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A drink is made from orange juice and lemonade in the ratio 3:7.

# Level 5-6 Numbers - Ratios

In KS3 Maths, comparing numbers comes in many forms – bars in a graph, sectors in a pie chart, or figures in a table. One of the easiest and most common ways is using ratios.

Imagine Person A has £50 and Person B has £40. How much more does A have? Ratios help us compare. A has £10 more, but that doesn't really show the comparison well. Ratios, like 50:40, are handy. Since 50 and 40 share a factor of 10, it simplifies to 5:4, the simplest form.

1.
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
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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!
10.
Divide £85 in the ratio 1 : 4.
£17 : £68
£23 : £62
£40 : £45
£60 : £25
Remember the two numbers must total £85