How_To_Be_Good_At_Math

NUMBERS • PROPORTION 71

Proportion as a fraction

We often write proportion as a fraction. Here are

10 cats. What fraction of them is ginger?

Proportion as a percentage

Percentages are another way of writing fractions,

so a proportion can be expressed as a percentage,

too. What percentage of the cats is grey?

Proportion

Proportion is another way of comparing. Instead of comparing

one amount with another, as with ratio, proportion is

comparing a part of a whole with the whole amount.

Four of the

10 cats are

ginger

One of the 10 cats is grey

We simplify fractions if we can, so we

divide the numerator and denominator

of^4 / 10 by 2 to make it^2 / 5.

To change^1 / 10 into a percentage, we

rewrite it as equivalent hundredths,

so^1 / 10 becomes^10 / 100.

Four out of the 10 cats are ginger.

So, ginger cats make up four-tenths

(^4 / 10 ) of the whole amount.

There is one grey cat out of 10, so the

proportion as a fraction is^1 / 10.

So, the proportion of ginger in the whole

group, written as a fraction, is^2 / 5.

We know that “ten out of one hundred”

is the same as 10%, so the percentage

of grey cats in the group is 10%.

4

10

2

5

÷ 2

÷ 2

=

1

10

10

100

× 1 0

× 10

=

10%

2

5

PROPORTION OF GINGER CATS =

PROPORTION OF GREY CATS =

We simplify the

fraction by

dividing both

numbers by 2

We make an

equivalent

fraction by

multiplying both

numbers by 10

Proportion tells us how

much we have of

something compared

to the whole amount.

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