Converting fractions into percentages

Converting fractions into percentages

A fraction is considered to be a percentage if its denominator is 100. In Figure , there are 100 squares. The fraction of 25 purple squares is $\frac{25}{100}$ which is equivalent to 25 percent (25%). There are 75 uncoloured squares which give a fraction of $\frac{75}{100}$ equivalent to 75 percent (75%).

The following table shows the relationship between percentage and fraction:

Percentage	5%	10%	25%	29%	50%	75%	90%	100%
Fraction	$\frac{5}{100} = \frac{1}{20}$	$\frac{10}{100} = \frac{1}{10}$	$\frac{25}{100} = \frac{1}{4}$	$\frac{29}{100}$	$\frac{50}{100} = \frac{1}{2}$	$\frac{75}{100} = \frac{3}{4}$	$\frac{90}{100} = \frac{9}{10}$	$\frac{100}{100} = 1$

A fraction with a denominator of 100 can be simplified further if both the numerator and the denominator have a Greatest Common Factor (GCF) greater than 1. For example, 75% which is $\frac{75}{100}$ can be simplified to get $\frac{3}{4}$ because the numerator and the denominator have GCF of 25. To simplify a fraction, divide the numerator and the denominator by their GCF. For example, the greatest common factor of 75 and 100 is 25. Thus,

$\frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4}$

The twenty-nine percent (29%) which is $\frac{29}{100}$ cannot be simplified further because the numerator and the denominator have GCF of 1.