---
title: "Substituting into Formulae"
description: "Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of o"
canonical: https://lightmysky.com/learn/mathematics/substituting-into-formulae-mt_vHzVa3SURC
source: https://lightmysky.com/learn/mathematics/substituting-into-formulae-mt_vHzVa3SURC.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`.

# Substituting into Formulae

Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations

Subject: Mathematics · Area: Algebra · Ages 11 to 12
Page: https://lightmysky.com/learn/mathematics/substituting-into-formulae-mt_vHzVa3SURC

## Ready when they can

- Substitute positive and negative values into algebraic expressions and evaluate
- Substitute values into formulae involving multiple operations and powers
- Use correct order of operations when evaluating expressions after substitution

## Lesson: Substituting into Formulae

Substituting means replacing each letter in a formula with the number you are given. Write the number in place of the letter, then work out the answer.

*(drawing: The formula is A = l x w. Substitute l = 5 and w = 3: A = 5 x 3 = 15.)*

**Example.** The formula for the area of a square is A = s². To find the area when s = 4, substitute: A = 4² = 4 x 4 = 16.

**Tip.** When a formula has more than one operation, work out powers first, then multiplication and division, then addition and subtraction. Handle one operation at a time, in order.

**Example.** The expression 3x + 7 works for any value of x. Substitute x = -4: 3 x (-4) + 7 = -12 + 7 = -5. Take care with the negative sign.

**Recap.** Swap each letter for its number, then follow the order of operations to find the answer.

## Practice

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

## Needs first

- [Algebraic Notation](https://lightmysky.com/learn/mathematics/algebraic-notation-mt_KwdjWEmMNo)

## Opens up

- [Simple formulae](https://lightmysky.com/learn/mathematics/simple-formulae-mt_3qrCtdoVAU)
- [Spreadsheets: Rows, Columns and a Formula That Updates Itself](https://lightmysky.com/learn/computing/spreadsheets-rows-columns-and-a-formula-that-updates-itself-mt_iWyPF0-Abz)
- [Solving linear equations](https://lightmysky.com/learn/mathematics/solving-linear-equations-mt_QhFEDyIwSO)
- [Linear Function Graphs](https://lightmysky.com/learn/mathematics/linear-function-graphs-mt_WBdHkc2HTf)
- [Generating Sequences](https://lightmysky.com/learn/mathematics/generating-sequences-mt_yXO7lQ9Yn7)