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Whole Number Ratios
A ratio such as 5:4 is a whole number ratio. Ratios sometimes include decimal
numbers. For example, the ratio 1.5:4.5, in which the left side and the right side
are both decimals.
To convert a ratio to whole numbers you multiply both sides by the same
number. You have to choose a number so that the result is a whole number.
The 1.5 in the ratio 1.5:4.5 is multiplied by 10 to give 15. You must multiply
the right side by 10 to give 45. This is shown in Example 3 below.
Note: converting the left and the right side of a ratio to integers is exactly the
same as converting the numerator and the denominator of a fraction to integers.
The fraction
1.5
4.5
is converted to integers by multiplying top and bottom by 10.
Example 3
Express 1.5:4.5 as a whole number ratio. Multiply the left and right by 10 to
remove the decimals.
1.5:4.5 = 15:45
Then simplify (divide both sides by 15) to give:
15:45 = 1:3
A ratio can have a fraction in one or both sides as shown in Example 4 below.
The process for converting to whole numbers is the same as for decimals.
Example 4
Write
2
3
:
5
6
as a whole number ratio.
Multiply both parts by 6:
2
3
× 6 = 4
5
6
× 6 = 5
giving:
2
3
:
5
6
= 4:5
or you can show less working:
2
3
× 6 :
5
6
× 6 = 4:5
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