---
title: "Ratio Problems"
description: "Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts"
canonical: https://lightmysky.com/learn/mathematics/ratio-problems-mt_h0gJcSuwdL
source: https://lightmysky.com/learn/mathematics/ratio-problems-mt_h0gJcSuwdL.md
retrieved: 2026-10-19
---

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# Ratio Problems

Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

Subject: Mathematics · Area: Ratio & Proportion · Ages 10 to 11
Page: https://lightmysky.com/learn/mathematics/ratio-problems-mt_h0gJcSuwdL

## Ready when they can

- If the ratio of red to blue beads is 3:5 and there are 15 blue beads, find the number of red beads
- Use multiplication facts to find the missing value: 'For every 2 apples there are 5 oranges; if there are 20 oranges, how many apples?'
- Explain the multiplicative relationship between two quantities in a ratio context

## Lesson: Solving Ratio Problems

You already know how to compare two amounts with a ratio, like 3:5. In a ratio problem, you are told one amount and asked to find the matching amount for the other side. The two amounts always scale up or down by the same multiplying number.

*(drawing: For every 3 red beads, there are 5 blue beads. This ratio stays the same even when the numbers get bigger.)*

**Example.** The ratio of red to blue beads is 3:5, and there are 15 blue beads. Blue went from 5 to 15, so it was multiplied by 3 (5 x 3 = 15). Red and blue always scale together, so multiply red by 3 too: 3 x 3 = 9. There are 9 red beads.

**Tip.** Find the multiplying number first. Divide the new amount by its matching ratio number, then multiply the other ratio number by that same amount.

**Recap.** To solve a ratio problem, work out how much one side was scaled, then scale the other side by the same amount.

## Practice

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

## Needs first

- [Multiplying fractions (age 10+)](https://lightmysky.com/learn/mathematics/multiplying-fractions-age-10-mt_AabJisinfi)
- [Bar Models for Ratios](https://lightmysky.com/learn/mathematics/bar-models-for-ratios-mt_ePXg_XyCKU)
- [Ratio and proportion vocabulary](https://lightmysky.com/learn/mathematics/ratio-and-proportion-vocabulary-mt_ESgc4YBw-a)
- [Multiplicative Comparison as an Equation](https://lightmysky.com/learn/mathematics/multiplicative-comparison-as-an-equation-mt_U4cIBXVug4)

## Opens up

- [Scale and similar shapes](https://lightmysky.com/learn/mathematics/scale-and-similar-shapes-mt_2OtRUM_0zW)
- [Unequal sharing and grouping](https://lightmysky.com/learn/mathematics/unequal-sharing-and-grouping-mt_FnUJMXPUZX)
- [Number Pattern Relationships](https://lightmysky.com/learn/mathematics/number-pattern-relationships-mt_fxPtngwUfz)
- [Comparing Prices Properly](https://lightmysky.com/learn/life-skills/comparing-prices-properly-mt_v3i0WMP-Sl)