This is the third of our Difficult quizzes on Ratios. As you will know if you have played our other quizzes, ratios are a way to express proportions of totals. They are very similar to fractions and, just like fractions, they can be simplified by multiplying or by dividing them.

Let’s give you an example:

If Anna has 8 stickers and Bella has 12, the ratio would be 8:12This can be simplified to 2:3 by dividing by 4:

8 ÷ 4 = 2, and 12 ÷ 4 = 3

The information would be shown in fractions as

That’s because 2 + 3 = 5, so 5 becomes the denominator in the fractions.

I do hope that makes sense! If not, try practising with the questions below. Keep playing until you can score a perfect ten out of ten. Good luck!

1.

How else can the ratio 0.8:4.2:3.4 be written?

4:20:17

4:21:18

4:21:17

5:21:17

0.8:4.2:3.4 = 4:21:17 (multiply by 5). This example should show you why it is important to be able to simplify ratios

2.

Anita, Bobby and Charles have been making bookmarks. They made 40 in all, in the ratio 7:8:5 respectively. How many bookmarks did each child make?

Anita 14, Bobby 16, and Charles 10

Anita 16, Bobby 10, and Charles 14

Anita 10, Bobby 14, and Charles 16

Anita 18, Bobby 14, and Charles 8

7 + 8 + 5 = 20 ∴ the fractional parts are as follows: Anita, ^{7}⁄_{20} x 40 = 14, Bobby, ^{8}⁄_{20} x 40 = 16, Charles, ^{5}⁄_{20} x 40 = 10

3.

Three children, Amy, Brian and Chloe, raised £70 for charity, in the ratio 4:6:7.5 respectively. How much money did each child raise?

Amy £16, Brian £30, Chloe £24

Amy £16, Brian £24, Chloe £30

Amy £24, Brian £16, Chloe £30

Amy £30, Brian £24, Chloe £16

4 + 6 + 7.5 = 17.5

£70 ÷ 17.5 = 4, so every “unit” in the ratio is worth £4

£4 x 4 = £16, so Amy raised £16

£4 x 6 = £24, so Brian raised £24

£4 x 7.5 = £30, so Chloe raised £30

£70 ÷ 17.5 = 4, so every “unit” in the ratio is worth £4

£4 x 4 = £16, so Amy raised £16

£4 x 6 = £24, so Brian raised £24

£4 x 7.5 = £30, so Chloe raised £30

4.

Arnold, Beth and Claire are saving their money. Arnold has £24, Beth has £12 and Claire has £32. What is the simplest ratio to express these amounts?

3:2:6

4:2:6

5:3:7

6:3:8

A:B:C: = 24:12:32 = 6:3:8 (dividing by 4)

5.

What are the fractional parts of 14:28:21?

14:28:21 = 2:4:3 (divide by 7). 2 + 4 + 3 = 9 which becomes the denominator in the fractional parts. Always try and simplify your ratios BEFORE you work out the fractional parts

6.

How else can the ratio 6:2.2:3.4 be written?

30:11:17

30:10:17

28:11:17

30:11:18

6:2.2:3.4 = 30:11:17 (multiply by 5). You need to find a number to multiply by which will make 2.2 and 3.4 into whole numbers

7.

What are the fraction parts of the ratio 3:5:6?

3 + 5 + 6 = 14 which becomes the denominator in the fractional parts

8.

An antique music shop sold 450 items this week: vinyl records, CDs and audio tapes in the ratio 5:12:1 respectively. How many of each item were sold?

25 vinyl records, 300 CDs, 125 audio tapes

125 vinyl records, 25 CDs, 300 audio tapes

125 vinyl records, 300 CDs, 25 audio tapes

300 vinyl records, 125 CDs, 25 audio tapes

5 + 12 + 1 = 18 ∴ the fractional parts are as follows: vinyl records, ^{5}⁄_{18} x 450 = 125, CDs,^{12}⁄_{18} x 450 = 300, and audio tapes, ^{1}⁄_{18} x 450 = 25

9.

How else can the ratio 6:2.1 be written?

3:1

60:20

30:10

20:7

6:2.1 = 60:21 (multiply by 10). This can be simplified to 20:7 by dividing by 3

10.

What are the fractional parts of the ratio 30:18 in their simplest form?

30 + 18 = 48. This can be simplified by dividing by six to 5 + 3 = 8 which becomes the denominator in the fractional parts. Always try to simplify if it is possible