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The maths department are making weekly booklets for you tocomplete at home.

This booklet is some maths work for you to complete over the next two weeks.

North Gosforth AcademyMathematics Home Booklet

Year 8 Foundation

20th April – 1st May

The topics covered are below. You have already covered these in your maths lessons and being at home gives you a chance to revise! Create yourself a useful revision resource and practise key skills!

Instructions:

There are plenty of examples – write these down. Write down any useful facts.

Complete questions to practise the skills and stretch questions to push yourself. Show working out!

Old maths books and revision guides are useful sources of information if you have them

Any access to the internet, even limited, gives you access to Hegarty maths, Corbett maths and Mathsgenie where tutorial videos are available

Topics in this booklet:

Fraction, Decimal and Percentages conversion Simplifying fractions Multiplying and dividing fractions Adding and subtracting fractions

0.3333…

18

Fraction Decimal Percentage

14

0.5

0.05

85%

12.5%

0.8

150%

LiteracyWhat does ‘numerator’mean?

What does ‘denominator’mean?

ResearchFind an example of decimals, percentages and fractions in real life and write about it here:

Bonus house points for anyone emailing a picture of what you have found.

Skill practiceComplete the table below:

Memory

What is the value of ‘f’?

Stretch: (extension)Try this section, but don’t worry if you can’t finish it.

Decimals and Percentages homework

Converting between Fractions, Decimals and Percentages

BRONZE SILVER GOLD

F D P F D P 1) Miss Smith scored 23/50 marks on a test. Miss Miller scored 45.5%. Who scored higher on the test?

12

0.5 50%

1350

0.26

26%

3 4

6 25

0.25

0.94

70%

35%

2) Company A offers 0.2 of profits as a bonus. Company B offers 19% as a bonus.Company C offers 6/25ths of profit as a bonus.Which company offers the biggest bonus?

3 5

1320

0.1 0.55

90%

85%

3 10

7 20 3) Order the following

in ascending order:

0.61, 58%, 0.575, 3/5

0.2 0.48

40%

62%

4 5

9 50

0.13

0.68 4) Order the following

in ascending order:

0.485, 12/25, 0.482, 49%27%

46%

39 100

1125

0.1 0.2

1 23% 14

%Well done!

Simplifying Fractions Homework

Literacy1) Write a fraction and label the numerator and denominator.

ResearchCan you find where the word ‘fraction’

comes fromand what it means? Write your findings

below.

÷2 MemoryTIP – Try to find the𝟔 𝟑 highest factor of𝟏𝟎 𝟓 both the numerator and denominator to

÷2 save yourself a step!

2) Give an example of:i)an improper

fraction

ii)a mixed number

iii) a unit fraction

Skills: Simplify fully𝟐

1) =𝟔𝟒2) =𝟐𝟎𝟒𝟒3) =𝟏𝟐𝟏𝟔4) =𝟏𝟖𝟗5) =𝟑

1)Explain below how you know you have

Stretchsimplified fully.

𝟏𝟔 𝟔2)Which is bigger, or ? (Show your

working!) 𝟒𝟖 𝟑𝟔

Multiplying Fractions HomeworkLiteracy𝟑

𝟒 means the same as 𝟑 ÷ 𝟒𝟑

This means that multiplying by 𝟒is the same as × 𝟑 and ÷ 𝟒

𝟑 𝒐𝒇 𝟐 means the same as 𝟑 × 𝟐𝟒 𝟑 𝟒 𝟑

3×2 6 1which is 4×3 = 12 = 2

ResearchWhat is the definition of ‘factorial’? Note: ′7 𝑓𝑎𝑐𝑡𝑜𝑟𝑖𝑎𝑙′ is written 7! (the symbol is as an exclamation mark).

Use your definition to find:3! = 5! = 5! = 3! =3! 5!

Memory To find a fraction of any

number, multiply by the numerator and divide by the denominator.

To find a fraction of a fraction, multiply the numerators to find the new numerator, and multiply the denominators to find the newdenominator.

Skills4 2 14 31) 5 × 7 = 5) 15 × 4 =2 4 15 22) 5 × 7 = 6) 8 × 7 =6 3 13 13) 17 × 10 = 7) 17 × 2 =8 5 8 64) 25 × 12 = 8) 9 × 7 =Simplify your answers where possible. Show ALL your working.

