cm and 441 cm respectively. The pavement has to be done with square stones. To perf ectly f it the courtyard, the size of the square stones should be a f actor of both the length and breadth of the courtyard. Please ref er to this f igure to see why it is so. Since we need to minimise the number of stones needed, the size of the stones should be the largest possible. This means the size of the stones should be the highest common f actor (HCF) of 720 cm and 441 cm, the length and breadth of the courtyard in centimeters. The HCF of 720 and 441 is 9. the needed size of square stones = 9 cm The number of stones needed = Area of the couryard Area of a single stone = 9 9 = 3920 Step 5 The least number of such stones required are (11) HCF LCM

11 (12) 11 ID : ww-6-natural-and-whole-numbers [11] Since each stack needs to be of the same height and is to contain cans of the same type, the number of cans in each stack should be a f actor of both 209 and 275. Since the number of cans in each stack should additionally be greatest possible, it should be the Highest Common Factor(HCF) of 209 and 275. Lets f ind the HCF of 209 and 275. All prime f actors of 209: is a factor of is a factor of = All prime f actors of 275: is a factor of is a factor of is a factor of = Step 5 The HCF of 209 and 275 is = 11 = 11 Step 6 The greatest number of cans each stack can have 11. (13) False Whole numbers are the numbers 0, 1, 2, 3,... It is not necessary that there is a whole number between any two whole numbers. For example, between the two whole numbers 2 and 3, there is no other whole number. Theref ore, the answer is f alse.

12 (14) False ID : ww-6-natural-and-whole-numbers [12] Whole numbers are the numbers that are not negative and are not f ractions: 0, 1, 2, 3... Natural numbers are the numbers used f or counting: 1, 2, 3... We can see that 0 is a whole number but not a natural number. Theref ore, the answer is f alse. (15) False Whole numbers are the numbers 0, 1, 2, 3... Negative numbers like -1, -2, are not whole numbers. The predecessor of 0 is -1, which is a negative number. T heref ore, every whole number does not have its predecessor. Answer is f alse.