---
title: "Equivalent fractions on a number line"
description: "Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams"
canonical: https://lightmysky.com/learn/mathematics/equivalent-fractions-on-a-number-line-mt_Ep7TDFuYUa
source: https://lightmysky.com/learn/mathematics/equivalent-fractions-on-a-number-line-mt_Ep7TDFuYUa.md
retrieved: 2026-10-19
---

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# Equivalent fractions on a number line

Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams

Subject: Mathematics · Area: Fractions · Ages 8 to 9
Page: https://lightmysky.com/learn/mathematics/equivalent-fractions-on-a-number-line-mt_Ep7TDFuYUa

## Ready when they can

- Use fraction strips to show 1/2 = 2/4 = 3/6
- Verify on a number line that 2/3 and 4/6 land on the same point
- Identify at least three fractions equivalent to 1/2 using diagrams

## Lesson: Equivalent fractions on a number line

You already know what equivalent fractions are, and you know how to place fractions on a number line. Now put those two ideas together. If two fractions land on the exact same point on a number line, they are equivalent, even though they look different.

*(drawing: This number line runs from 0 to 1 in 6 equal steps. Both 2/3 and 4/6 point to step 4, the exact same spot.)*

**Example.** Maya cuts a paper strip into 6 equal parts and shades 3 of them. She cuts a same-size strip into 2 equal parts and shades 1. Both shaded parts cover the exact same length of the strip, so 3/6 and 1/2 are equivalent.

Cutting every step into smaller steps never moves the point. Halfway along 4 steps is step 2. Halfway along 6 steps is step 3. Halfway along 8 steps is step 4. The point stayed where it was, so 2/4, 3/6 and 4/8 are all names for 1/2.

**Tip.** There is a short way to write another name for the same point: multiply the top number and the bottom number by the same number. Starting from 1/2, times 3 gives 3/6. Then check it on the line, where 3/6 sits on the same point as 1/2.

**Recap.** Equivalent fractions are just different names for the same point on a number line.

## Practice

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

## Needs first

- [Equivalent fractions](https://lightmysky.com/learn/mathematics/equivalent-fractions-mt_FbDKeLfBCo)
- [Fractions on a number line (age 8+)](https://lightmysky.com/learn/mathematics/fractions-on-a-number-line-age-8-mt_NoB20kVa4w)

## Opens up

- [Generalising from repeated reasoning](https://lightmysky.com/learn/mathematics/generalising-from-repeated-reasoning-mt_aivrWs6jrS)
- [Choosing mathematical tools](https://lightmysky.com/learn/mathematics/choosing-mathematical-tools-mt_d-WZC2OyMB)
- [Fraction-Decimal Equivalents](https://lightmysky.com/learn/mathematics/fraction-decimal-equivalents-mt_DRlbMok2lT)
- [Equivalent fractions (age 9+)](https://lightmysky.com/learn/mathematics/equivalent-fractions-age-9-mt_ebPelt-qAl)
- [Equivalent fractions (age 8+)](https://lightmysky.com/learn/mathematics/equivalent-fractions-age-8-mt_FP-mjXaq3B)