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A ratio is a way of showing proportions of amounts. For example, if there are double the number of green marbles compared with the number of yellow marbles, then we can show this by writing 2:1. This would be read as: 'the ratio of green marbles to yellow marbles is two to one'. Two parts of the marbles are green and one part is yellow, but: what is 'part(s) of' as a fraction? It's easy: 2 + 1 = 3, so ^{2}⁄_{3} are green, and ^{1}⁄_{3} is yellow.

1.

Peter has 20 blue pens. How many red pens must he buy if the ratio of blue to red pens has to be 2:3?

30

10

60

40

2:3 = 1:1.5 (dividing by 2). This means that there is 1 blue pen for every 1.5 red pens ∴ there are 1.5 as many red pens as there are blue pens = 1.5 × 20 = 30. CHECK 20:30 = 1:1.5 (dividing by 20). Your answer MUST preserve (keep) the same ratio. ALWAYS try to REDUCE your ratios so as to get a '1' in one of the terms of the ratio. Incidentally, 20 + 30 = 50 pens in all!

2.

Each of the following ratios show the ratio of girls to boys in three classes. If each class has the same number of pupils, which of the classes has the greatest ratio of girls to boys: 16:20, 8:10, 1:1.25?

16:20

1:1.25

They all have the same ratio of girls to boys

8:10

16:20 = 4:5 (divide by 4), 8:10 = 4:5 (divide by 2), 1:1.25 = 4:5 (multiply by 4) ∴ they all have the same ratio of 4:5. You can also have decimal ratios!

3.

The ratio of green bottles to white bottles is 3:4. What fraction of the bottles is white?

4 + 3 = 7. You DON'T have to know what the total number of items is in order to find the fractional amounts of each type of item

4.

How else can the ratio 8:56 be written?

7:56

7:1

1:7

7:8

8:56 = 1:7 (dividing by 8)

5.

3:2

2:3

3:5

2:5

You need only use the numbers in the numerators to form the ratio: the fractions MUST sum to 1

6.

The ratio of brown rats to black rats is 4:8. If there are 24 black rats, how many brown rats are there?

12

6

4

8

Divide the ratio 4:8 by 4 to give 1:2. This means that there is 1 brown rat for every 2 black rats ∴ there are half as many brown rats = 12. CHECK 12:24 = 1:2 (dividing by 12). Your answer MUST preserve (keep) the same ratio. ALWAYS try to REDUCE your ratios so as to get '1' in one of the terms of the ratio. Incidentally, 12 + 24 = 36 rats in all!

7.

One hundred paintings have to be selected for an art exhibition. If the ratio of amateur paintings to professional paintings has to be 2:3, how many amateur paintings and professional paintings have to be selected?

40 amateur paintings and 60 professional paintings

60 amateur paintings and 40 professional paintings

30 amateur paintings and 70 professional paintings

20 amateur paintings and 80 professional paintings

2 + 3 = 5 ∴ the fractional parts are ^{2}⁄_{5} × 100 = 40 amateur paintings & ^{3}⁄_{5} × 100 = 60 professional paintings. CHECK 40:60 = 2:3 (dividing by 20). Your answer MUST preserve (keep) the same ratio

8.

If the ratio of boys to girls is 1:1, which of the following statements is correct?

The number of boys is more than the number of girls

The number of boys equals the number of girls

The number of boys is less than the number of girls

Nothing can be said about the number of boys and girls in this case

1:1 means that half are boys and half are girls because 1 + 1 = 2 ∴ the fractional parts are each one half

9.

The ratio of small houses to big houses is 4:7. Which of the following would not be acceptable on the basis of this ratio?

8 small houses, 14 big houses

16 small houses, 28 big houses

14 small houses, 8 big houses

12 small houses, 21 big houses

Form the ratio 14:8 = 7:4 which is NOT the same as 4:7. All the others form ratios that can be reduced to 4:7

10.

How else can the ratio 1.25:4 be written?

16:5

5:16

1.25:16

5:4

1.25:4 = 5:16 (multiplying by 4)