Fraction Calculator with Steps

Two Fractions

Leave the whole-number boxes at 0 for plain fractions.

First — whole number

First — numerator

First — denominator

Operation

Second — whole number

Second — numerator

Second — denominator

ANSWER

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Mixed number—

Decimal—

Percentage—

Common denominator used—

Before simplifying—

Divided by (GCD)—

Dividing by a fraction is the same as multiplying by its reciprocal — flip the second fraction and multiply.

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Why adding fractions needs a common denominator

A denominator names the size of the pieces. Two halves and three quarters cannot be added directly because the pieces are different sizes — you first have to cut both into pieces of the same size. That is all a common denominator is. The least common denominator is simply the smallest size that both fractions divide into evenly, which keeps the numbers manageable.

Multiplication needs none of this. Multiplying fractions multiplies the tops and the bottoms directly, which is why students often find multiplication easier than addition — the opposite of what happens with whole numbers.

Simplifying with the greatest common divisor

A fraction is in lowest terms when the numerator and denominator share no factor other than 1. Dividing both by their greatest common divisor gets there in a single step rather than by repeated halving. This calculator shows the GCD it used, so the simplification is something you can verify rather than something that just happens.

Mixed numbers and improper fractions

7/4 and 1¾ are the same quantity written two ways. Improper fractions are easier to compute with, which is why every operation here converts to improper form first and only converts back at the end. Cooking, carpentry and imperial measurement prefer mixed numbers; algebra almost always prefers improper ones.

Negative fractions

A minus sign can sit in front of the fraction, on the numerator, or on the denominator, and all three mean the same value. The convention used here keeps the sign on the numerator and keeps the denominator positive, which avoids the confusing double negatives that appear when a negative denominator is carried through a subtraction.

Frequently Asked Questions

Why do fractions need a common denominator to be added?

The denominator says how big each piece is. You cannot add halves to quarters until both are cut into pieces of the same size. Multiplication needs no common denominator, which is why it is actually the easier operation.

How do I divide one fraction by another?

Multiply by the reciprocal — flip the second fraction upside down and multiply. Dividing by 2/3 is the same as multiplying by 3/2.

What does simplifying a fraction mean?

Dividing the numerator and denominator by their greatest common divisor so they share no remaining factor. This calculator shows the GCD it used so you can check the step.

What is the difference between a mixed number and an improper fraction?

They are the same value written differently. 7/4 is improper, 1¾ is mixed. Calculations are done in improper form because it is simpler, then converted back at the end.