1. Starter
What is a ratio?

2. 1 : 4
This is a ratio.
This example tells us that for every 1 part of something we need, we need 4 parts of something else.

3. 1 : 6 For example, orange squash.
For every 1 part of cordial, we need 6 parts water.

4. 2 : 5
Or pink paint.
For every 2 parts of red paint, we need 5 parts of white paint.

5. What is the highest common factor (HCF) of 6 and 8?12 2 10 4

6. What is the highest common factor (HCF) of 6 and 8?12 2 10 4

7. What is the highest common factor (HCF) of 12 and 16?48 12 4 24

8. What is the highest common factor (HCF) of 12 and 16?48 12 4 24

9. What is the highest common factor (HCF) of 10 and 25?50
2.5

10. What is the highest common factor (HCF) of 10 and 25?50
2.5

11. What is the highest common factor (HCF) of 24 and 36?12 8 24

12. What is the highest common factor (HCF) of 24 and 36?12 8 24

13. To simplify or cancel down ratios, we need to divide by the highest common factor (HCF) of both parts.

14. 16 : 20 4 Simplify: What’s the highest common factor of 16 and 20?
So divide both numbers by 4

15. Simplify:
16 : 20
÷ 4
÷ 4
4 : 5

16. 6 : 27 3 Simplify: What’s the highest common factor of 6 and 27?
So divide both numbers by 3

17. Simplify:
6 : 27
÷ 3
÷ 3
2 : 9

18. Show me a ratio which simplifies to 2:7
What is wrong: To simplify the ratio 32:48 keep dividing both sides by 2 until you can’t do it any more
True / Never / Sometimes:
To simplify the ratios keep dividing both sides by 2 until you can’t do it any more

19. What is the same / different:
4:5 and £4:500p
2:3, 34:51 and 3:2
Convince me that 19:95 is equivalent to 1:5

20. What is the hidden message? “I am Batman”
Pair Task
What is the hidden message?
“I am Batman”
…But shhhh don’t tell anyone!

21. Simplify the following:
1) 3 : 6 2) 10 : 15 3) 9 : 12 4) 5 : 10
5) 12 : 6 6) 25 : 10 7) 12 : 16 8) 6 : 30
Leave all ratio answers in their simplest form:
This month there were 14 sunny days and 16 wet days. Find the ratio of sunny days to wet days.
In a bag of sweets, 10 are yellow and 15 blue. Find the ratio of yellow sweets to blue sweets.
A coach has room for 28 sitting and 16 standing passengers Find the ratio of sitting to standing passengers.
In a class there are 12 girls and 18 boys. Find the ratio of girls to boys in the class.
Simplify the following:
1) 6 : 15 : 21 2) 8 : 16 : 32 3) 9 : 12 :21
4) 9 : 18 : 45 5) 16 : 32 : 56 6) 36 : 48 : 72

22. Answers
1) 1 : 2 2) 2 : 3 3) 3 : 4 4) 1 : 2
5) 2 : 1 6) 5 : 2 7) 3 : 4 8) 1 : 5
1) 7 : 8 2) 2 : 3 3) 7 : 4 4) 2 : 3
1) 2 : 5 : 7 2) 1 : 2 : 4 3) 3 : 4 : 7
4) 1 : 2 : 5 5) 2 : 4 : 7 6) 3 : 4 : 6

23. Starter Standard: 56 ÷ 7 64 ÷ 8 144 ÷ 12 42 ÷ 6 88 ÷ 8 = 8 = 12 = 7
= 11
Challenging:
272 ÷ 8
48 ÷ 3
114 ÷ 6
105 ÷ 5
333 ÷ 9
= 34
= 16
= 19
= 21
= 37

24. £20 is divided between Ann and Jim in the ratio 3 : 2
How much money does each get?
3 + 2 = 5 parts £4 £4 £4 £4 £4
Ann
Jim
£12 £8
£20 ÷ 5 = £4

25. £70 is divided between Joe and Kate in the ratio 3 : 4
How much money does each get?
3 + 4 = 7 parts
£10
£10
£10
£10
£10
£10
£10
Joe
Kate
£30
£40
£70 ÷ 7 = £10

