2 parts of the circle are shaded is called the numerator. the circle is divided into 7 equal parts
|
|
- Lesley Cunningham
- 6 years ago
- Views:
Transcription
1 Fractions CHAPTER. Fractions revision of this circle is shaded. is a fraction. The top number shows that The top number of the fraction parts of the circle are shaded is called the numerator The bottom number shows that The bottom number of the fraction the circle is divided into equal parts is called the denominator Equivalent fractions are fractions that are equal. If both the numerator and the denominator of a fraction are multiplied by the same number then an equivalent fraction is obtained. 6 and are all equivalent fractions. A fraction can be simplified if the numerator and denominator can both be divided by the same number. This process is called cancelling. 6 6 When a fraction cannot be simplified, it is in its simplest form or in its lowest terms. Example Find the simplest form of 8 Solution 6 is the highest common factor of 8 and Divide both 8 and by 6 The simplest form of 8 is Fractions sometimes have to be put in order of size. To do this when fractions have the same denominator, compare the numerators.
2 CHAPTER Fractions When fractions have different denominators: find the lowest common denominator (lowest common multiple of the denominators) change each fraction to its equivalent fraction with this denominator compare the numerators to put the fractions in order. Example Write the fractions and in order of size. Start with the smallest fraction. Solution The lowest common denominator for the three fractions is Equivalent fractions for each of and with a denominator of are Starting with the smallest fraction, the order is 8 that is An improper fraction is one in which the numerator is greater than the denominator. For example, and 8 are improper fractions. The improper fraction can be thought of as over or as quarters. Similarly, the improper fraction can be thought of as over or as fifths. A mixed number consists of a whole number and a fraction. For example, and 6 8 are mixed numbers. Mixed numbers can be changed to improper fractions and vice versa. For example, to change to an improper fraction, work out how many quarters there are in There are quarters in and so there are 8 ( ) quarters in Add the extra quarters to get quarters. 8 So ( ) To change the improper fraction 6 to a mixed number, firstly work out how many whole ones there are. 6 sixths is ; sixths is and so sixths is whole ones and sixths remainder is the whole number 6 is the fraction Exercise A Copy the fractions and fill in the missing number to make the fractions equivalent. a b c d e 8 f g 6 h 8 8 Copy the fractions and fill in the missing number to make the fractions equivalent. a 8 b 8 8 c d e 6 f g 6 h
3 . Addition and subtraction of fractions CHAPTER Write each fraction in its simplest form. a 6 b 6 8 c Write each fraction in its simplest form. d e f 6 g 8 h 6 a b c d e 8 6 f g 8 h Write each set of fractions in order. Start with the smallest fraction. a b 6 c 6 d e f 6 8 g h 6 Julie and Susan have identical chocolate bars. Julie eats of her chocolate bar. Susan eats 8 of her chocolate bar. Who eats more chocolate? Give a reason for your answer. Ahmid says that is bigger than 6 because is bigger than Is Ahmid correct? You must give a reason for your answer. 8 Change these mixed numbers to improper fractions. a b c 6 d 8 e f 6 Change these improper fractions to mixed numbers. a b c. Addition and subtraction of fractions of the rectangle is shaded red and of the rectangle is shaded green. of the rectangle is shaded. So d e f To add fractions with the same denominator, add the numerators but do not change the denominator. For example, 6 which in its simplest form is To add fractions with different denominators, firstly find the lowest common denominator and then change each fraction to its equivalent fraction with this denominator. Example Work out Solution and The lowest common denominator is Change each fraction to its equivalent fraction with a denominator of So Add the numerators but do not change the denominator.
4 CHAPTER Fractions Example Work out 8 Give your answer as a mixed number. Solution The lowest common denominator is 8 Change to the equivalent fraction with a denominator of Add the numerators but do not change the denominator. Change the improper fraction to a mixed number. 8 8 Fractions can be subtracted in a similar way. Example Work out Solution 6 and 6 The lowest common denominator is Change each fraction to its equivalent fraction with a denominator of Subtract the numerators but do not change the denominator. Exercise B In questions give each answer as a mixed number or a fraction in its simplest form. Work out a b c d 8 e f g h Work out a 8 b c 6 d e f 6 8 g h 8 Work out a b c d e f g h 6 Work out a b c 8 d 8 e 6 f g h 6 Work out a b c 6 d e 8 f 6 g h 6 6
5 . Addition and subtraction of mixed numbers CHAPTER. Addition and subtraction of mixed numbers When adding mixed numbers, add the whole numbers and the fractions separately. Example 6 Work out Solution Add the whole numbers. Add the fractions. Add the two results. Sometimes adding the fractions gives an improper fraction. For example, adding the fraction parts of and gives is an improper fraction. As a mixed number, 6 6 So Mixed numbers can be subtracted in a similar way. Example Work out Solution Subtract the whole numbers. Subtract the fractions. Add the two results. 6 Example 8 Work out Solution 8 Method and Change mixed numbers to improper fractions. 8 and The lowest common denominator is Change each fraction to its equivalent fraction with a denominator of 8 Subtract the numerators but do not change the denominator. Give the answer as a mixed number.
