> ## Content Index
> Fetch the complete content index at: https://www.esheets.io/llms.txt
> Use this file to discover other available public pages before exploring further.

# Forming Algebraic Expressions and Equations
- URL: https://www.esheets.io/forming-algebraic-expressions-and-equations/
- Published: 2026-10-06T18:58:49.000Z
- Updated: 2026-10-06T18:58:49.000Z
- Author: Richard Linnington
- Tags: Maths, Algebra

Practise translating words and everyday contexts into algebra before any solving happens. This GCSE Foundation worksheet builds from simple phrases to costs, ages and perimeter, then finishes with forming equations from known totals.

Write expressions for the first six questions and equations for the final two. Stop once each equation is formed. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Eight questions, worth one mark each, practise forming algebraic expressions and equations at GCSE Foundation level (Grades 2–4).

Start with subtraction wording and equal sharing, then use brackets, combine costs and follow an age chain. Form a rectangle’s perimeter expression before writing two equations from totals: one about packs and loose items, and one about ages. You do not solve the equations.

#### What you’ll practise

- Translating words, division and fraction ideas into expressions.
- Keeping subtraction in order and using brackets for a whole sum.
- Combining costs, linked ages and rectangle side lengths.
- Distinguishing expressions from equations and using a known total.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked examples.

# Forming algebraic expressions and equations

Write an algebraic expression for Questions 1–6\. Form an equation for Questions 7–8\. Do not solve the equations.

## Topic guide

### Expressions and equations

An expression describes a quantity, such as 3x + 2\. An equation states that two expressions are equal, such as 3x + 2 = 23\. For this worksheet, translate the information into algebra and stop. You do not need to find the value of the letter.

### From words to operations

- “7 more than n” means n + 7.
- “7 less than n” means n − 7: start with n, then subtract 7.
- “5 times x” means 5x, which is the same as 5 × x.
- “x shared equally between 4 people” gives x/4 for each person. “x divided by 4” means the same thing.
- “Half of x” means x/2 or 0.5x.

Writing symbols next to each other can mean multiplication: 5x means 5 × x and ab means a × b. Put a numerical coefficient before its letter. In the answer boxes you can type 5\*x, a\*b or x/2 as well as implicit multiplication such as 5x and ab.

### Brackets hold a whole expression together

If a whole sum or difference is multiplied, put it in brackets. For example, four times the sum of z and 7 is 4(z + 7). Without brackets, 4z + 7 multiplies only z by 4.

### Combining quantities and using totals

Form each part separately, then add the parts to find a total cost or quantity. For a rectangle, perimeter = 2(length) + 2(width). If the length is n + 5 and the width is n + 2, its perimeter is 2(n + 5) + 2(n + 2), equivalently 4n + 14.

When a total is given and an equation is requested, put your expression on one side of an equals sign and the known total on the other. Stop once the equation is formed.

### Worked examples

1. **A simple expression:** A ribbon is r centimetres long. Cut off 6 centimetres. The remaining length is r − 6 centimetres: subtract 6 from the original length.
2. **Brackets:** Increase a number h by 5, then triple the result. The increased number is h + 5, so the expression is 3(h + 5). The equivalent form 3h + 15 is also correct.
3. **Combined costs:** A roll costs r pence and a bun costs b pence. Six rolls and two buns cost 6r + 2b pence. Each number multiplies its own item’s cost.
4. **Forming an equation:** Three bags each contain n counters. With 8 extra counters, there are 41 counters altogether. The bags contribute 3n, so the equation is 3n + 8 = 41\. Do not solve it.

### Common mistakes

- Reversing “less than”: 6 less than x is x − 6, not 6 − x.
- Writing x5 instead of the standard notation 5x for five times x.
- Dropping a variable from a product: a times b is ab or a\*b, not just a, and not a + b.
- Forgetting brackets: 3(x + 5) is different from 3x + 5.
- Adding an equals sign to an expression when no equation is requested.
- Omitting the equals sign and total when an equation is requested.
- Solving Questions 7–8 instead of giving the formed equation. Keep the quantity expression and stated total on separate sides; either side may come first.
- Assuming only one appearance is correct: 2(y + 4), 2y + 8 and 8 + 2y are equivalent expressions. You may simplify within a side of an equation, but do not move terms across the equals sign for this worksheet.