---
title: "Fractions, Decimals & Percentages"
description: "Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use pro"
canonical: https://lightmysky.com/learn/mathematics/fractions-decimals-and-percentages-mt_hlGKg5M7qJ
source: https://lightmysky.com/learn/mathematics/fractions-decimals-and-percentages-mt_hlGKg5M7qJ.md
retrieved: 2026-10-19
---

> **Agent view.** This is the Markdown twin of the page, for tools and assistants.
> When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md
> API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md
> Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt
> Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json
> Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`.

# Fractions, Decimals & Percentages

Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use properties of regular polygons systematically

Subject: Mathematics · Area: Mathematical Thinking · Ages 9 to 10
Page: https://lightmysky.com/learn/mathematics/fractions-decimals-and-percentages-mt_hlGKg5M7qJ

## Ready when they can

- Use the structure 25 × 16 = 25 × 4 × 4 = 100 × 4 = 400 by exploiting factor pairs
- Recognise that 0.75 = 3/4 = 75% and use whichever form is most efficient for the problem
- Use the fact that angles on a straight line sum to 180° as a structural tool to find missing angles

## Lesson: Three ways to write the same amount

A fraction, a decimal, and a percentage can all show the exact same amount. 3/4 of a pizza, 0.75 of a pizza, and 75% of a pizza are the same slice, just written in different clothes. Once you can switch between the three, you pick whichever one makes a problem easiest.

*(drawing: Same amount, three names: 3/4, 0.75, and 75%.)*

**Example.** A jacket costs 40 pounds and is 25% off. Instead of working with the percentage, Zara thinks: 25% is the same as 1/4. So the discount is 40 divided by 4, which is 10 pounds.

**Tip.** Multiplying gets easier if you break a number into a factor pair first. 16 is the same as 4 times 4, so 25 times 16 becomes 25 times 4 times 4, which is 100 times 4, which is 400. Look for friendly pairs before you multiply.

**Tip.** Angles on a straight line always add up to 180 degrees. If you know one angle, subtract it from 180 to find the missing one straight away.

**Recap.** Fractions, decimals, and percentages are the same amount in different forms, and factor pairs and angle facts are shortcuts hiding in plain sight.

## Practice

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

## Needs first

- [Using Mathematical Structure](https://lightmysky.com/learn/mathematics/using-mathematical-structure-mt__Itf4aQZUj)
- [Factors, multiples, and primes](https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-mt_FHIAv6dfhU)
- [Angle Sum Rules](https://lightmysky.com/learn/mathematics/angle-sum-rules-mt_oqziWKry-L)
- [Spotting Patterns](https://lightmysky.com/learn/learning-to-learn/spotting-patterns-mt_wvcFlwOrDl)

## Opens up

- [Using structure in shapes and expressions](https://lightmysky.com/learn/mathematics/using-structure-in-shapes-and-expressions-mt_hImiKNiaNh)
- [Two-Way Tables](https://lightmysky.com/learn/mathematics/two-way-tables-mt_oD1Rgg52n3)