6 CHAPTER Fractions Method Subtract the whole numbers. Subtract the fractions. Add the two results. Exercise C Work out a b 8 c 6 d e f g h Work out a b 8 c d Work out a b c 6 d 8 Work out a b c d 6 e f 6 g h Work out a b 8 8 c 6 8 d 6 e 8 f 6 g 8 h 6. Multiplication of fractions and mixed numbers Multiplication by an integer is the same as repeated addition. So is the same as 8 To multiply a fraction by an integer, multiply the numerator of the fraction by the integer. Do not change the denominator of the fraction. Example Work out 6 Solution 6 6 Multiply the numerator of the fraction by the integer. Do not change the denominator. Simplify the fraction. The answer is an integer in this case. To multiply 6 by Multiply the numerators 6 Multiply the denominators Simplify the fraction. 6 ( ) of the area of the square is shaded. To multiply two fractions, multiply the numerators and then multiply the denominators. 8
7 . Multiplication of fractions and mixed numbers CHAPTER Example Work out Solution Multiply the numerators Multiply the denominators is in its simplest form. When multiplying fractions, it is sometimes possible to simplify the multiplication by cancelling. Example Work out Solution Cancel the and the When multiplying mixed numbers, first write the mixed numbers as improper fractions. Example Cancel the and the Work out Solution 8 8 Change each mixed number into an improper fraction. Cancel the and the Change the improper fraction into a mixed number. Exercise D Give each answer in its simplest form. Work out a b c d e 8 f g 8 h
8 CHAPTER Fractions Work out a b c d e f g h Work out a b 8 c d 6 8 f 6 h 6 e g 8 Work out a b c d e f g h Work out a b c d e 8 f 6 g 6 h 8 6 Work out a 6 6 b 8 c ( 6 ) 8 d ( ). Division of fractions and mixed numbers of this rectangle is shaded red. Divide the red area by Now 8 of the rectangle is shaded. So 8 also 8 So dividing by is the same as multiplying by is the reciprocal of To work out consider how many times goes into There are in whole squares, this is lots of So also So dividing by is the same as multiplying by is the reciprocal of Similarly, the reciprocal of (or ) is and the reciprocal of is To divide by a fraction change the division sign into a multiplication sign write down the reciprocal of the second fraction. 6
9 . Division of fractions and mixed numbers CHAPTER Work out Solution Example Example Work out 6 Give your fraction in its simplest form. The reciprocal of is Multiply by Solution The reciprocal of 6 6 So multiply 6 by is 6 Write the improper fraction as a mixed number. When dividing mixed numbers, first write the mixed numbers as improper fractions. Example Work out Solution Write the mixed numbers as improper fractions. The reciprocal of is Write the improper fraction as a mixed number. Exercise E Give each answer in its simplest form. Work out a 6 b 8 c 6 d 8 e f g h 6 Work out a b c e 8 f g 8 d 6 8 h 6 Work out a b c d e f g h Work out a b c d 6 8 e f 6 g h Work out a ( ) b c 8 ( 8 ) d 6
10 CHAPTER Fractions.6 Fractions of quantities A unit fraction has a numerator of and the denominator is a non-zero positive integer. Examples of unit fractions are and To find a unit fraction of an amount, think of that amount divided into equal parts. Example 6 Find of Solution 6 6 of 6 Finding of an amount is the same as dividing the amount into equal parts. To find a fraction of an amount where the numerator is more than, think of the calculation in two stages. Firstly, divide the amount by the denominator. Then multiply the result by the numerator. Example Find of Solution Divide by The result is 8 Multiply 8 by of 6 Another way to find a fraction of a quantity is to multiply the quantity by the fraction. For example 8 6 In mathematics, the word of means the same as Example 8 Find of Solution 8 of of means the same as of Change the improper fraction into a mixed number. Exercise F Find a of b of 8 c of d 6 of e of f 8 of g of 8 h of 6 Find a of b of c of d of e 6 of f of g of h 8 of 8
11 . Fraction problems CHAPTER Find a of b of grams c of 8 cm d of e 6 of m f of cm g of 8 kg h of 6 km Find a of b of c of 6 d of 6 e 8 of f of 8 g of 8 h of Find a of b 8 of c 6 of d 8 of 6 Find a of 8 b 8 of 6 c 6 of 8 d of 6 e 6 of 6 m f of g of 66 kg h of km Find a of b 8 of m c 6 of 6 km d of 8 cm e of kg f of grams g of h of 68.. Fraction problems Problems can involve fractions. In a cinema Example of the audience are women. 8 of the audience are men. All the rest of the audience are children. What fraction of the audience are children? Solution 8 6 Add and 8 to find the fraction of the audience who are women or men. Subtract from to find the fraction of the audience who are children. of the audience are children. Example A school has 8 pupils. 86 of these pupils are girls. of the girls like swimming. of the boys like swimming. Work out the total number of pupils in the school who like swimming. Solution 86 6 Work out the number of girls who like swimming Work out the number of boys in the school. Work out the number of boys who like swimming. 6 6 pupils like swimming. Work out the total number of pupils who like swimming. 6
