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Dividing Fractions Calculator

The dividing fractions calculator flips the second fraction and multiplies: 3/4 divided by 2/5 is 3/4 x 5/2 = 15/8, which is 1 7/8 as a mixed number.

When rewriting over a denominator, the denominator to rewrite the first fraction over.

Answer15/8

As a mixed number
1 7/8
As a decimal Exact.
1.875
The problem
3/4 / 2/5 = 15/8
Multiply by the reciprocal Dividing by a fraction is multiplying by it upside down. This is why dividing by 1/2 makes a number bigger.
3/4 x 5/2 = 15/8
Reduced
already in lowest terms
As a percentage
187.5%
Comparison Compared by cross-multiplying rather than by converting to decimals, so the answer is exact even when the decimals are not.
3/4 is larger than 2/5
  • Every answer is exact and in lowest terms. No step converts to a decimal, which is what lets 1/3 + 1/6 come out as exactly 1/2.
  • A mixed number's sign applies to the whole quantity: -2 1/3 means -(2 + 1/3), which is -7/3.

How the Fraction Calculator works

To divide by a fraction, multiply by its reciprocal: the same fraction turned upside down. Teachers often call it keep, change, flip. Keep the first fraction, change division to multiplication, flip the second fraction.

The example, 3/4 / 2/5. Keep 3/4, change to multiply, flip 2/5 to 5/2: 3/4 x 5/2 = 15/8. 15 and 8 share no factor, so 15/8 is in lowest terms, and as a mixed number it is 1 7/8.

Why flipping works. Dividing by a number undoes multiplying by it. Multiplying by 2/5 and then by 5/2 gets you back where you started, because 2/5 x 5/2 = 1. So dividing by 2/5 is the same as multiplying by 5/2. The same reasoning is behind dividing by 2 being the same as multiplying by 1/2.

Why the answer can be bigger. Division asks how many of the second number fit into the first. How many halves fit into 3? Six, so 3 / 1/2 = 6. Dividing by a fraction less than 1 always gives a larger result, which looks wrong until you read it as "how many fit".

Whole and mixed numbers. Write whole numbers over 1 and convert mixed numbers to improper fractions before flipping. 2 1/2 / 1 1/4 = 5/2 / 5/4 = 5/2 x 4/5 = 20/10 = 2.

Dividing by zero. 0 has no reciprocal, because nothing times 0 is 1, so dividing by a fraction equal to 0 is undefined and the calculator says so.

Fraction Calculator FAQ

How do you divide fractions?

Multiply the first fraction by the reciprocal of the second. 3/4 / 2/5 = 3/4 x 5/2 = 15/8 = 1 7/8.

What does keep, change, flip mean?

Keep the first fraction, change the division sign to multiplication, and flip the second fraction upside down. Then multiply across.

Why does dividing by a fraction give a bigger number?

Because it counts how many of the fraction fit into the number. Six halves fit into 3, so 3 divided by 1/2 is 6.

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