Find the Whole From a Fraction

Find the whole from a fraction

When you know a fraction of a number and need to find the whole, think in reverse. If a fraction like (\frac{a}{b}) of a number is given, the whole number is the amount that would be split into b equal parts, with a parts matching the known value.

Method

1. Identify the fraction and the known part. For example, if (\frac{3}{4}) of a number is 18, then 18 is the known part.
2. Find one part by dividing the known value by the numerator: (18 \div 3 = 6).
3. Find the whole by multiplying one part by the denominator: (6 \times 4 = 24).

Shortcut

You can also use one equation: [ \text{whole} = \text{known part} \times \frac{\text{denominator}}{\text{numerator}} ] So in the example, (18 \times \frac{4}{3} = 24).

Check your answer

Substitute your result back into the original fraction. If (\frac{3}{4}) of 24 is 18, your answer is correct.

Tip

If the division does not come out evenly, keep the answer exact and simplify it when needed.