12 CHAPTER Fractions Exercise G Simon spends of his money on rent and of his money on transport. a What fraction of his money does he spend on rent and transport altogether? b What fraction of his money is left? Dawn drives for of a journey. The journey lasts for 8 minutes. For how many minutes does Dawn drive? There are 8 students in a school. of the students are boys. Work out the number of boys in the school. Last season, Pearson Athletic won of its matches, drew and lost the rest. What fraction of its matches did it lose? of a garden is lawn. of the garden is a vegetable patch. The rest of the garden is a flower bed. What fraction of the garden is a flower bed? 6 8 of an iceberg lies below the surface of the water. The total volume of an iceberg is m. What volume of this iceberg is below the surface? There are 6 students in a class. Javed says that 8 of these students are boys. Explain why Javed cannot be right. 8 John walks miles to the next village. He then walks a further miles to the river. How far has he walked altogether? Tammy watches films. The first film is hours long and the second one is hours long. Work out the total length of the two films. Two sticks are metres and metres long. Work out the difference between the lengths of the two sticks. of a square is shaded. of the shaded part is shaded blue. What fraction of the whole square is shaded blue? In a crowd, of the people are female. of the females are girls. What fraction of the crowd is girls? DVDs are sold for each. of the goes to the DVD company. How much of the goes to the DVD company? A school buys some textbooks. The total price of the textbooks is The school gets a discount of 8 off the price of the textbooks. Work out how much the school pays for the textbooks. Alison, Becky and Carol take part in a charity relay race. The race is over a total distance of 8 kilometres. Each girl runs an equal distance. Work out how far each girl runs. 6
13 Chapter review questions CHAPTER Chapter summary You should now know: that equivalent fractions are fractions that are equal how to find an equivalent fraction by multiplying both the numerator and denominator by the same number how to cancel a fraction to obtain its simplest form how to order fractions by writing each fraction with the same denominator that an improper fraction is one in which the numerator is greater than the denominator that a mixed number consists of a whole number and a fraction how to convert between mixed numbers and improper fractions that to add (or subtract) fractions with the same denominator, add (or subtract) the numerators but do not change the denominator that to add or subtract fractions with different denominators, firstly find the lowest common denominator and then change each fraction to its equivalent fraction with this denominator how to add (or subtract) mixed numbers by adding (or subtracting) the whole numbers and the fractions separately how to multiply fractions by multiplying the numerators and then multiplying the denominators how to multiply or divide mixed numbers by firstly writing the mixed numbers as improper fractions how to divide by a fraction by changing the division sign into a multiplication sign writing down the reciprocal of the second fraction how to find a fraction of an amount by dividing the amount by the denominator and then multiplying the result by the numerator. Chapter review questions Work out a of 8 b of c of 6 d of e 6 of Work out a of b of 8 c of d of e of Change to improper fractions a b 8 Work out a b c d e Simon spent of his pocket money on a computer game. He spent of his pocket money on a ticket for a football match. Work out the fraction of his pocket money that he had left. (8 June ) 6
14 CHAPTER Fractions 6 Asif, Curtly and Barbara share some money. Asif receives 8 of the money. Barbara receives of the money. What fraction of the money does Curtly receive? (88 March ) Work out ( 6 ) (8 November ) 8 Work out, giving your answers as mixed numbers a b Work out and simplify where possible a b c 8 d e 8 Work out a b c 6 d 8 e Work out and simplify where possible a b c d e 6 Work out and simplify where possible a of b of c of 6 d of 8 e of Work out, giving each answer in its simplest form a 8 b 6 c 6 d 6 e 6 Work out, giving each answer in its simplest form a b c d 8 6 e 8 Work out a 6 b 8 (88 March ) 6 Work out 6 Give your fraction in its simplest form. (88 January ) Work out, giving your answers as mixed numbers a b 8 a Work out the value of Give your answer as a fraction in its simplest form. b Work out the value of + Give your answer as a fraction in its simplest form. (8 June ) A school has pupils. of these pupils are girls. of the girls like sport. of the boys like sport. Work out the total number of pupils in the school who like sport. (8 November ) Work out (88 March ) Work out Give your answer as a mixed number in its simplest form. 66
St Anselm s College Maths Sample Paper 2
St Anselm s College Maths Sample Paper 2 45 mins No Calculator Allowed 1 1) The speed of light is 186,000 miles per second. Write the speed of light in words. 2) The speed of light is more accurately given
More information20 Arithmetic: Fractions
MEP Y Practice Book B 0 Arithmetic: Fractions 0. Revision: Whole Numbers and Decimals In this section we revise addition, subtraction, multiplication and division of whole numbers and decimals, before
More information4 One ticket costs What will four tickets cost? 17.50
TOP TEN Set X TEST 1 1 Multiply 6.08 by one thousand. 2 Write one quarter as a decimal. 3 35% of a number is 42. What is 70% of the number? 4 One ticket costs 17.50. What will four tickets cost? 17.50
More informationHillhead High School. Fractions. What you need to know. S.O Grady 1
Fractions What you need to know S.O Grady What is a fraction? A fraction is a part of a whole (). Fractions consist of two numbers, a numerator and a denominator. Top number How many parts we have Bottom
More informationnumerator - how many parts count b) What fraction of the bar is shaded? d) What fraction of the rectangle is shaded?
. [Fractions] Skill. Illustrating proper fractions. numerator - how many parts count denominator - how many equal parts in one whole Q. What fraction of the circle is shaded? The circle is divided into
More information12+ ENTRANCE EXAMINATION
12+ ENTRANCE EXAMINATION SAMPLE PAPER MATHEMATICS INFORMATION FOR CANDIDATES Time: 1 hour 30 minutes In each question you should put your answer in the box provided. The mark for each question is shown
More informationIntroduction to Fractions
Introduction to Fractions A fraction is a quantity defined by a numerator and a denominator. For example, in the fraction ½, the numerator is 1 and the denominator is 2. The denominator designates how
More informationYear 9 mathematics: holiday revision. 2 How many nines are there in fifty-four?