Stretch28 51) 45 × 14 =2 3 52) 5 × 4 × 3 =4 3 73) 7 × 10 × 11 =1 2 3 4 54) 2 × 3 × 4 × 5 × 6 =

You need to read and learn the Literacy and Memory sections, look up answers to the Research section, answer all questions from the Skills section, and (unless you have already spent more than 45 minutes on this homework) attempt the Stretch section. Answers can be written on the sheet or in your book if you need more space.

Remember you need a commondenominator to add and subtract fractions2 15 + 3

x3 x5= 6 5 1115 + 15 = 15

10) 1 + 1 1 + 3

753 3 + 1 8 4 + 1

Adding and subtracting fractionsDescribe what mathematical information

the pictures are telling you about fractions. Try to

connect the pictures Identify and explain jobs in which your fraction

knowledge would be needed.

You MUST have a common denominator (the bottoms must be the same) to add or subtract fractions.Steps:1. Find the new bottom bythe LCM2. Change the bottom and the tops!

1) 1 + 2 + 32 5 10

2) 7 − 1 + 59 3 63) 3 2 + 1 154) 1 34

3− 2 55 2 2 8

4 3 − 3 96 5 − 2 49 58 − 2 79 97 − 3 285 + 3

=61 + 3 =101

State the mathematical definitions for the following:NumeratorDenominatorUnitary fractionMixed NumberImproper fraction

Find some examples where fractions are used in everyday life

Watch the following Corbett Maths videos, which will explain how to add, subtract, multiply and divide fractions: 132, 133, 134, 139, 140and 142

Calculate these, remember to give your answers in their simplest form: Calculate these,

remember to give your

Add/Subtract

Divide

answers in their simplest form:

Multiply

Example: to divide by a fraction, multiplyby its reciprocal (flip the fraction)

F ractions Worded Problems

RED2

1. Ben eats of a packet of crisps each day. How many packets of crisps will he eat in one week?5

12. Each wine glass can hold of a litre of wine. I have 5 glasses, how much wine do I have?

31

3. Andy and Bob have a pizza each. After they have eaten some of their pizzas, Andy has of his pizza left3

1and Bob has of his left. What fraction of pizza do they have left in total?

42

4. £40 is shared between several people so each receives of a pound. How many people receive a share?7

35. A donkey eats a hay bale a week. How many hay bales does he eat in 24 days?

52 1

6. Charlene has a bag of sweets. She gives to her friend and eats . What fraction of the bag of sweets does5 4

Charlene have left?1

7. If I had to transfer 3 litres of water from one container to another with only a mug which can hold of a8

litre each time, how many times will I need to use the mug?2

8. If one sheet of paper is cm thick, how thick is a pad containing 180 sheets?5

AMBER9. Percy spent 1/4 of his money on a food and another 3/10 of his money on a drink.

a) What fraction of his money did he spend in total?

b) What fraction of his money did he have left?

10. Sally has a piece of cloth. She used 1/3 of the cloth to make a pillow cover and another 4/7 of the cloth tomake a tablecloth. What fraction of the cloth was left?

11. A container is 1/3 full of water and 1/4 full of oil. What fraction of the container is empty?3

12. Dave and Ed are putting together bags of marbles to sell for charity. Dave has of a bag left over and Ed5

2has of a bag left. Can they combine what they each have left to make another full bag?

33 2

13. Freya wants to make two cakes. She has of a bag of flour. The first cake requires of a bag of flour and4 5

3the second cake needs of a bag of flour. Does Freya have enough flour to make both cakes?

10

GREEN1

14. George’s van can carry a maximum of 5 tonnes. George needs to deliver two loads weighing 3 tonnes4

5and 1 tonnes. Can George take both loads at once? (You must show your workings)

62 7

15. Harriet is sowing grass seed in her garden. She has 1 bags of grass seed. Her front garden needs of a3 8

5bag and the back garden needs of a bag. Does Harriet have enough grass seed? (You must show your

6workings)16. For the school’s sports day, a group of students prepared 12 1/2 litres of lemonade. At the end of the day they had 2 5/8 litres left over. How many litres of lemonade were sold?17. 3 4/6 mini-pizzas were left in the fridge; the children ate 1 2/3 of them. How much pizza is left for the adults? Give your answer as a mixed number and as an improper fraction?