Fraction Simplifier

When to use it

Fractions turn up wherever a whole is cut into parts: a recipe in cups, a drill bit in sixty-fourths, a discount written as three-quarters, a share of an inheritance. This page reduces a fraction to its simplest form and immediately shows the same value as a decimal and a percentage, which is usually what you need in order to compare it with something else.

It is also the quickest way to check homework: type the numerator and denominator and see whether the simplified result matches yours. Improper fractions are handled too, so 27/6 comes back as 9/2 with a mixed number of 4 1/2 alongside.

How the maths works

Both numbers are divided by their greatest common divisor, the largest whole number that divides both exactly. The value does not change; only the writing gets smaller. The decimal is numerator ÷ denominator, and the percentage is that decimal multiplied by 100. When the numerator is larger than the denominator, the page also builds a mixed number: whole parts plus the remainder over the denominator.

Signs are handled separately: if exactly one of the two numbers is negative the result carries a minus sign, and a negative over a negative comes out positive.

A worked example

Simplify 18/24.

1. Divisors of 18 and 24 include 2, 3 and 6; the largest is 6.
2. 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so the fraction is 3/4.
3. Decimal: 18 ÷ 24 = 0.75.
4. Percentage: 0.75 × 100 = 75%.

A second case: 27/6 divides by 3 to give 9/2, which is 4.5 and 450%, with a mixed number of 4 1/2. The improper form is not wrong — it is simply harder to read at a glance.

Fractions at a glance

The decimal column is what a calculator or a spreadsheet will use; the percentage column is what a report will quote. Both come from the same division.

Common mistakes

• Typing decimals. The fields take whole numbers, so 1.5/2 must first become 15/20.
• Thinking the value changed. 18/24 and 3/4 are the same number; simplification only rewrites it.
• Dividing by zero. A zero denominator has no value, and the page refuses it rather than returning infinity.
• Adding tops and bottoms. 1/2 + 1/3 is not 2/5; find a common denominator first, which is what the GCD and LCM tool is for.

Keep exploring

• GCD & LCM Calculator — the common denominator behind fraction arithmetic.
• Ratio Simplifier — the same comparison written with a colon.
• Percentage Calculator — move between a share and a percentage of a base.
• Guide: Grades, Fractions and Proportions.