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Dividing fractions with whole numbers

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Dividing a Fraction by a Whole Number

To divide a fraction by a whole number, rewrite the whole number as a fraction over 1, flip it to find its reciprocal, then multiply. Dividing three-fourths by two becomes three-fourths times one-half, which equals three-eighths. Learn the rule with worked steps.

The rule: multiply by the reciprocal

To divide a fraction by a whole number, rewrite the division as multiplication by the whole number's reciprocal. The reciprocal of a whole number n is 1/n, so dividing by 2 is the same as multiplying by 1/2.

Dividing a fraction by a whole number The worked example three-fourths divided by 2. Rewrite 2 as 2 over 1, flip it to get the reciprocal one-half, then multiply three-fourths by one-half to get three-eighths. 34 ÷ 2 = 34 × 12 = 38 fraction same fraction reciprocal of 2 answer "Divide by a whole number = multiply by its reciprocal"
Dividing 3/4 by 2 becomes multiplying 3/4 by the reciprocal of 2, which is 1/2, giving 3/8.

Step by step

  1. Write the whole number as a fraction over 1 (2 becomes 2/1).
  2. Flip it to find its reciprocal (2/1 becomes 1/2).
  3. Multiply the original fraction by that reciprocal: numerator × numerator, denominator × denominator.
  4. Simplify the result if possible.

Why this works

Dividing by a number and multiplying by its reciprocal always give the same result, because a number times its reciprocal equals 1. Splitting 3/4 into 2 equal parts means each part is half of 3/4, which is exactly 3/4 × 1/2.

Related skills

This is the reverse direction of dividing fractions and mixed numbers, which covers a fraction divided by another fraction. It also uses the same reciprocal idea as multiplying proper fractions, just applied to division instead.

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