Ratio - Reduction

Reduction

Note that ratios can be reduced (as fractions are) by dividing each quantity by the common factors of all the quantities. This is often called "cancelling." As for fractions, the simplest form is considered that in which the numbers in the ratio are the smallest possible integers.

Thus, the ratio 40:60 may be considered equivalent in meaning to the ratio 2:3 within contexts concerned only with relative quantities.

Mathematically, we write: "40:60" = "2:3" (dividing both quantities by 20).

Grammatically, we would say, "40 to 60 equals 2 to 3."

An alternative representation is: "40:60::2:3"

Grammatically, we would say, "40 is to 60 as 2 is to 3."

A ratio that has integers for both quantities and that cannot be reduced any further (using integers) is said to be in simplest form or lowest terms.

Sometimes it is useful to write a ratio in the form 1:n or n:1 to enable comparisons of different ratios.

For example, the ratio 4:5 can be written as 1:1.25 (dividing both sides by 4)

Alternatively, 4:5 can be written as 0.8:1 (dividing both sides by 5)

Where the context makes the meaning clear, a ratio in this form is sometimes written without the 1 and the colon, though, mathematically, this makes it a factor or multiplier.