Divide a Whole Number by a Fraction

Dividing a Whole Number by a Fraction

When you divide a whole number by a fraction, you are asking how many parts of that fraction fit into the whole number. A useful idea is that division by a fraction is related to multiplication by its reciprocal.

Method

1. Keep the whole number as it is.
2. Flip the fraction to get its reciprocal. For example, ( \frac{2}{3} ) becomes ( \frac{3}{2} ).
3. Multiply the whole number by the reciprocal.
4. Simplify the result if needed.

Example pattern

If you see ( 6 \div \frac{2}{3} ), rewrite it as: [ 6 \times \frac{3}{2} ] Then multiply and simplify.

Why this works

Dividing by a fraction asks how many fraction-sized groups are in the number. Multiplying by the reciprocal gives the same answer in a faster form.

Check your answer

You can check by multiplying your answer by the fraction you divided by. If the product gives the original whole number, your answer is correct.

Tip

If the fraction is greater than 1, the result may be smaller than the whole number. If the fraction is less than 1, the result may be larger.