Fraction of a Number

Eighteen problems a sheet, each asking for a fraction of a whole number - three quarters of 20. The number is built from the fraction rather than picked independently: it is always a multiple of the denominator, so every answer comes out whole and no sheet ends in a remainder a student meeting this for the first time has no method for.

The fraction is always given in lowest terms, which keeps the work to one step in each direction - divide by the denominator, multiply by the numerator - rather than asking a student to simplify and find a fraction of a number at the same time. The multiplier stays between 2 and 8, so the numbers stay inside the times tables even when the denominator is large.

Frequently asked questions

How do you find a fraction of a number?

Divide the number by the denominator, then multiply by the numerator. For three quarters of 20: 20 divided by 4 is 5, and 5 times 3 is 15.

Will the answers always be whole numbers?

Yes. The number on each problem is generated as a multiple of the denominator, so the division is exact every time.

Why is the fraction never something like 2/4?

Fractions are drawn already in lowest terms, so simplifying is not folded into a question about something else. The Simplifying Fractions page practises that skill on its own.

Is this the same as multiplying fractions?

It is the same arithmetic - “of” means multiply - written the way it is usually met first, with a whole number rather than a second fraction. Multiplying Fractions has that version.