DAY 1 ANSWERS Mental questions 1 Multiply seven by seven. 49 2 How many nines are there in fifty-four? 54 9 = 6 6 3 What number should you add to negative three to get the answer five? -3 0 5 8 4 Add two
More informationFractions Presentation Part 1
New Jersey Center for Teaching and Learning Slide / Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and
More informationHomework 1 Number Work (1)
Homework 1 Numer Work (1) 1. Order each list of numers, smallest first :- d 5.3, 5.46, 5.03, 5.1, 5.31, 5.18 e 9.4, 10.32, 10.06, 9.78, 9.14, 10.1, 10.77 2. Complete the following and find the answers
More informationTERM 2 MATHS NOTES COMMON FRACTIONS
1 TERM 2 MATHS NOTES COMMON FRACTIONS Table of Contents DEFINITIONS AND KEY WORDS:... 3 Proper Fractions:... 3 Improper Fractions:... 3 Mixed Fractions:... 3 CONVERTING FRACTIONS... 4 EXERCISE 1... 4 EQUIVALENT
More informationSt Andrew s Academy Mathematics Department S1 BLOCK 1
St Andrew s Academy Mathematics Department S1 BLOCK 1 FRACTIONS 1 ½ ½ ¼ ¼ ¼ ¼ 1 / 6 1 / 6 1 / 6 1 / 6 1 / 6 1 / 6 1 / 8 1 / 8 1 / 8 1 / 8 1 / 8 1 / 8 1 / 8 1 / 8 1 / 10 1 / 10 1 / 10 1 / 10 1 / 10 1 /
More informationAdding Fractions with Different Denominators. Subtracting Fractions with Different Denominators
Adding Fractions with Different Denominators How to Add Fractions with different denominators: Find the Least Common Denominator (LCD) of the fractions Rename the fractions to have the LCD Add the numerators
More informationTHOMAS WHITHAM SIXTH FORM
THOMAS WHITHAM SIXTH FORM Number Levels - 8 Year 9 T H O M A S W H I T H A M. P B W O R K S. C O M Number() Basic Number work. List the first multiples of a) b) 9 c) d). Find the lowest common multiple
More informationGrade 7 Math notes Unit 5 Operations with Fractions
Grade 7 Math notes Unit Operations with Fractions name: Using Models to Add Fractions We can use pattern blocks to model fractions. A hexagon is whole A trapezoid is of the whole. A parallelogram is of
More informationAdding and Subtracting Fractions Part 1: The same sized slice
Adding and Subtracting Fractions Part : The same sized slice Exercise What to do We are learning to add simple fractions Each of these fraction problems can be shown with fraction symbols. Use fraction
More informationThe Willows Primary School Mental Mathematics Policy
The Willows Primary School Mental Mathematics Policy The Willows Primary Mental Maths Policy Teaching methodology and organisation Teaching time All pupils will receive between 10 and 15 minutes of mental
More informationOCR Statistics 1. Probability. Section 2: Permutations and combinations. Factorials
OCR Statistics Probability Section 2: Permutations and combinations Notes and Examples These notes contain subsections on Factorials Permutations Combinations Factorials An important aspect of life is
More informationReigate Grammar School. 11+ Entrance Examination January 2012 MATHEMATICS
Reigate Grammar School + Entrance Examination January 0 MATHEMATICS Time allowed: 45 minutes NAME Work through the paper carefully You do not have to finish everything Do not spend too much time on any
More informationChapter 7 Math Guide
I can write fractions as a sum Write as unit fractions This means the fractions are broken into each individual unit/1 single piece. The fraction is /6. The model shows that pieces are shaded in. If you
More informationEDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 2. Chapter 1. Working with whole numbers. SECTION A 1 Place value and rounding 2. 2 Negative numbers 4
EDEXCEL FUNCTIONL SKILLS PILOT Maths Level 2 Chapter 1 Working with whole numbers SECTION 1 Place value and rounding 2 2 Negative numbers 4 3 Factors and multiples 6 4 Estimating and checking 8 5 s for
More informationMATH 074 REVIEW FOR CHAPTER 2 and 3 - Sections , ( Fractions) a) 18: b) 20: c) 48: d) 60: e) 59:
MATH 074 REVIEW FOR CHAPTER 2 and 3 - Sections 2.1-2.4, 3.1-3.5 ( Fractions) A. Can you list all the factors of a given number? 1. List all the factors of each of the following numbers. a) 18: b) 20: c)
More informationALDENHAM SCHOOL Entrance Paper SAMPLE PAPER. Mathematics
ALDENHAM SCHOOL 13 + Entrance Paper SAMPLE PAPER Mathematics Length of Examination 1 hour Do not open until you are told to do so Surname:. School: First name:... Age: Years Months.. INSTRUCTIONS FOR CANDIDATES
More informationDescription Reflect and Review Teasers Answers
1 Revision Recall basics of fractions A fraction is a part of a whole like one half (1/ one third (1/3) two thirds (2/3) one quarter (1/4) etc Write the fraction represented by the shaded part in the following
More informationTest B. Calculator allowed. Mathematics test. First name. Last name. School KEY STAGE 2 LEVELS 3 5
Ma KEY STAGE 2 LEVELS 3 5 Mathematics test Test B Calculator allowed First name Last name School 2007 For marker s use only Page 5 7 Marks 9 11 13 15 17 19 21 23 TOTAL Borderline check Jamie Kate Hassan
More informationIntegers four rules, rounding and ordering 5
1 Integers four rules, rounding and ordering 1.1 Face value and place value Each digit in a number has a face value and a place value. An integer is any positive or negative whole number. Zero is also
More informationMock 2 Maths 2015 Answers
Q1. a) To work out how many children like Gospel add all the numbers that fall within the Gospel circle: [Gospel = 18 + 9 + 7 + 6 = 40] b) To work out how many children like Country add all the numbers
More informationDulwich College MATHEMATICS ONE HOUR
Dulwich College ENTRANCE AND SCHOLARSHIP EXAMINATION AT 11+ SPECIMEN PAPER MATHEMATICS ONE HOUR Answer all the questions. Do all your written work on this paper. Calculators must not be used. Numbers in
More information1. Find the least common multiple (LCM) of the numbers 8, 6. A) 48 B) 2 C) 24 D) 1 E) 8
