--- 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: 2026-11-12 --- > **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 Substitution replaces letters with given numbers. Use the same value every time a letter occurs. In 3x, the 3 multiplies x; it does not join its digits. Put brackets around a substituted negative value. For sums, add the substituted numbers. To add two negatives, add their sizes and keep the minus sign. Adding a positive number moves right on a number line. *(drawing: A = l × w. With l = 5 and w = 3, A = 5 × 3 = 15. Three rows of five dots show this multiplication.)* **Example.** A square's area is A = s². With s = 4, A = 4 × 4 = 16. In 4t², only t is squared. With t = 5, calculate 4 × 5² = 4 × 25 = 100. Brackets change this: (4t)² squares the whole product, giving (4 × 5)² = 400. In 4t² + 6, add 6 after calculating the square and product. After substitution, work inside brackets first, starting with the innermost pair. Within each group, calculate powers, then multiplication and division from left to right, then addition and subtraction from left to right. Multiplication and division have equal priority. Addition and subtraction also have equal priority. The notation x^2 means x², and x^3 means x³. **Example.** For 3x + 7 with x = -4, write 3 × (-4) + 7. A positive number times a negative number gives a negative answer: 3 × (-4) = -12. Then -12 + 7 = -5. Subtracting a positive number from a negative number moves farther below zero. **Example.** A square uses two copies of its base: with t = -5, t² = (-5) × (-5) = 25. A cube uses three copies: t³ = 25 × (-5) = -125. Two negative factors give a positive product. A positive times a negative gives a negative product. Subtracting a negative adds its opposite: 8 - (-5) = 8 + 5 = 13. The value of -b is the opposite of b. If b = 5, then -b = -5. Brackets show what a power covers. In (ab)², multiply a and b, then square their product. In ab², square b, then multiply by a. For (a² - b²) ÷ (c + d), calculate each bracket separately before dividing. The divisor must not be zero. *(drawing: Finish the inner sum, then the multiplication and subtraction inside the outer brackets. Multiply by 3 last.)* **Example.** For a triangle, A = b × h ÷ 2, where b is the base and h is the perpendicular height. With b = 8 cm and h = 3 cm, A = 8 × 3 ÷ 2 = 12 cm². Replace both letters, multiply, then divide by 2. **Recap.** Swap each letter for its number, then follow the order of operations to find the answer. *The lesson, questions and flashcards were written for this dataset.* ## 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)