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Level 5-6 Numbers - Ratios
A drink is made from orange juice and lemonade in the ratio 3:7.

Level 5-6 Numbers - Ratios

Ratios compare quantities fairly. Learn to write, simplify, and use ratios to scale recipes, share amounts, and read maps.

Fascinating Fact:

A drink mix that needs 1 part syrup to 4 parts water makes 1:4, so 100 ml syrup mixes with 400 ml water.

In KS3 Maths, ratios are used to compare amounts and keep things in proportion. You will practise writing ratios, simplifying them, converting to fractions, and using them to scale recipes, maps, and diagrams.

  • Ratio: A way to compare quantities using “to” or a colon, like 3:2.
  • Simplest form: A ratio where both parts are divided by the same highest common factor.
  • Proportion: A statement that two ratios are equal, such as 1:2 and 2:4.
How do you simplify a ratio?

Write the ratio as a:b and divide both a and b by their highest common factor. For example, 12:18 ÷ 6 gives 2:3.

What is the difference between a fraction and a ratio?

A fraction compares a part with a whole, like 3/5. A ratio compares two quantities directly, like 3:5.

How do you share £60 in the ratio 2:3?

Add the parts (2 + 3 = 5). Each part is £60 ÷ 5 = £12. The shares are £24 and £36.

1 .
A road map is drawn to a scale of 1 cm = 8 km. A distance of 6.5 cm on the map represents how many kilometres of the road?
52 km
56 km
65 km
81 km
The ratio for a 1cm = 8km scale is 1 : 800,000!
2 .
Divide 240 litres in the ratio 3 : 5.
50 : 150
80 : 140
90 : 150
90 : 170
3 + 5 = 8 so first divide 240 litres by 8 then multiply by both 3 and 5
3 .
Dean buys 75 shares for £262.50. How much would 325 shares cost Dean?
£1,037.10
£1,137.50
£1,317.50
£1,731.40
25 is a good figure to work with here - just divide £262.50 by 3 to find what 25 shares would cost, and go from there
4 .
A drink is made from orange juice and lemonade in the ratio 3 : 7. How much lemonade is needed if 60 ml of orange juice is used?
110 ml
120 ml
130 ml
140 ml
60 ml / 3 = 20 ml and 7 x 20 ml = 140 ml
5 .
Divide £85 in the ratio 1 : 4.
£17 : £68
£23 : £62
£40 : £45
£60 : £25
Remember the two numbers must total £85
6 .
What is 150 cm : 4 m in its simplest form?
2 : 7
3 : 8
4 : 9
5 : 9
The common factor is 50 cm. There are 3 x 50 cm in 150 cm and there are 8 x 50 cm in 4 m
7 .
15 pints of milk cost £7.80. What is the cost of 22 pints of milk?
£10.80
£11.44
£14.44
£15.03
15 : 22 is roughly 2 : 3. £7.80 ÷ 2 = £3.90 so you know your answer will be approximately £3.90 x 3 = £11.70
8 .
The ratio of two bags of flour is 3 : 4. If the smaller bag holds 900 g of flour, how much does the larger bag hold?
1,000 g
1,100 g
1,200 g
1,300 g
A ratio such as 3:4 means 3/7 of one thing and 4/7 of another thing. The 7 comes from adding 3 and 4. The ratio 3:4 can also be written as a fraction 3/4 for calculations. In this case 900/x = 3/4 where x is the big bag of flour: so x = (4 x 900)/3. Use this method when dealing with ratios
9 .
What is £8 : 420p in its simplest form?
13 : 25
17 : 28
19 : 33
40 : 21
The quantities in the ratio MUST be in the same units: in this case change the £8 to 800p
10 .
What is 12 kg : 4,800 g in its simplest form?
5 : 2
6 : 3
7 : 4
8 : 5
It may be easier to first convert 12kg into 12,000g
You can find more about this topic by visiting BBC Bitesize - Ratio

Author:  Frank Evans (Specialist 11 Plus Teacher and Tutor)

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