. Find the least common multiple (LCM) of the numbers 8, 6. A) 48 B) C) 4 D) E) 8. Find the least common multiple (LCM) of the numbers 0, 6. A) 0 B) C) 60 D) E) 80. Find the least common multiple (LCM)
More information1. Find the least common multiple (LCM) of the numbers 8, 10. A) 80 B) 2 C) 40 D) 1 E) 8
. Find the least common multiple (LCM) of the numbers 8, 0. A) 80 B) 2 C) 40 D) E) 8 2. Find the least common multiple (LCM) of the numbers 6, 4. A) 6 B) 2 C) 84 D) E) 42. Find the least common multiple
More informationMathematics Third Practice Test A, B & C - Mental Maths. Mark schemes
Mathematics Third Practice Test A, B & C - Mental Maths Mark schemes Introduction This booklet contains the mark schemes for the higher tiers tests (Tests A and B) and the lower tier test (Test C). The
More informationUNIT 5 INTRODUCTION TO FRACTIONS
UNIT INTRODUCTION TO FRACTIONS INTRODUCTION In this Unit, we will investigate fractions and their multiple meanings. We have seen fractions before in the context of division. For example, we can think
More informationTime. On the first day of Christmas. Memory. Notation
Hour Minute Second Duration Period Notation 24 hour OR 12 hour clock (am or pm or 12 midnight or 12 noon) On the first day of Time 1 year = 52 weeks = 365 days 1 week = 7 days 1 day = 24 hours 1 hour =
More informationName Date Class. Total (A) Total (B) Total (C) Test Total (A+B+C) R (0-9) I y (10-19) I G (20-25) Maths Basic Skills Week 1
rk bo k,let t r a h Maths Basic Skills Week 1 Name Date Class. 1. What are the next two numbers? 11. Six times a number is forty two. 21. In a sale, there is twenty-five per -19' -15' -11'... '... What
More informationNumber Line: Comparing and Ordering Integers (page 6)
LESSON Name 1 Number Line: Comparing and Ordering Integers (page 6) A number line shows numbers in order from least to greatest. The number line has zero at the center. Numbers to the right of zero are
More informationSixth Grade Spiraling Review Week 1 of Second Six Weeks
Week 1 of Second Six Weeks Day 1 Scott bought fruit for a baseball tournament. The table shows the amount of each type of fruit he bought. Type of Fruit Peaches Apples Bananas Oranges Amount (lb) 3 5 19
More informationPaper B Maths Paper 11+ Candidate Number. Seat Number.. Please put your name in the space provided above.
Paper B. 2016 Maths Paper 11+ Name Candidate Number. Seat Number.. Please put your name in the space provided above. This maths paper contains 36 questions, which you have 40 minutes to complete. The paper
More information1. A number when rounded off to the nearest thousand is What is the number? (S) (1) (2) (3) (4)
Questions 1 to 10 carry 1 mark each. Questions 11 to 15 carry 2 marks each. For each question, four options are given. One of them is the correct answer. Make your choice (1, 2, 3 or 4) and shade your
More information1 /4. (One-Half) (One-Quarter) (Three-Eighths)
LESSON 4: Fractions: A fraction is a part of a whole. Slice a pizza, and you will have fractions: 1 /2 1 /4 3 /8 (One-Half) (One-Quarter) (Three-Eighths) The top number tells how many slices you have and
More informationMANIPULATIVE MATHEMATICS FOR STUDENTS
MANIPULATIVE MATHEMATICS FOR STUDENTS Manipulative Mathematics Using Manipulatives to Promote Understanding of Elementary Algebra Concepts Lynn Marecek MaryAnne Anthony-Smith This file is copyright 07,
More informationTopic. Easter Intervention. If you have any questions, feel free to
Easter Intervention Foundation Questions Topic Angles Transformations Multiples, Factors, Primes Indices Algebra Area and Perimeter Factions, Decimals and Percentages Ratio Equations Probability Averages
More informationSTATION #1: VARIABLES ON BOTH SIDES (BASIC) Copy and solve each equation. Show all work. OPTIONAL CHALLENGE QUESTIONS:
STATION #1: VARIABLES ON BOTH SIDES (BASIC) Copy and solve each equation. Show all work. 1. 18 6x = 2x + 6 2. z = 84 6z 3. 3 f = 6f + 24 4. 3(2 + m) = 2(3 m) 5. 4(2y 1) + 5 = 3y + 1 1. Solve the equation:
More information2017 1MA0 Practice Questions FOUNDATION PAPER AIMING C. You re halfway there already only one paper to go.
2017 1MA0 Practice Questions FOUNDATION PAPER AIMING C You re halfway there already only one paper to go. These questions have been compiled to help you practice topics which have not yet been tested in
More informationKING EDWARD S SCHOOL B I R M I N G H A M. Admission Examination 2011 MATHEMATICS. Time allowed: One hour
this paper must not be taken from the examination room A B C KING EDWARD S SCHOOL B I R M I N G H A M Admission Examination 2011 Your name (in full)... Your candidate number... Name of your present school...
More information1 Write the proportion of each shape that is coloured, as a fraction in its simplest form.
1 Write the proportion of each shape that is coloured, as a fraction in its simplest form. a b c d e f 2 For each shape in question 1, write the proportion that is coloured as a ratio, coloured : all tiles
More informationYear 4 Time Block 2. For the next set of questions you will have 10 seconds to work out the answer and record it on your answer sheet.
Test 7 (end of week 2) Year 4 Time Block 2 I will read every question twice. In this first set you will have 5 seconds to work out the answer and record it on your answer sheet. 1. Write the number 4307
More informationSTATION #1: VARIABLES ON BOTH SIDES (BASIC) Copy and solve each equation. Show all work. 2. z = 84 6z z = 12 OPTIONAL CHALLENGE QUESTIONS:
STATION #1: VARIABLES ON BOTH SIDES (BASIC) Copy and solve each equation. Show all work. 1. 18 6x = 2x + 6 x = 3 2. z = 84 6z z = 12 3. 3 f = 6f + 24 f = 3 4. 3(2 + m) = 2(3 m) m = 0 5. 4(2y 1) + 5 = 3y
More informationWhat must be added to 60 to make one hundred? What is seventy minus forty?