26. £60 in the ratio 5 : 1
Answer  £50 : £10
True
Unsure
False

27. 72 cm in the ratio 7 : 5
Answer  49 cm : 35 cm
True
Unsure
False

28. 34 kg in the ratio 4 : 3
Answer  15 kg : 20 kg
True
Unsure
False

29. Answers
1. £6 : £ L : 9L : 6L
2. 240ml : 560ml : 8 : 32 sheep
3. 16 : 40 sweets 9. Dr Barnados: £80
RSPCA: £60
4. £32 : £40
10. Mr Allen: £60
5. 30 : 54 pens Mr Broome: £150
Mr Collins: £210
6. £50 : £20 : £50

30. Starter
Fill in the gaps.
1 : 2 =  : : 4 = 12 : 
16 : 12 =  : 6  : 8 = 7 : 4
5 :  = 25 : : 12 = 1 : 

31. Starter
Fill in the gaps.
1 : 2 = 3 : : 4 = 12 : 16
16 : 12 = 8 : : 8 = 7 : 4
5 : 8 = 25 : : 12 = 1 : 1.5

32. On a farm, the ratio of pigs to cows is 2 : 3
On a farm, the ratio of pigs to cows is 2 : 3. The ratio of cows to sheep is 5 : 7. What is the ratio of pigs to cows to sheep?
pigs
cows
LCM of 3 and 5 is 15
cows
sheep 10 15 21
10 : 15 : 21

33. A pet shop sells mice, rats and gerbils
A pet shop sells mice, rats and gerbils. The ratio of mice to rats is 4 : 3 and the ratio of mice to gerbils is 7 : 4. If there are 32 gerbils in stock at present, how many rats are there?
LCM of 4 and 7 is 28
mice
rats
mice
gerbils 28 21 16
28 : 21 : 16
 56 : 42 : 32
 42 rats

35. Answers
12 : 15 : 18
6 : 15 : 20
9 : 21 : 28
10 sheep
30 bottles of rose
42 forks
64 years old
420 children

37. Starter Calculate the following: 1) 3 x 2 2) 4 x 1.5 = 6 3) 6 x 2.5
= 15
= 5
= 17.5

38. Recipes Restaurants have to make money.
If too much food is made, it will be thrown away.
If not enough food is made, the customers won’t come again.
In either case, the restaurant will fail.
So, calculating the right amounts is essential!

39. Here are the ingredients needed to make ratatouille for 4 people.
Recipes
Here are the ingredients needed to make ratatouille for 4 people.
To find out how much of each we’ll need to make it for 6 people, we need to use ratio.
Ratatouille
Serves 4
2 large aubergines
4 small courgettes
2 yellow peppers
4 large tomatoes
5 tbsp olive oil
1 onion
3 garlic cloves

40. Recipes The ratio of people in the recipe and people we have is 4 : 6
We can simplify this by dividing both amounts by 2 – we get 2 : 3
To calculate the scale factor, simplify so the ratio is in the form 1 : n
The ratio is now 1 : 1.5 so the scale factor is 1.5

41. Recipes For 6 people: Ratatouille x 1.5 2 x 1.5 = 3 large aubergines
Serves 4
2 large aubergines
4 small courgettes
2 yellow peppers
4 large tomatoes
5 tbsp olive oil
1 onion
3 garlic cloves
4 x 1.5 = 6 small courgettes
2 x 1.5 = 3 yellow peppers
4 x 1.5 = 6 large tomatoes
5 x 1.5 = 7 ½ tbsp olive oil
1 x 1.5 = 1 ½ onions
3 x 1.5 = 4 ½ garlic cloves

42. How much of each ingredient will be needed to make 50 fingers?
Recipes
Your turn…!
x 2.5
Shortbread fingers
Makes 20
120g butter
50g caster sugar
170g plain flour
300g
125g
425g
How much of each ingredient will be needed to make 50 fingers?
Hint  20 : 50

