Page 138 - Mathematics Coursebook

14.1 Simplifying ratios

14.1 Simplifying ratios

In this necklace there are two red beads and six yellow beads.
You can write the ratio of red beads to yellow beads as 2 : 6.

For every one red bead there are three yellow beads, so you red : yellow
can simplify the ratio 2 : 6 to 1 : 3. 2 : 6
You write a ratio in its simplest form by dividing the numbers ÷ 2 ÷2
in the ratio by the highest common factor. Here, the highest common factor 1 : 3
of 2 and 6 is 2, so divide both the numbers by 2.

Worked example 14.1

The rectangle is made up of blue squares and green squares.
a Write down the ratio of blue squares to green squares.
b Write the ratio in its simplest form.

a blue : green = 8 : 12 There are 8 blue squares and 12 green squares in the rectangle.
b 8 : 12 The highest common factor of 8 and 12 is 4, so divide both numbers by 4.
÷ 4 ÷ 4
1 : 3

) Exercise 14.1

1 For each of these necklaces, write down the ratio of red beads to yellow beads.
a b c d

2 For each of these necklaces, write down the ratio of green beads to blue beads in its simplest form.
a b c d

3 Write each of these ratios in its simplest form.
a 2 : 8 b 2 : 12 c 3 : 6 d 3 : 15 e 4 : 8 f 4 : 12
g 25 : 5 h 60 : 5 i 36 : 6 j 14 : 7 k 24 : 8 l 54 : 9
4 Write each of these ratios in its simplest form.
a 4 : 10 b 4 : 14 c 6 : 8 d 6 : 21 e 8 : 10 f 8 : 14
g 12 : 9 h 24 : 9 i 15 : 10 j 24 : 10 k 28 : 12 l 21 : 9
5 Helena sees this recipe for pastry. Pastry
She says that the ratio of margarine to flour is 4 : 1. 200 g fl our pinch salt

Is Helena correct? Explain your answer.
50 g margarine water to mix
6 Bryn is drawing a scale diagram of a building. 50 g lard
For every 10 m of the building he draws a line 5 cm long.
Bryn thinks he is using a ratio of 2 : 1. Alun thinks Bryn is using a ratio of 200 : 1.
Is either of them correct? Explain your answer.

14 Ratio and proportion 137