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Year 7 Interactive Maths - Second Edition


Percentages

A fraction that is written out of one hundred is called a percentage.  The symbol used for per cent is %.

For example, 1/100 means 1% (i.e. 1 per cent), 5/100 means 5% (i.e. 5 per cent) and 20/100 means 20% (i.e. 20 per cent)


Note:

50/100 means 50% and it can be represented by the shaded part of the following grid.

50% of this square grid is shaded.

100/100 means 100% and it can be represented by the shaded part of the following grid.

100% of this square grid is shaded.

100% means the whole.


From the preceding discussion, we notice that:

A percentage is the numerator of a fraction with a denominator of 100.

For example, 1/2 = 50/100 is a fraction equivalent to 50%.  The % (per cent) symbol is used in place of 'over 100'.  Thus, 100% = 100/100 = 1


Changing a Percentage to a Fraction

To convert a percentage to a fraction, write it as a fraction with a denominator of 100 and then simplify the fraction if possible.


Example 1

Express 65% as a fraction.

Solution:

65% = 13/20     {Divide the numerator and denominator by 5}


Mixed Number Percentage

To convert a mixed number percentage to a fraction, change the mixed number to an improper fraction, write the percentage as a fraction with a denominator of 100 and simplify the fraction if possible.


Example 2

Express 6 2/3% as a fraction.

Solution:
6 2/3% = 1/15

Key Terms

percentage, per cent, mixed number percentage


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