43. Extension: Pancake day!

44. Answers 12 tomatoes 1200g prawns 2 potatoes 12 tsp mayonnaise
2 onions tsp tomato sauce
4 tbsp olive oil 12 lettuce leaves
4 pints vegetable stock
2 carrots
8 slices of bread
1 ½ tsp olive oil 15 roast potatoes
1 ½ large onions 5 carrots
3 cloves of garlic 2 ½ cans of peas
375g minced beef 10 slices of beef
300g chopped tomatoes 5 Yorkshire puddings
4 ½ mushrooms
300g spaghetti
275g butter 3 ½ watermelons
275g sugar 7 bunches of grapes
5 medium eggs 14 bananas
2 ½ tsp vanilla essence 21 oranges
275g flour apples
250g jam g strawberries

45. Plenary Rosa prepares the ingredients for pizzas.
She uses cheese, topping and dough in the ratio
2 : 3 : 5 Rose uses 70 grams of dough.
Work out the number of grams of cheese and the number of grams of topping Rosa uses.
Cheese g
Topping g
(Total 3 marks) 45

46. Starter
Match the questions and answers.

47. Answers

48. Which is the Best Buy?
1.2kg for £3.89
700g for £2.14

49. What is the price per gram?
1.2kg for £3.89
700g for £2.14
What is the price per gram?
1200g = 389p
700g = 214p
÷ 1200
÷ 1200
÷ 700
÷ 700
1g = 0.324p
1g = 0.305p
This is less money per gram, so it is the best buy

50. Which is the Best Buy?
TRESCO Supermarket Sells cheese on its deli counter for £1.88 per 160g
WEIGHTROSE Supermarket sells cheese on its deli counter for £13.55 per kg

51. What is the price per gram?
£13.55 per kg
What is the price per gram?
160g = 188p
1000g = 1355p
÷ 160
÷ 160
÷ 1000
÷ 1000
1g = 1.175p
1g = 1.355p
This is less money per gram, so it is the best buy

52. D A B C A can of coke that costs 60p Buy one can for 70p, get one free
Order these starting with the best value for money.
A can of coke that costs 60p D
Buy one can for 70p, get one free A
Buy 2 can for 60p each, get one free B
Two cans of coke for £1 C

53. A D B C 5 books for £10 One book for £3 A £4.80 book has 50% off
Order these starting with the best value for money.
5 books for £10 A
One book for £3 D
A £4.80 book has 50% off B
Buy one book for £5, get one free C

54. Extension: Best buys investigation

55. Answers Carrots  1.2 kg bag @ £1.00
Pork sausages  Packs of 4 for £12.00
Andrex toilet roll  4 pack, 2 for £3.50
Bacon  300g pack, 2 for £4
Diet Coke  2L bottles, 3 for £4.50
Deodorant  Gillette 200ml, 3 for 2 (£2.33 each)
Radox handwash  500ml, 3 for 2, £1.90 each

56. Group Activity Your budget is £50.
You must spend as little as possible, purchasing everything required on the list, for the best value.

58. How well do you know your currencies?
What currency is used in Japan?
What currency is used in France?
What currency is used in Ireland?
4. What currency is used in India?
What currency is used in Australia?
6. What currency is used in the USA?
Japan – Yen India – Rupee, Ireland – euro, Australia, aussie dolalr. 6 US Dollar

60. Exchange Rates
What are exchange rates?
The rate at which one currency may be converted into another.

61. Exchange Rates
When will I use this?
Any time you go abroad where the currency is not Pounds Sterling.

63. Exchange Rates
The exchange rate is £1 to $1.70. I need to convert my £56 into US Dollars.
£56 x 1.7 = $95.20
X 1.70
£1 = $1.70
÷ 1.70

64. Exchange Rates
On my return journey I have $12 left. What is this worth in Pounds (£)?
$12 ÷ 1.7
= £7.06
X 1.70
£1 = $1.70
÷ 1.70

65. Extension: Complete the round the world activities.

66. Think/pair/share
Use the table to calculate the following exchange rates:
Pounds Sterling to Japanese Yen
Japanese Yen to US Dollars
US Dollars to Australian Dollars
Australian Dollars to Euros
Euros to Pounds Sterling
Extension: What are the reverse rates?

67. Group Activity You are travelling the world!
But how much did you spend?

68. Plenary
A student bought a pair of sunglasses in the USA. He paid $35.50 In England, an identical pair of sunglasses costs £26.99 The exchange rate is £1 = $1.42
In which country were the sunglasses cheaper, and by how much? Show all your working.
(Total 3 marks)