Download percentages as fractions

number AND algebra • real numbers
Percentages as fractions
7A
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The term per cent means ‘per hundred’. The symbol for per cent is %. For example, 7%
means 7 out of 100.
Whether a percentage is a whole number, a mixed number, a proper fraction, or a decimal, it
can be expressed as a fraction.
To convert a whole number percentage into a fraction, write it over 100 and simplify.
To convert a mixed number percentage into a fraction:
•• change the mixed number into an improper fraction first
•• multiply the denominator by 100
•• simplify if possible.
If the percentage is a proper fraction, multiply the denominator by 100 and simplify.
To convert a percentage containing a decimal number into a fraction:
•• place the decimal number over 100
•• change the numerator to a whole number by multiplying both the numerator and the
denominator by a required multiple of 10
•• simplify if possible.
Worked Example 1
Write 47% as a fraction.
Think
Write
Write the percentage and then change it to a fraction with a
denominator of 100.
47
47% = 100
Worked Example 2
Write 20% as a fraction in simplest form.
Think
1
2
Write
Write the percentage, change it to a fraction with a
denominator of 100 and then cancel by dividing numerator
and denominator by the same number.
20% =
Write the answer and check that the fraction cannot be
simplified further.
=
20
1
100
5
1
5
Worked Example 3
Write the following percentages as fractions in simplest form.
1
1
a %
b 15 %
4
3
Think
a
1
Write the percentage and then multiply the denominator
by 100.
2
Simplify.
Write
a
1
%
4
=
1
4 × 100
=
1
400
Chapter 7 Percentages
221
number AND algebra • real numbers
b
1
Write the percentage and then change the mixed
number to an improper fraction.
2
Multiply the denominator by 100 and simplify by
cancelling. Check to make sure that the fraction cannot be
simplified further.
b
15 13 % = 46
%
3
=
=
=
46
3 × 100
46
300
23
150
23
150
Worked Example 4
Write 36.4% as a fraction in simplest form.
Think
Write
1
Write the percentage and change it to a fraction out
of 100.
36.4% =
2
Change the numerator to a whole number by multiplying it
by an appropriate multiple of 10, multiply the denominator
by the same multiple of 10 and simplify the fraction.
=
=
3
Write the answer.
=
36.4
100
36.4 × 10
100 × 10
364
1000
91
250
91
250
remember
1. Per cent means ‘out of 100’.
2. The symbol for per cent is %.
3. To convert a percentage to a fraction, write it as a fraction with a denominator of 100
and simplify.
4. If the percentage is a fraction, multiply the denominator by 100 and simplify.
5. If the percentage is a mixed number, either:
(a) change the mixed number to an improper fraction, write it as a fraction out of 100
and simplify the fraction or
(b)change the mixed number to an improper fraction, multiply the denominator by 100
and simplify.
6. If the percentage contains a decimal number, place it over 100 and then multiply the
numerator and the denominator by an appropriate multiple of 10 to make the numerator
a whole number. Simplify where appropriate.
222
Maths Quest 7 for the Australian Curriculum