---
title: "Fractions of amounts (harder)"
description: "Solve problems involving increasingly harder fractions to calculate quantities, including non-unit fractions where the answer is a whole number"
canonical: https://lightmysky.com/learn/mathematics/fractions-of-amounts-harder-mt_3y7xKP9MjU
source: https://lightmysky.com/learn/mathematics/fractions-of-amounts-harder-mt_3y7xKP9MjU.md
retrieved: 2026-10-19
---

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# Fractions of amounts (harder)

Solve problems involving increasingly harder fractions to calculate quantities, including non-unit fractions where the answer is a whole number

Subject: Mathematics · Area: Fractions · Ages 8 to 9
Page: https://lightmysky.com/learn/mathematics/fractions-of-amounts-harder-mt_3y7xKP9MjU

## Ready when they can

- Find 3/5 of 20
- Calculate 2/3 of 18 and explain the two-step process (divide then multiply)
- Solve: A bag has 24 sweets, 3/8 are red — how many red sweets?

## Lesson: Fractions of amounts: the two-step trick

You already know how to find a unit fraction of a number, like 1/4 of something: you just divide. Now you are ready for fractions like 2/3 or 3/5, where the top number is more than 1. There is a simple two-step trick: first divide by the bottom number, then multiply by the top number.

*(drawing: Split 20 into 5 equal groups. Each group has 4. Take 3 of those groups: 4 x 3 = 12. So 3/5 of 20 is 12.)*

**Example.** Let's calculate 2/3 of 18. Step 1: divide 18 by 3, the bottom number. 18 divided by 3 is 6. Step 2: multiply that answer by 2, the top number. 6 times 2 is 12. So 2/3 of 18 is 12.

**Tip.** Always divide first, then multiply. If you multiply by the top number first, the numbers get big and harder to work with. Dividing first keeps things small and friendly.

**Recap.** To find a fraction of an amount, divide by the bottom number, then multiply by the top number.

## Practice

15 questions on this page, each with its working shown.

## Needs first

- [Adding fractions (same denominator)](https://lightmysky.com/learn/mathematics/adding-fractions-same-denominator-mt_CBHwluE6Lp)
- [Fractions of a group of objects](https://lightmysky.com/learn/mathematics/fractions-of-a-group-of-objects-mt_k2WE0-22-4)

## Opens up

- [Modelling with multiplication and fractions](https://lightmysky.com/learn/mathematics/modelling-with-multiplication-and-fractions-mt_K3R0yaHVcx)
- [Multi-Step Problem Solving (age 8+)](https://lightmysky.com/learn/mathematics/multi-step-problem-solving-age-8-mt_SmghasIvbT)
- [Decimals and fractions](https://lightmysky.com/learn/mathematics/decimals-and-fractions-mt_wB-GBDkoNr)
- [Scaling by fractions and simple rates](https://lightmysky.com/learn/mathematics/scaling-by-fractions-and-simple-rates-mt_ZOJ6EbdPOb)