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Ratio is the relation between two numbers or quantities. It is useful for showing the number of times one value contains or is contained within the other. For instance in the ratio 1:3, if 1 is sand and 3 is water, you would need three times the amount of water in relation to sand. Ratios are excellent tools which help us to visualize how different numbers of things compare to one another. They are also very similar to fractions. The ratios 1:3 and 2:3 can also be represented by the fractions ^{1}⁄_{3} and ^{2}⁄_{3}

1.

There are 2 white cubes for every 1 blue cube. What proportion are blue cubes to white cubes?

2.

In a box of chocolates there are 4 milk chocolates to 3 dark chocolates. How many dark chocolates in a box of 49 chocolates?

7

21

28

30

There are 3 dark chocolates in every 7. There are seven 7s in 49 so we multiply 3 by 7

3.

In a grid of 10 squares 4 are white and the rest are blue. What is the ratio of white to blue?

1:2

2:4

4:6

5:6

10 - 4 = 6 so there are 6 blue squares for every 4 white squares

4.

The proportion of brick houses in every 20 is ^{3}⁄_{10}. How many brick houses in a street of 100 houses?

6

10

30

50

5.

In every 10 tiles there are 2 red tiles. What is the proportion of red tiles?

6.

A cookie recipe needs 250g flour, 150g of sugar and 150g of butter to make 6 cookies. How much butter is needed to make 18 cookies?

150g

300g

400g

450g

18 is 3 x 6 so we multiply 150g by 3

7.

If there is a 10:1 ratio between black squares and white squares which number represents white squares?

1

2

5

10

The 10 represents black and the 1 represents white because black was mentioned first and white second

8.

Jo mixes 400ml of orange juice to every 200ml of pineapple juice to make a fruit cocktail. How much orange juice will she need to make 900ml of fruit cocktail?

200ml

400ml

600ml

800ml

There is 400ml in every 600ml. 900ml = 1.5 x 600ml. So multiply 400ml by 1.5

9.

In every 12 tiles the proportion of blue tiles is ^{3}⁄_{4}. How many blue tiles in every 12?

3

6

8

9

10.

For every 4 liters of gasoline a car can travel 80km. How much gasoline is required for a journey of 100km?

5 liters

8 liters

10 liters

12 liters

If 4 liters can travel 80km we divide by 4 to find 1 liter will travel 20km. So 5 liters will travel 100km

^{1}⁄_{2}is the same as 1:2