2.1 1. How many groups of ten can be made out of 100 marbles? 2.2 2. Order these numbers starting with the smallest: 49, 27, 17, 34 2.2 3. Write the number one hundred and nineteen in digits. 2.3 4. Write
More information= 2. 1st March
1st March 45 36 2 1 2 = 2 Holly is saving money for a guitar that costs 50 In January, she saves 15.15 In February, she saves 8.82 In March, Holly saves 13.37 Work out how much more money does Holly need
More informationYear 5 Mental Arithmetic Tests
Year 5 Mental Arithmetic Tests 1 Equipment Required Printed question and answer sheet for the reader Printed blank answer page for child Stopwatch or timer Pencil No other equipment is required to complete
More informationEssential Mathematics. Study Guide #1
Math 54CM Essential Mathematics Name Date Study Guide # Exam # is closed book and closed notes. NO CALCULATORS. Please clearly show any work necessary to get partial credit. Be sure to show your answer
More informationMark schemes for Mental mathematics Tests A, B and C
Ma KEY STAGE LOWER TIER & HIGHER TIERS 004 Mathematics tests Mark schemes for Mental mathematics Tests A, B and C 004 First published in 004 Qualifications and Curriculum Authority 004 Reproduction, storage,
More information4 Here are the times, in seconds, of five runners in a 100 m race. Tom 11.16, Ed 11.06, Brad 11.44, James 11.47, Derek 11.22
1 a) Write these numbers in words i) 2746 ii) 73060 iii) 602700 b) Write these in figures i) five thousand and fifty three ii) three hundred and forty five thousand 2 Round these to the nearest integer
More informationLevel 4 End of year Test Revision
1 Level 4 End of year Test Revision Scientific Notation 1) Write the following numbers in scientific notation: a) 987 000 b) 53 086 c) 9 127 d) 607 e) 87 f) 1 million g) 0.000 097 h) 0.000456 i) 0.00345
More informationName Date Handling Numbers Level 1 revision 1. Put these numbers in order of size starting with the lowest and going up to the highest
1. Put these numbers in order of size starting with the lowest and going up to the highest a. 17 53 35 86 24 71 b. 3057 215 3507 7305 512 125 c. 15043 10543 30345 3345 33045 53004 2. In each of the following,
More informationWhat must be added to 30 to make one hundred? =
2.1 1. How many groups of ten can be made out of 70 marbles? 2.2 2. Order these numbers starting with the smallest: 30, 17, 12, 23 2.2 3. Write the number two hundred and seven in digits. 2.3 4. Write
More informationDumfries and Galloway Council. Added Value Revision pack. Name... Suzanne Stoppard. National 4
Dumfries and Galloway Council Added Value Revision pack Name... Suzanne Stoppard National 4 Self Assessment Summary- Part one Non Calculator Assessment standard Traffic Lights Pupils Signature Parents
More informationHALF YEARLY EXAMINATIONS. Maria Regina College. Scholastic Year 2017 / YEAR 6 WRITTEN MATHEMATICS TIME: 1hr 15min. Name: Total mark 80.
HALF YEARLY EXAMINATIONS Maria Regina College Scholastic Year 2017 / 2018 YEAR 6 WRITTEN MATHEMATICS TIME: 1hr 15min Name: Class: School: Total mark 80 1. Work out. a) 356 + = 500 b) 5005 15 = c) 30 x
More informationST NICHOLAS COLLEGE HALF YEARLY PRIMARY EXAMINATIONS February 2016 YEAR 6 MATHEMATICS TIME: 1h 15 min
ST NICHOLAS COLLEGE HALF YEARLY PRIMARY EXAMINATIONS February 2016 YEAR 6 MATHEMATICS TIME: 1h 15 min Name: 1. Work out. Class: Total Mark 80 a) 324 + 92 = b) 912-234 = c) 418 x 7 = d) 424 8 = 2a) Write
More informationName: Teacher: *P43382A0228* GCSE Mathematics 1MA0. Formulae: Foundation Tier. You must not write on this formulae page.
GCSE Mathematics 1MA0 Formulae: Foundation Tier You must not write on this formulae page. Key Anything stage you write 3: on End this formulae of page Term will gain NO Test credit. 5 Name: Area of trapezium
More informationSECTION A. INSTRUCTION: Answer all questions in this section. Pick the appropriate answer. from the options lettered A to E.
SECTION A INSTRUCTION: Answer all questions in this section. Pick the appropriate answer from the options lettered A to E. 1. Find the L.C.M. of 18, 24 and 36. a 72 b 48 c 42 d 36 e 30 2. What is the value
More informationGCSE Foundation! Set B! Non - Calculator Paper
Name: GCSE Foundation! Set B! Non - Calculator Paper Equipment 1. A blue or black ink ball-point pen. 2. A pencil. 3. An eraser. 4. A ruler. 5. A pair of compasses. 6. A protractor. Guidance 1. Read each
More informationWS Stilwell Practice 6-1
Name Date Pd WS Stilwell Practice 6-1 Write each ratio in three different ways. Write your answer in simplest form. 1) 2) triangles to total circles to triangles 3) 4) all figures to circle triangles to
More information2 a. What is the total cost of a fidget. 1. Calculate the following: spinner costing 4.68 and a cricket ball. a costing 8.59?
