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Subtracting Fractions Calculator

The subtracting fractions calculator puts 5/6 and 1/4 over their least common denominator, 12, and subtracts the numerators: 10/12 - 3/12 = 7/12.

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

Answer7/12

As a mixed number Already a proper fraction: smaller than one, so there is no whole part.
7/12
As a decimal The digits in brackets repeat forever. A decimal cannot write this fraction exactly, which is why the fraction is the better answer.
0.58(3)
The problem
5/6 - 1/4 = 7/12
Common denominator The least common multiple of 6 and 4. Multiplying the denominators together would give 24, which also works but needs reducing afterward.
12
Rewritten over it
10/12 - 3/12 = 7/12
Reduced
already in lowest terms
As a percentage
58.3333%
Comparison Compared by cross-multiplying rather than by converting to decimals, so the answer is exact even when the decimals are not.
5/6 is larger than 1/4
  • 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

Subtracting fractions works exactly like adding them: the fractions need a common denominator, and then only the numerators are subtracted.

The steps, for 5/6 - 1/4.

1. Find the least common denominator of 6 and 4. It is 12.

2. Rewrite each fraction: 5/6 = 10/12 and 1/4 = 3/12.

3. Subtract the numerators and keep the denominator: 10/12 - 3/12 = 7/12.

4. Simplify. 7 and 12 share no factor, so 7/12 is the answer.

Order matters. Unlike addition, subtraction is not commutative: 1/4 - 5/6 is -7/12, the same size with the opposite sign. If the second fraction is larger, the answer is negative.

Subtracting mixed numbers. Converting to improper fractions first avoids borrowing. For 3 1/4 - 1 2/3: 13/4 - 5/3 = 39/12 - 20/12 = 19/12 = 1 7/12. Working with the parts separately would need 1/4 - 2/3, which is negative, so you would have to borrow 1 from the 3 and rewrite 3 1/4 as 2 5/4 first. Both methods agree; the improper-fraction route has fewer places to slip.

Subtracting from a whole number. Write the whole number as a fraction over the same denominator. 2 - 3/8 = 16/8 - 3/8 = 13/8, or 1 5/8.

Checking the answer. Add it back: 7/12 + 1/4 = 7/12 + 3/12 = 10/12 = 5/6, the number you started from. The calculator works in exact whole-number arithmetic, so its answers check out exactly rather than to within a rounding error.

Fraction Calculator FAQ

How do you subtract fractions with unlike denominators?

Rewrite both over the least common denominator, then subtract the numerators. 5/6 - 1/4 = 10/12 - 3/12 = 7/12.

How do you subtract mixed numbers?

Convert both to improper fractions, subtract over a common denominator, and convert back. 3 1/4 - 1 2/3 = 13/4 - 5/3 = 39/12 - 20/12 = 19/12 = 1 7/12.

What if the answer is negative?

That means the second fraction was larger. 1/4 - 5/6 = 3/12 - 10/12 = -7/12. The calculator keeps the sign on the numerator.

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