MODULE 1 WORKBOOKFractions

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7 May 2019

Contents

p 3

p 9

p 14

p 21

Lesson 1

Lesson 2

Lesson 3

Apply (Non-Calculator)

Apply (Calculator) p 24

2

Module 1

Fractions PODS Before continuing, make sure you have watched and have access to the following Pods. To find these, simply log in to GCSEPod and enter the codes given into the search bar (or click on the titles below).

1. Converting between decimals and fractions | MATHS-29-0022. Ordering fractions | MATHS-09-0013. Fractions of a given number | MATHS-09-0024. Adding and subtracting fractions | MATHS-09-0035. Multiplying fractions and cancelling | MATHS-09-0046. Dividing fractions | MATHS-09-005

Lesson 1 Conversions

PODS

1. Converting between decimals and fractions | MATHS-29-0022. Ordering fractions | MATHS-09-001

Quiz

Watch the pods and answer the questions below.

Do not use a calculator.

1. Write 0.2 as a fraction and simplify it as much as possible.

a) 2/10

b) 1/5

c) 2/5

d) 10/2

………………………………………………………………………………………………………………………………………………………………..

3

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2. Write 0.125 as a fraction and simplify it as much as possible.

a) 125/1000

b) 12/5

c) 1/8

d) 1/80

………………………………………………………………………………………………………………………………………………………………..

3. Write 18 out of 30 as a fraction in its simplest form.

a) 6/10

b) 60/100

c) 18/30

d) 3/5

………………………………………………………………………………………………………………………………………………………………..

4. Write 2.75 as a mixed number in its simplest form.

a) 2/75

b) 2 !"

c) 2 #$

d) 2 !"%&&

………………………………………………………………………………………………………………………………………………………………..

5. Write 18% as a fraction and simplify it as much as possible.

a) 9/50

b) 18/100

c) 3/25

d) 4.5/25

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4

6. Which conversion would help you to show that 5/9 is smaller than 2/3?

a) 6/9

b) 10/27

c) 7/12

d) 1.5/3

………………………………………………………………………………………………………………………………………………………………..

7. Which of these fractions is the largest?

a) 2/3

b) 7/12

c) 5/8

d) 15/24

………………………………………………………………………………………………………………………………………………………………..

8. Convert %&$

to a decimal.

a) 2.5

b) 10.4

c) 4.1

d) 5.2

………………………………………………………………………………………………………………………………………………………………..

9. Convert 3 (" into a decimal.

a) 3.25

b) 3.4

c) 32.5

d) 32.5

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5

10. Write 0.24 as a fraction in its simplest form.

a) 2/4

b) 6/25

c) 24/100

d) 12/50

………………………………………………………………………………………………………………………………………………………………..

6

Practise

Practise converting and ordering fractions.

Do not use a calculator.

1. Frank eats 3 and ¼ pizzas. How many quarters is this altogether?

………………………………………………………………………………………………………………………………………………………………..

2. Sandra scores 12 out of 30 in her maths test. Write this as a fraction in its simplest form.

………………………………………………………………………………………………………………………………………………………………..

3. Use the following facts to simplify 162/270 as fully as possible.

9 x 18 = 162 and 15 x 18 = 270

………………………………………………………………………………………………………………………………………………………………..

4. Jack divides 2 positive numbers on his calculator and gets an answer of 0.75. What arethe lowest integers that he could have divided to get this answer?

………………………………………………………………………………………………………………………………………………………………..

5. Put the following fractions in ascending order;

#$, *%(, "+, %"($

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7

6. Convert "#*

into a mixed number.

………………………………………………………………………………………………………………………………………………………………..

7. Write a fraction from the decimal number which has 4 hundredths and 3 tenths.

Simplify your answer.

………………………………………………………………………………………………………………………………………………………………..

8. The arrow represents a value between 3/7 and 4/7. Give, as a fraction, a possiblevalue for this.

………………………………………………………………………………………………………………………………………………………………..

9. Write down any fraction which could fit into this inequality to make it true;

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10. Continue this sequence: 1 "-, 1 %

-, +-,___, ____.

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8

Lesson 2

Fractions of Amounts

POD

3. Fractions of a given number

Quiz

Watch the pod and answer the questions below.

Do not use a calculator.

1. Find 1/7 of 56.

a) 8

b) 8/7

c) 392

d) 5/6

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

2. Find 2/5 of £35.

a) £7

b) £70

c) £3.5

d) £14

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

3. Find 6/7 of £60 to the nearest penny.

a) £8.57

b) £51.43

c) £51.42

d) £70

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9

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4. Find 5/3 of 27.

a) 45

b) 16.2

c) 9

d) 5.4

………………………………………………………………………………………………………………………………………………………………..

5. What is 200ml as a fraction of 800ml in its simplest form?

a) 200/800

b) 2/8

c) ¼

d) 8/2

………………………………………………………………………………………………………………………………………………………………..

6. Write 400ml as a fraction of 2 litres in its simplest form.

a) 40/200

b) 1/5

c) 2/400

d) 1/200

………………………………………………………………………………………………………………………………………………………………..

