Skill: Convert percents to fractions

Explanation and Free Practice Resources

Percent is understood as a rate per hundred: $p\%$ denotes the rational number $\frac{p}{100}$ , so conversion preserves the quantity represented rather than merely removing the percent symbol. Whole-number and simple terminating-decimal percents, including values greater than $100\%$ , can be expressed as equivalent simplified proper or improper fractions, supporting comparison and proportional reasoning; repeating-decimal and more advanced symbolic cases are outside this scope.

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Detailed Explanation: Convert percents to fractions

A percent means “per 100.” Therefore, to change a percent to a fraction, write the number before the percent sign over $100$ , then simplify.

Example: Convert $125\%$ to a fraction.

Write $125$ over $100$ :

125\%=\frac{125}{100}

Simplify the fraction. Both $125$ and $100$ are divisible by $25$ :

\frac{125\div25}{100\div25}=\frac{5}{4}

Therefore,

\boxed{125\%=\frac{5}{4}}

This fraction is improper because $125\%$ is greater than $100\%$ . It can also be written as the mixed number $1\frac14$ .

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