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14.1 Comparing and using ratios

14.1 Comparing and using ratios

You see ratios used in a variety of situations, such as mixing ingredients in a recipe or sharing
an amount among several people.

Ratios can also be used to make comparisons.
For example, suppose you wanted to compare two mixes of paint.
Pink paint is made from red and white paint in a certain ratio (red : white).
If two shades of pink paint have been mixed from red and white in the ratios 3 : 4 and 2 : 3, which shade
is darker?
!e best way to compare ratios is to write each ratio in the form 1 : n, where n is a number.

!en you can compare the ratios by comparing the values of n.

Worked example 14.1

Pablo mixes two shades of pink paint in the ratios of red : white paint, Perfect pink 3 : 4
as shown opposite.
a Which shade of pink paint is darker? Rose pink 2 : 3
b When Pablo mixes Perfect pink paint, he uses 4 litres of red paint.
How much white paint does he use?
c Pablo makes 12 litres of Rose pink paint. How much white paint
does he use?

a Perfect pink Rose pink First, write each ratio in the form 1 : n.
•
red : white red : white Divide 3 and 4 by 3 to get the ratio 1 : 1.333... or 1. 3 .
3 : 4 2 : 3 Divide 2 and 3 by 2 to get the ratio 1 : 1.5.
8 3 8 3 8 2 8 2 •
•
1 : 3 1 : 1.5 1.5 > 1. 3 , so there is more white in Rose pink than in
Perfect pink.
Perfect pink is darker. This means that Perfect pink is darker.
•
b red : white = 1 : 1. 3 First, write out the ratio of red : white in the form 1 : n.
= 4 = 4
•
4 : 5.3 Multiply both sides of the ratio by 4, as he uses 4 litres
of red.
1
•
1
He uses 5 litres of white paint. The answer is 5.3 which you can write as 5 .
3
3
c Total number of parts = 2 + 3 = 5 First, work out the total number of parts.
12 ÷ 5 = 2.4 litres per part Share the 12 litres into 5 equal parts to fi nd the value
of one part.
White = 3 × 2.4 = 7.2 litres White has three out of the fi ve parts, so multiply
2.4 litres by 3.

) Exercise 14.1

1 Sanjay mixes two shades of blue paint in the following ratios of blue : white.
a Write each ratio in the form 1 : n.
b Which shade of blue paint is darker? Sky blue 3 : 5 Sea blue 4 : 7

136 14 Ratio and proportion