7. £2 is made up of one 50p coin, three 20p coins and the rest are 5p coins. Whatfraction of the coins are 5p coins written in the simplest form?

a) 5/18

b) 15/20

c) 18/22

d) 9/11

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

8. Dasha goes to the fruit shop and buys 18 items. Half of the items are apples, 1/3 arepears and the rest are oranges. How many oranges does she buy?

a) 9

b) 3

c) 6

d) None

………………………………………………………………………………………………………………………………………………………………..

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9. If 3/7 of a number is 36, what is the number?

a) 12

b) 5.14

c) 15.4

d) 84

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

10. What is one third of ¾ of 80?

a) 60

b) 30

c) 20

d) 10

………………………………………………………………………………………………………………………………………………………………..

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Practise

Practise converting to fractions.

Do not use a calculator.

1. A maths test has 30 marks. If you answer 3/5 correctly, how many marks do you get?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

2. You decide to give 1/20 of your weekly salary to charity. If you make £250, how muchwill you keep?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

3. There are 30 people on a bus. 5/6 of the people get off. How many people are left onthe bus?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

4. Carl spends 3/5 of his wages on rent. If he earns £2000 per month, how much doeshe spend on rent?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

5. Calculate ¾ of 3.2 metres.

………………………………………………………………………………………………………………………………………………………………..

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Practise

Practise converting to fractions.

You may use a calculator.

1. Jack has a packet of seeds for his garden. He gives half of them to Tom. Tom thengives 1/8 of these to Clare. If Claire gets 5 seeds, how many seeds were in the packet?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

2. Lucy is playing a song. She stops it after 50 seconds which is 2/7 of the way through.How long is the song in minutes and seconds?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

3. The price of a shirt is reduced by 1/5 in a sale. If there is £7.20 off, how much was theshirt before the sale?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

4. A house price has increased by 1/5 in the last 3 years. The house was £215000 3 yearsago. How much is it worth now?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

5. Ahmed has a railcard which gets him 1/3 off the price of any ticket. His ticket shouldcost £34.95. How much does Ahmed pay for the ticket?

………………………………………………………………………………………………………………………………………………………………..

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Lesson 3

Four operations with fractions

PODS

4. Adding and subtracting fractions5. Multiplying fractions and cancelling6. Dividing fractions

Quiz

Watch the pods and answer the questions.

Do not use a calculator.

1. Add together ½ and %#.

a) ("

b) (+= %

#

c) "+

d) %+

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

2. Find the sum of #$ and #

* giving your answer as a mixed number.

a) -*

b) 1 %*

c) +%(= %

%(

d) 1 %%(

………………………………………………………………………………………………………………………………………………………………..

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3. Which of the following equations is incorrect?

a) %"+ %

$= -

(&

b) #%&+ %

(= %+

(&= $

"

c) (!+ #

"= +

%(= %

(

d) %#+ #

$= %#

%(

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

4. Convert %!#

to a mixed number.

a) 17 %#

b) 3 %!

c) 6 %#

d) 5 (#

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

5. Write 2 #*

as an improper fraction.

a) %+*

b) %-*

c) (#*

d) %-#

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

6. Subtract (" from *

-.

a) (($"

b) +$"

c) %&$"

d) +$= #

(

………………………………………………………………………………………………………………………………………………………………..

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15

7. What is the value of (#× $" as a fraction in its simplest form?

a) *%"

b) $!."

c) ((%"= 1 !

%"

d) %&%(= "

+

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

8. After ‘cross cancelling’, the expression "%+× ($%"can NOT be written as;

a) %$× +#

b) %(× 1

c) %$× ##

d) %(

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

9. Calculate the value of 2 %$× 3 (

" giving your answer as a mixed number.

a) 6 %%&

b) %"#(&

c) $"+*

d) 7 %#(&

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

10. Calculate #$÷ $

!giving your answer as a mixed number.

a) (%%+

b) %((*= #

!

c) %+(%

d) 1 "%+

………………………………………………………………………………………………………………………………………………………………..

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16

Practise

Practise adding, subtracting, multiplying and dividing fractions.

Do not use a calculator.

1. Calculate the perimeter of this rectangle:

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

2. What is 1/10 more than 2/5? Give your answer in its simplest form.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

3. Each box is the sum of the 2 boxes beneath it. Calculate the values of the missingboxes.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

17

4. A bike ride is 5 #$𝑘𝑚. How far is half way? Give your answer as a fully simplified mixed

number in km.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

5. Adam is making homemade lemonade to sell at a fair. He has 4 (-𝑙𝑖𝑡𝑟𝑒𝑠 of lemonade.

Each cup holds %%&

litre. How many cups can he fill?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

18

Practise

Practise adding, subtracting, multiplying and dividing fractions.

You may use a calculator.

