Pythagorist
Fractions

Dividing Fractions Calculator

Divide any two fractions using the flip-and-multiply method. Full step-by-step working shows how to find the reciprocal and multiply across.

First fraction
÷Divide
Second fraction
22

= 2

= 2 (decimal)

Step-by-step working

  1. Find the reciprocal of the second fraction

    Reciprocal of 14=4\text{Reciprocal of } \frac{1}{4} = 4

    Flip the second fraction — swap the numerator and denominator.

    Result:4

  2. Change division to multiplication

    12÷14=12×4\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times 4

    Dividing by a fraction is the same as multiplying by its reciprocal.

  3. Multiply across

    42\frac{4}{2}

    1 × 4 = 4 (numerator). 2 × 1 = 2 (denominator).

    Result:\frac{4}{2}

  4. Simplify

    42=2\frac{4}{2} = 2

    GCD(4, 2) = 2. Divide both by 2.

    Result:2

The formula

ab÷cd=ab×dc=adbc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}
a/ba/bFirst fraction
c/dc/dSecond fraction (divisor)
d/cd/cReciprocal of the divisor

Example substitution

34÷12=34×21=64=32\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2}

Flip the second fraction (reciprocal), then multiply across.

Worked examples

1/2 ÷ 1/4

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

2/3 ÷ 4/9

  1. 1
    Reciprocal of 4/9: 9/4
  2. 2
    Multiply: 2/3 × 9/4 = 18/12
  3. 3
    Simplify: 3/2
Answer: 3/2

5/6 ÷ 5/3

  1. 1
    Reciprocal of 5/3: 3/5
  2. 2
    Multiply: 5/6 × 3/5 = 15/30
  3. 3
    Simplify: 1/2
Answer: 1/2

Frequently asked questions

How do you divide fractions?+

Flip the second fraction (find its reciprocal) and change the division to multiplication. For example, ¾ ÷ ½ = ¾ × 2/1 = 6/4 = 3/2.

What is the reciprocal of a fraction?+

The reciprocal of a fraction is obtained by swapping the numerator and denominator. The reciprocal of 3/4 is 4/3. Any number multiplied by its reciprocal equals 1.

How do you divide a whole number by a fraction?+

Write the whole number as a fraction over 1, then flip the second fraction and multiply. For example, 6 ÷ ¾ = 6/1 × 4/3 = 24/3 = 8.

How do you divide mixed numbers?+

Convert both mixed numbers to improper fractions, then flip the second and multiply.

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