Expressions using Letter-Numbers

Overview

Here we use letters (variables) to stand for numbers. These letter-numbers help us write general rules and expressions, forming the basis of algebra.

Key concepts

• A variable is a letter that can take different number values.
• An algebraic expression mixes variables, numbers and operations, e.g. 2x + 5.
• Coefficient: the number multiplied with a variable.
• Like terms have the same variable part and can be added.
• Substituting a value for the variable gives a number.

Important formulae

• Perimeter of square = 4 × s
• nth even number = 2n; nth odd number = 2n − 1
• Like terms: ax + bx = (a + b)x

Solved example

1. Find the value of 3x + 4 when x = 5.
2. Substitute x = 5: 3 × 5 + 4.
3. = 15 + 4 = 19.

Important questions

1. Write an expression for a number increased by 7.
2. Simplify 5a + 3a − 2a.
3. Find 2y − 1 when y = 6.
4. Write a rule for the perimeter of an equilateral triangle of side s.

Quick revision

Letters represent unknown numbers. Combine only like terms, and substitute values to evaluate. Algebra lets us write patterns and rules briefly.