Revision Pack REMOVE November 2017 This is the Upper summer pack to help you revise. NO CALCULATORS to be used unless π is needed or the question says to. 1. Calculate the following: a. 47 9 + 9 76 Name:
More informationDay 1. Mental Arithmetic Questions KS3 MATHEMATICS. 60 X 2 = 120 seconds. 1 pm is 1300 hours So gives 3 hours. Half of 5 is 2.
Mental Arithmetic Questions. The tally chart shows the number of questions a teacher asked in a lesson. How many questions did the teacher ask? 22 KS MATHEMATICS 0 4 0 Level 4 Answers Day 2. How many seconds
More informationEmanuel School. Mathematics. Specimen Paper. Paper Hill Form (10+) Entry Time allowed: 1 hour
Emanuel School Mathematics Specimen Paper Paper Hill Form (10+) Entry Time allowed: 1 hour 1. Your first name and surname. 2. Your present school. 3. Boy/girl: Fill in the boxes above and read the following
More information2) There are 7 times as many boys than girls in the 3rd math class. If there are 32 kids in the class how many boys and girls are there?
Word Problem EXTRA Practice 1) If Fay scored 78 more points last season, she would have tied the school record. She scored 449 points last season. What is the school record for most points scored? points
More informationThese are skills that we have covered within our math outcomes this year
Patterns & Relationships Whole Number Multiplication & Division Fractions, Decimals, and Percents Measurement, Data, and Geometry Word Problem Analysis These are skills that we have covered within our
More informationHyde Community College
Hyde Community College Numeracy Booklet 1 Introduction What is the purpose of this booklet? This booklet has been produced to give guidance to pupils and parents on how certain common Numeracy topics are
More information2. Attempt to answer all questions in the spaces provided in this book.
ENTRANCE AND SCHOLARSHIP EXAMINATION 2017 MATHEMATICS 1 HOUR CALCULATORS NOT ALLOWED CANDIDATE NAME Instructions to Candidates: 1. Write your name on the line above. 2. Attempt to answer all questions
More information10 Arithmetic: Fractions
MEP Y Practice Book A 0 Arithmetic: Fractions 0. Fractions This unit deals with the important topic of fractions. These are numbers of the form a b when a and b are whole numbers and b 0. We first see
More informationGrade 7/8 Math Circles February 3/4, 2015 Arithmetic Aerobics Solutions
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles February 3/4, 2015 Arithmetic Aerobics Solutions Mental Math is Good For You! You
More informationA1.2 Multiplying and Dividing with Decimals. A1.3 Fractions and Decimals. A1.4 Negative Numbers. A1.5 Operations wiith Negative Numbers
STRAND A: NUMBER A Decimals and Fractions Text Contents Section A. Decimals A.2 Multiplying and Dividing with Decimals A. Fractions and Decimals A. Negative Numbers A. Operations wiith Negative Numbers
More informationMark scheme. Mathematics tests. for Mental mathematics tests A, B and C. National curriculum assessments KEY STAGE 3. satspapers.
Ma KEY STAGE LOWER TIER & HIGHER TIERS Mathematics tests Mark scheme for Mental mathematics tests A, B and C 2008 National curriculum assessments QCA wishes to make its publications widely accessible.
More information1. Greg Louganis scored points for highboard diving event at the Olympic Games. What figure shows:
Decimals. 1. Greg Louganis scored 70.91 points for highboard diving event at the Olympic Games. What figure shows: a) hundreds b) hundredths c) tenths. 2. A piece of wood.2cm is cut from a piece 6.4cm
More information[WORD PROBLEMS] Advanced Word Problems for Key Stage Two children.
Levels 5 & 6 Advanced Word Problems for Key Stage Two children. Q1. 427 children visit a castle. They go in groups of 15. One group has less than 15. Every group of children has one adult with them. How
More information1MA0/1F Edexcel GCSE Mathematics (Linear) 1MA0 Practice Paper 1F (Non-Calculator) Set A Foundation Tier Time: 1 hour 45 minutes
1MA0/1F Edexcel GCSE Mathematics (Linear) 1MA0 Practice Paper 1F (Non-Calculator) Set A Foundation Tier Time: 1 hour 45 minutes Materials required for examination Ruler graduated in centimetres and millimetres,
More information55 PROBLEMS. Ready to project versions of the problems and solutions available on.
55 PROBLEMS Ready to project versions of the problems and solutions available on ALGEBRA 1 a, b, and c are three different positive integers where a + b + c = 10 What is the maximum value of abc? ALGEBRA
More informationPrimaryTools.co.uk 2012 MATHEMATICS KEY STAGE TEST A LEVELS 3 5 CALCULATOR NOT ALLOWED PAGE TOTAL MARKS First Name Last
MATHEMATICS KEY STAGE 2 2006 TEST A LEVELS 3 5 CALCULATOR NOT ALLOWED PAGE 5 7 9 11 13 15 17 19 21 TOTAL MARKS First Name Last Name School Lin David Rosie 2 Instructions You may not use a calculator to
More information2017 1MA0 Practice Questions. You re halfway there already only one paper to go.
2017 1MA0 Practice Questions You re halfway there already only one paper to go. These questions have been compiled to help you practice topics which have not yet been tested in this exam session. You may
More informationReleased November /5. Small Steps Guidance and Examples. Block 4: Length & Perimeter
Released November 2017 4/5 Small Steps Guidance and Examples Block 4: Length & Perimeter Year 4/5 Autumn Term Teaching Guidance Overview Small Steps Year 4 Year 5 Kilometres Perimeter on a grid Perimeter
More informationSecond Practice Test 1 Level 5-7
Mathematics Second Practice Test 1 Level 5-7 Calculator not allowed Please read this page, but do not open your booklet until your teacher tells you to start. Write your name and the name of your school
More informationCounting Stick: Infants: First and Second Class: Third and Fourth Class: Fifth and Sixth Class
Counting Stick: What is it? A 1-metre long stick divided into ten sections, each 10 cms long. What can it be used for and with what classes? The stick can be used for a variety of number activities and
More informationTest 1. For all of the questions in this test, do the calculation entirely in your head with no written working and just write down the answer.
