Fractions

Fraction Calculator

Add, subtract, multiply or divide any two fractions instantly — with full step-by-step working shown. Supports mixed numbers and negative fractions. Used by millions of students worldwide.

First fraction
+
Second fraction
34\frac{3}{4}

= 0.75 (decimal)

Step-by-step working

  1. Find the lowest common denominator (LCD)

    LCD(2,4)=4\text{LCD}(2,\, 4) = 4

    The lowest common denominator of 2 and 4 is 4. Both fractions will be converted to this denominator.

  2. Convert the first fraction

    12=24\frac{1}{2} = \frac{2}{4}

    Multiply numerator and denominator of the first fraction by 2.

    Result:\frac{2}{4}
  3. Convert the second fraction

    14=14\frac{1}{4} = \frac{1}{4}

    Multiply numerator and denominator of the second fraction by 1.

    Result:\frac{1}{4}
  4. Add the numerators

    24+14=34\frac{2}{4} + \frac{1}{4} = \frac{3}{4}

    Add the numerators together. The denominator stays the same: 2 + 1 = 3.

    Result:\frac{3}{4}

Fraction operation formulas

ab+cd=ad+bcbdab×cd=acbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \qquad \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}
a,ca, cNumerators of the fractions
b,db, dDenominators of the fractions

Worked examples

1/2 + 1/3

  1. 1
    LCD(2,3): = 6
  2. 2
    Convert: 3/6 + 2/6
  3. 3
    Add: 5/6
Answer: 5/6

2/3 × 3/4

  1. 1
    Numerators: 2 × 3 = 6
  2. 2
    Denominators: 3 × 4 = 12
  3. 3
    Simplify: 6/12 = 1/2
Answer: 1/2

3/4 ÷ 1/2

  1. 1
    Reciprocal: 2/1
  2. 2
    Multiply: 3/4 × 2/1 = 6/4
  3. 3
    Simplify: 6/4 = 3/2
Answer: 3/2 = 1.5

Frequently asked questions

How do you add fractions with different denominators?+

To add fractions with different denominators, first find the lowest common denominator (LCD). Convert both fractions to equivalent fractions with the LCD, then add the numerators and simplify the result.

How do you multiply fractions?+

To multiply fractions, multiply the numerators together and multiply the denominators together. Then simplify the resulting fraction by dividing by the greatest common divisor (GCD).

How do you divide fractions?+

To divide fractions, flip the second fraction (find its reciprocal) and then multiply. For example, ½ ÷ ¼ becomes ½ × 4/1 = 4/2 = 2.

What is a mixed number?+

A mixed number combines a whole number and a proper fraction, such as 2¾. To calculate with mixed numbers, first convert them to improper fractions, perform the operation, then convert back.

How do you simplify a fraction?+

To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, 6/8 simplifies to 3/4 because GCD(6,8) = 2.

Can fractions be negative?+

Yes. A negative fraction can have the negative sign on the numerator, denominator, or in front of the fraction. For example, −¾, (−3)/4, and 3/(−4) are all equivalent.

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