What if the percent is greater than 100, like 150%?

The same rule applies: write 150 over 100 to get 150/100, then simplify. Dividing both by 50 gives 3/2, which equals the improper fraction 3/2 or the mixed number 1 1/2. Percents above 100 simply represent values greater than one whole.

Converting Percents and Fractions — Definition, Formula & Examples

Converting percents and fractions means rewriting a percent as a fraction or rewriting a fraction as a percent. Since "percent" means "per hundred," every percent can be written as a fraction with 100 in the denominator, and every fraction can be turned into a percent by finding its equivalent value out of 100.

A percent $p\%$ is equivalent to the fraction $\dfrac{p}{100}$ , which may then be simplified to lowest terms. Conversely, a fraction $\dfrac{a}{b}$ is converted to a percent by computing $\dfrac{a}{b} \times 100\%$ .

Key Formula

p\% = \frac{p}{100} \qquad \text{and} \qquad \frac{a}{b} = \frac{a}{b} \times 100\%

Where:

$p$ = The percent value (e.g., 75 in 75%)
$a$ = The numerator of the fraction
$b$ = The denominator of the fraction

How It Works

To convert a percent to a fraction, write the percent value over 100 and simplify by dividing the numerator and denominator by their greatest common factor. For example,

45\%

becomes

\frac{45}{100}

, which simplifies to

\frac{9}{20}

. To convert a fraction to a percent, divide the numerator by the denominator, then multiply the result by 100. Alternatively, you can find an equivalent fraction with a denominator of 100 — the numerator then equals the percent. Both directions rely on the core idea that "percent" literally means "out of one hundred."

Worked Example

Problem: Convert 60% to a fraction in simplest form.

Step 1: Write the percent over 100.

60\% = \frac{60}{100}

Step 2: Find the greatest common factor (GCF) of 60 and 100. The GCF is 20.

\gcd(60, 100) = 20

Step 3: Divide both the numerator and denominator by 20 to simplify.

\frac{60 \div 20}{100 \div 20} = \frac{3}{5}

Answer:

60\% = \dfrac{3}{5}

Another Example

Problem: Convert the fraction 7/8 to a percent.

Step 1: Divide the numerator by the denominator.

7 \div 8 = 0.875

Step 2: Multiply the decimal result by 100 to get the percent.

0.875 \times 100 = 87.5

Step 3: Attach the percent symbol.

\frac{7}{8} = 87.5\%

Answer:

\dfrac{7}{8} = 87.5\%

Visualization

Why It Matters

Converting between percents and fractions shows up constantly in pre-algebra, statistics, and everyday life — from calculating sales tax and tip amounts to interpreting test scores. In science courses, you often need to express experimental data as either a fraction or a percent depending on the context. Mastering this skill also builds the number sense you need for working with ratios, proportions, and probability.

Common Mistakes

Mistake: Forgetting to simplify the fraction after placing the percent over 100.

Correction: Always check whether the numerator and denominator share a common factor. For instance, 80/100 should be reduced to 4/5, not left as 80/100.

Mistake: Dividing by 10 instead of 100 when converting a percent to a fraction.

Correction: Remember that "percent" means per hundred, so the denominator must be 100. Writing 25% as 25/10 gives the wrong value; the correct fraction is 25/100 = 1/4.

Related Terms

Fraction — The form you convert a percent into
Decimal — Intermediate step when converting fractions to percents
Numerator — Top number that equals the percent when denominator is 100
Denominator — Bottom number, set to 100 for percent conversion
Fraction Rules — Simplifying rules used after conversion
Improper Fraction — Result when a percent exceeds 100
Mixed Number — Alternate form for percents over 100
Ratio — Percents and fractions both express ratios