Test 1 In questions 1 to 10 you are reminded of 10 useful strategies which may help you in later questions. 1 3 19 Try 3 20 and then subtract 3 2 12.0 Divide by 2 and then by 2 again 3 27 5 Multiply by
More informationSection A: For each question, four options are given. (10 marks)
Algebra and Fraction Revision Section A: For each question, four options are given. (10 marks) (1) Multiply 30 by w. Subtract 11 from the result gives (A) 11w 30 (B) w 330 (C) 11-30w (D) 30w 11 ( ) (2)
More informationTHE NORTH LONDON INDEPENDENT GIRLS SCHOOLS CONSORTIUM MATHEMATICS
THE NORTH LONDON INDEPENDENT GIRLS SCHOOLS CONSORTIUM Group 2 YEAR 7 ENTRANCE EXAMINATION MATHEMATICS Friday 8 January 2016 Time allowed: 1 hour 15 minutes First Name:... Surname:... Instructions: Please
More informationCompare fractions. Introduction. Additional materials Numeracy Level 1
Additional materials Numeracy Level Introduction You may see fractions in newspapers, on adverts and sale signs, or used with weights and measures. You need to be able to read and understand them, and
More informationThe bottom number in the fraction is called the denominator. The top number is called the numerator.
For Topics 8 and 9, the students should know: Fractions are a part of a whole. The bottom number in the fraction is called the denominator. The top number is called the numerator. Equivalent fractions
More informationSample: Do Not Reproduce RAT3 STUDENT PAGES. RATIONAL NUMBERS Student Pages for Packet 3: Ordering and Equivalence.
Name Period Date RATIONAL NUMBERS Student Pages for Packet : Ordering and Equivalence RAT. RAT.2 Ordering Fractions on a Number Line Use sense-making strategies to compare and order fractions. Identify
More information3. What must be added to seven hundred thirty to make one thousand?
MENTAL PAPER --- YEAR 6--- HALF YEARLY For the following group of questions, you have 5 seconds to work out each answer and write it down. Għal dawn il-mistoqsijiet li ġejjin, għandek 5 sekondi biex taħdem
More informationThese tests contain questions ranging from Level 2 to Level 4. They get progressively more difficult. Children should have five seconds to
These tests contain questions ranging from Level to Level. They get progressively more difficult. Children should have five seconds to answer questions in each test and ten seconds to answer questions.
More informationRatio. Worksheet 1 Finding Ratio. Complete the number bonds Complete the models. 5. Reteach 5A
7 CHAPTER Ratio Worksheet 1 Finding Ratio Complete the number bonds. 1. 2. 11 15 4 8 3. 21 4. 30 9 17 Complete the models. 5. 20 15 6. 44 27 Reteach 5A 193 Complete the table to show the ratios. These
More informationw = 17 1st March What fraction of the rectangle is not shaded? In this rectangle,! is shaded purple is shaded green.
1st March 6 7 2 In this rectangle,! is shaded purple!!! is shaded green. What fraction of the rectangle is not shaded? w = 17 Work out 6w + 7 The volume of the cube and the cuboid are equal. Find the length
More informationUK JUNIOR MATHEMATICAL CHALLENGE. April 25th 2013 EXTENDED SOLUTIONS
UK JUNIOR MATHEMATICAL CHALLENGE April 5th 013 EXTENDED SOLUTIONS These solutions augment the printed solutions that we send to schools. For convenience, the solutions sent to schools are confined to two
More informationGCSE Mathematics Non Calculator Foundation Tier Mock 1, paper 1 ANSWERS 1 hour 45 minutes. Legend used in answers
MathsMadeEasy 3 GCSE Mathematics Non Calculator Foundation Tier Mock 1, paper 1 ANSWERS 1 hour 45 minutes Legend used in answers Blue dotted boxes instructions or key points Start with a column or row
More informationSample Pages. out of 17. out of 15. a $1.15 b $0.85. a 4280 b 2893 c 724. a Which of these are odd? b Which of these are even?
1:1 out of 15 1:2 out of 17 7 + 8 13 4 12 9 3 3 4 2 9 plus 5. 8 + 6 4 groups of 5. 1 8 + 1 1 1 5 4 12 + 7 9 2 16 + 4 7 4 10 7 17 subtract 7. 11 6 20 minus 12. 6 7 + 2 2 7 9 4 3 Write these numbers on the
More informationMERCHANT TAYLORS SCHOOL
MERCHANT TAYLORS SCHOOL 11+ OFFICIAL PRACTICE PAPER MATHEMATICS Time Allowed: 60 minutes Instructions: Answer as many questions as possible. Some of them are easy at the start and become more difficult.
More informationPercentage means, a 'number over 100'. For example: 16% = 16 5% = 5 12% = 12 35% =
Q1. [0.2 0.2 = 0.04] The skill you need here is multiplications of decimal numbers. Count the total number of decimal places in the two numbers. Your answer should also have the same number of decimal
More informationYear 6 Maths Assessment Guidance - NUMBER Meeting expectations 3 Working Within Year 6 4 Secure within Year 6
6.1.a.1 Calculate intervals across zero (^) 6.1.a.2 Consolidate counting forwards or backwards in steps of powers of 10 for any given number to 1 000 000 (+) 6.1.a.3 Consolidate counting in multiples of
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write a fraction to represent the shaded part of the object. 1) A) 1 3 3 1 C) 3 4 2) D) 1 4 A) 1 6
More information