1. Each box is the sum of the 2 boxes beneath it. Calculate the values of the missingboxes.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

2. Calculate the value of 3 %-× 2 #

!÷ "

*

Give your answer as a mixed number in its simplest form.………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

3. Liam has £50. He gives 2/7 to his Nana and 1/6 to his Mum. He shares the rest with his2 brothers so that they all get an equal amount. Rounding all values to the nearestpenny, calculate how much money Liam keeps?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

19

4. Sam spends 1 #$

hours revising maths every day. He takes a 30-minute break and then

spends twice as long as he spent on maths studying Biology, followed by half as longas he spent on maths reading. If he starts at 9am, what time does he finish?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

5. Louis gives one fifth of his money to Tom, and two sevenths to Leo. What fraction ofthe original amount has he got left?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

20

Apply

Apply what you have revised about Fractions.

Do not use a calculator.

Remember

A fraction is one number divided by another – do this sum to convert it to a decimal.

The rules of fractions are:

To add and subtract you need a common denominator. Find equivalent fractions by multiplying the top and the bottom of a fraction by the same number.

To multiply you just multiply the numerators and then multiply the denominators. Convert mixed numbers to improper fractions first. You multiply if you are finding a fraction “of” an amount.

To divide, simply flip the second fraction and then multiply the two together.

1. Alice and Pavel each have identical pizzas. Alice has cut hers into 9 equal sections andPavel has cut his into 7 equal parts. Alice eats 5 slices and Pavel eats 4. Who has eatenthe most pizza?You must show all of your working.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

2. Fred earns £400 per week. He pays 1/5 of this amount in tax, 1/10 for insurance and1/10 to save for a pension. How much is left after these deductions?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

21

3. Ivy and Eddie do some gardening and earn £60 which they split such that Ivy gets 2/5and Eddie gets the rest. How much money does Eddie receive?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

4. Ethan and Isaac raise money by walking their neighbours’ dogs. Ethan keeps 3/5 ofthe money as it was his idea. If Isaac gets the rest of the money, which is £20, howmuch did they raise in total?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

5. Sally washes cars at her local garage. Her wages are either ‘3/5 of the takings’ or ‘halfof the takings plus £20’. Which offer should she choose if the takings are;

a) £150

b) 200

You must show all of your working.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

6. Find the value of A in the following equation

14+𝐴8+38+34= 2

You must show your working.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

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22

7. This isosceles triangle has a perimeter of 3cm. Calculate the value of x.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

8. Rebecca has 30 metres of string. She needs 5/6 metre to make a necklace. How manynecklaces can she make?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

9. Faizal buys ¾ kg of tomatoes. He gives Fiona 2/5 of them. He needs 500g of tomatoesfor his recipe. Does he have enough? You must explain your answer.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

10. Calculate (-𝑜𝑓 #

$ giving your answer in its simplest form.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

23

Apply

Apply what you have revised about Fractions.

You may use a calculator.

Remember

A fraction is one number divided by another – do this sum to convert it to a decimal.

The rules of fractions are:

To add and subtract you need a common denominator – find equivalent fractions by multiplying the top and the bottom of a fraction by the same number.

To multiply you just multiply the numerators and then multiply the denominators – convert mixed numbers to improper fractions first. You multiply if you are finding a fraction “of” an amount.

To divide simply flip the second fraction and then multiply the two together.

1. Tim sits a maths test and a biology, and scores 19/23 and 13/17 respectively. By findingequivalent fractions, show which test he has scored higher in.You must show all of your working.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

2. Jess earns £435 per week. She pays 2/7 of this amount in tax, 1/9 for insurance and2/21 to save for a pension. How much is left after these deductions? Give your answerto the nearest penny.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

24

3. David gets a 55-minute lunch break. He runs for ½ of the time and uses 3/10 of thetime to get changed. How many minutes does he have left over?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

4. Sarah and Vicki do some gardening and earn £95. They take out 1/9 to cover theircosts. Vicki then takes 2/7 of the remaining amount and Sarah has the rest. How muchmoney does Sarah receive? Give your answer to the nearest penny.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

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5. A cow’s weight increases by 2/7 in the first 2 months of her life. If she was 30kg atbirth, what will she be expected to weigh 2 months later? Give your answer in kg,correct to 2d.p.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

6. A car loses 1/8 of its value as soon as it is driven. Following this, it loses a further 1/10 ofthis reduced value during the first year. If a new car cost £12600, how much would itbe worth after 1 year?

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

7. A school has 1100 pupils. 525 of the pupils are girls.2/5 of the girls say that maths is their favourite subject.13/25 of the boys say that maths is their favourite subject.How many students say that maths is their favourite subject?

………………………………………………………………………………………………………………………………………………………………..

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25

8. The shapes below have the same area. Work out the perimeter of the blue shape.

………………………………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………………………………..

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9. A company has just announced that it has made a profit of £4 million. It is going togive 2/7 of this to charity. How much will it give to charity? Give your answer correctto the nearest penny.

………………………………………………………………………………………………………………………………………………………………..

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10. There are 350 people in a gymnastics club. 6/7 of these are female. Of these, 4/5 areunder 12. How many people are there who are either male or 12 plus or both?

………………………………………………………………………………………………………………………………………………………………..

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