1. Week 5 Number: Understand and use ratio and proportion
Functional MATHS
Week 5
Number: Understand and use ratio and proportion

2. Can you answer the maths quiz?

3. Did you get it right?
÷2×2=108

4. What did we do last week?

5. Finding the fraction of a number
For Example: ¾ of 500g
Divide the total number (500g) by the denominator (the bottom number) which gives you the unit value (the amount for ¼)
500g/4 = 125g
Then multiply by the numerator (top number)
to give you the value you require:
125g x 3 = 375g

6. Finding the fraction of a number
Jeans in the sale
1/3 off!
Original cost is £45
One third = 1/3
£45/3 = £15 is a third of the total price
£45-£15 = £30

7. Percentage of an amount
Mr and Mrs Jones,
BILL
3 months = £150
BRITISH GAS INCREASE PRICES BY 15%

8. Have you done your directed study?
Please have it out in front of you so we can go through this together

10. What are we going to do today?
Ratio and Proportion
Solve problems involving ratio :
Understand ratio notation
Simplify ratios
Calculate amounts of parts using ratio

11. Ratio
Understand
ratio Notation

12. Ratio is a way of comparing amounts of something.
What is ratio?
Ratio is a way of comparing amounts of something.
It shows how much bigger one thing is than another.

13. How is ratio written?
4 : 1
This ratio has 5 parts altogether as = 5.
This will be important a bit later on!

22. Simplifying Ratios The ratio of green to yellow blocks is
green : yellow = 4 : 2
Which can be simplified to:
4 : 2 ÷2 ÷2
2 : 1

23. 1 : 2
2 : 3
1 : 3
1 : 2
2 : 9
1 : 2
7 : 5
2 : 3
1 : 2
4 : 5
2 : 5

24. Sharing in
Ratio

25. Share £10 between Mandy and Lara in the ratio 3 : 2
Number of equal parts = = 5 2 2 2 2 2 2 2 2 2 2
Amount in 1 part = 10 ÷ 5 = £ 2
Mandy gets = £ 2  3 = £ 6
Lara gets = £ 2  2 = £ 4

26. Number of equal parts = 4 + 3 = 7
A 35 ml orange drink is made by mixing orange juice and water in the ratio 4 : 3.
Number of equal parts = = 7 5 5 5 5 5 5 5 5 5 5 5 5 5 5
Amount in 1 part = 35 ÷ 7 = 5 ml
Orange Juice = 5  4 = 20 ml
Water = 5  3 = 15 ml

27. Number of equal parts = 3 + 1 = 4
Uncle John wants to share £20 between Mark and Amy in the ratio 3 : 1. How much money will each get?
Number of equal parts = = 4 5 5 5 5 5 5 5 5
Amount in 1 part = 20 ÷ 4 = £ 5
Mark gets = 5  3 = £ 15
Amy gets = 5  1 = £ 5

28. Number of equal parts = 6 + 3 + 1 = 10
A recipe for pastry uses flour, margarine and water in the ratio 6 : 3 : 1. What weight of each is needed to make a mixture that weighs 300 g?
Number of equal parts = = 10 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
Amount in 1 part = 300 ÷ 10 = 30 g
Flour = 30  6 = 180 g
Margarine = 30  3 = 90 g
Water = 30  1 = 30 g

30. Copyright © AQA and its licensors. All rights reserved.
6 balls and 3 bats
Ratio
Balls :
Bats 6 3
Proportion
9 object altogether
(a) What fraction are balls?
(b) Can you simplify the fraction
(c) What fraction are bats
(d) Can you simplify the fraction
Copyright © AQA and its licensors. All rights reserved.
Version 2.0

31. Copyright © AQA and its licensors. All rights reserved.
6 balls and 3 bats
Ratio
Balls :
Bats 6 3
This can be rewritten as 3 lots of 2 : 1
The ratio can be simplified by dividing into 3 groups
Balls :
Bats 2 1
For every 2 balls, there is 1 bat.
Bats :
Balls 1 2
For every 1 bat, there are 2 balls.
What link can you see between the simplified ratios and the simplified fractions?
Copyright © AQA and its licensors. All rights reserved.
Version 2.0

32. Copyright © AQA and its licensors. All rights reserved.
x of x Version 3.0

33. Find value of one share if you know the value of the other share…

34. £20

35. £20 ??

36. £20
£30

37. £20
£30
How did you work it out?

38. Try these problems, some in pictures and some in words…

39. Jim’s
Jemima’s
Write down the ratio using the
colon notation…

40. £800
Jim’s
Jemima’s
Find the value of Jim
and Jemima’s shares…

41. £??
£280
£??
Find the value of the whole amount
and the missing share…

42. Write down the ratio using the
smallest whole numbers you can…

43. Best Buys

44. Tesco sell pineapples at £4.20 for 3. Where should the minions shop?
The minions go shopping for pineapples! Asda sell pineapples for £3 for 2.
Tesco sell pineapples at £4.20 for 3.
Where should the minions shop?
What is the cheapest the minions can pay for 12 pineapples?

45. The minions go banana-shopping. Bob finds 4 bananas cost 88p.
Pete finds 9 bananas cost £1.89
Which is the cheaper deal…?

46. Directed Study

47. Directed Study
For your directed study this week please complete the skills builder worksheet