Simplify Calculator
Simplify a fraction to its lowest terms, or simplify a square root — with the steps shown, free in your browser.
1. Simplify a Fraction
2. Simplify a Square Root
How to simplify a fraction
Find the greatest common divisor (GCD) of numerator and denominator, then divide both by it. Example: 12/18 — GCD is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2/3.
How to simplify a square root
Find the largest perfect square that divides the number, take its root outside. Example: √72 = √(36 × 2) = 6√2 (about 8.49).
More worked examples
Fraction — 45/60. The GCD of 45 and 60 is 15. 45 ÷ 15 = 3 and 60 ÷ 15 = 4, so 45/60 simplifies to 3/4.
Fraction — 7/11. 7 and 11 share no common factor except 1, so 7/11 is already in lowest terms.
Fraction — 100/250. The GCD of 100 and 250 is 50. 100 ÷ 50 = 2 and 250 ÷ 50 = 5, so 100/250 simplifies to 2/5.
Square root — √200. The largest perfect square dividing 200 is 100. √200 = √(100 × 2) = 10√2 (about 14.14).
Square root — √45. The largest perfect square dividing 45 is 9. √45 = √(9 × 5) = 3√5 (about 6.71).
Frequently Asked Questions
What does simplify mean in maths? Writing a fraction or root in its simplest form, with no common factor left (except 1).
Can a fraction already be in lowest terms? Yes — if numerator and denominator share no factor except 1, it is already simplified, for example 2/3.
How do I find the GCD quickly? List the factors of the smaller number and pick the largest one that also divides the bigger number. For 12 and 18: factors of 12 are 1, 2, 3, 4, 6, 12 — the largest dividing 18 is 6.
What if the numerator is bigger than the denominator? Simplify the same way, then convert to a mixed number if you like. Example: 22/6 → GCD 2 → 11/3 → 3⅔.
Is this calculator free? Yes. It runs in your browser; nothing is uploaded.
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Educational tool only. For schoolwork, always check your teacher's required format.