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Simplify Fractions Calculator

With numerator 20, denominator 32, simplify fractions comes to 5/8 — in lowest terms. It is reached in 6 steps, the last of which is 20 / (32 + (0)), and each one is printed on the page with its numbers filled in. The formula is the one published by Euclid, Elements VII.2, not an approximation fitted to it.

Reduce a fraction to lowest terms, showing the greatest common divisor it was divided by.

Formula and sources checked · How we check

Numerator 20, Denominator 32

5/8

In lowest terms for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.

It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.

In lowest terms
5/8
Greatest common divisor
max(1, gcd(abs(20), abs(32)))4
Numerator in lowest terms
1 * abs(20) / 45
Denominator in lowest terms
abs(32) / 48
Whole part, if it is top-heavy
1 * floor(abs(5) / 8)0
As a decimal
20 / (32 + (0))0.625
As a percentage
0.625 * 10062.5 %

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Worked example

Twenty thirty-seconds reduces to five eighths. Both numbers share a greatest common divisor of 4, so one division finishes the job: dividing by 2 twice gets to the same place with an extra step.

How to work it out yourself

  1. 1.A fraction simplifier and a reduce-to-lowest-terms calculator are the same tool under two names: both divide the top and the bottom by the largest number that goes into each, and the simplified fraction that comes out is the one in lowest terms.
  2. 2.Type the numerator and the denominator. Put a minus sign on the numerator if the fraction is negative.
  3. 3.Find the greatest common divisor of the two numbers, then divide both by it. That single division reaches lowest terms; dividing by any smaller common factor leaves more to do.
  4. 4.Check the divisor line. If it is 1, the fraction was already in lowest terms and nothing changed.

The formula

  1. Greatest common divisormax(1, gcd(abs(20), abs(32)))
  2. Numerator in lowest terms1 * abs(20) / 4
  3. Denominator in lowest termsabs(32) / 4
  4. Whole part, if it is top-heavy1 * floor(abs(5) / 8)
  5. As a decimal20 / (32 + (0))
  6. As a percentage0.625 * 100

Source: Euclid, Elements VII.2 — the algorithm for the greatest common divisor

Questions people actually ask

What is 20/32 in simplest form?
Five eighths. The greatest common divisor of 20 and 32 is 4, and dividing both by it gives 5/8. You can get there by halving twice — 20/32, 10/16, 5/8 — but the greatest common divisor does it in one step, which is why it is the number worth showing.
How do I know a fraction is already in lowest terms?
When the greatest common divisor of the numerator and denominator is 1, which means they share no factor above one. This calculator prints that divisor, so a result of 1 tells you the fraction was already reduced rather than leaving you to guess whether anything happened.
Where does the minus sign go?
On the numerator, or in front of the whole fraction. Writing it on the denominator is not wrong arithmetically but nobody does it: 3/−4 means −3/4, and −3/−4 is positive 3/4. This calculator moves the sign to the front so the answer reads the way it would be written by hand.
Can the denominator be zero?
No. A denominator of zero is division by zero, which has no value, so it is not a fraction at all — not "infinity" and not "undefined but close to something". The field refuses it rather than printing a number.

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