Algebra is a way of doing maths with letters that stand for numbers. It lets us write rules that work for any number, solve puzzles where a number is unknown, and describe patterns in science, business and computing. The big idea is simple: a letter such as n is just a number we either do not know yet or that can change. In this lesson you will learn the language of algebra – variables, constants, terms and expressions – how to turn words into algebra, and how to substitute numbers into an expression.

Varying quantities, variables and constants

Many quantities in everyday life vary (change): the temperature during the day, the price of a taxi ride as the distance increases, your height as you grow, the credit left on a phone as you use it. Other quantities stay the same: there are always 7 days in a week and 60 minutes in an hour.

• A variable is a quantity that can change or is unknown. We represent it with a letter: t for temperature, d for distance, n for “a number”.
• A constant is a quantity that does not change. In the expression 5 + 3k, the number 5 is a constant and k is a variable.
• Any letter can be used, but choosing a letter that reminds you of the quantity (h for height, c for cost) makes the algebra easier to read. A letter always stands for a number – a means “the number of apples”, not “apples”.

How algebra is written

In arithmetic language	In algebra	Note
3 × n	3n	Leave out the × sign and write the number first.
a × b	ab	Letters are usually written in alphabetical order.
1 × x	x	We do not write the 1.
y × y	y2	“y squared”.
n ÷ 4	n4 or n/4	Division is usually written as a fraction.

Terms, expressions and equations

• A term is a single number, a single letter, or numbers and letters multiplied (or divided) together: 7, x, 5y, 3ab, p².
• The number in front of a letter is its coefficient: in 5y the coefficient is 5.
• An expression is one or more terms joined by + or − signs: 4a − 2b + 7 is an expression with three terms. The sign in front of a term belongs to that term.
• An equation contains an equals sign: 3x + 5 = 11. An expression has no equals sign. (You will solve equations in Term 3.)

Turning words into expressions

Words	Expression
5 more than n	n + 5
5 less than n	n − 5 (not 5 − n!)
n subtracted from 20	20 − n
twice n / double n	2n
the product of a and b	ab
n shared equally among 4	n4
3 times the sum of x and 2	3(x + 2)
the square of y	y2

Tip: “more than” and “less than” describe what happens to n. “5 less than n” starts with n and takes 5 away. Test it with a number: 5 less than 12 is 7, and 12 − 5 = 7 ✔

Substitution

To substitute means to replace each letter with a given number and then work out the value. Put the number in brackets if it helps, and follow the order of operations: Brackets, Orders (powers), Division and Multiplication, Addition and Subtraction (BODMAS, also called BIDMAS or PEMDAS).

Worked examples

Example 1: Substituting into expressions

Question: If a = 3, b = 5 and c = 2, find the value of
(a) 4a + b
(b) 2ab
(c) 5b − 3c
(d) a(b + c)
(e) a + bc
(f) a² + b

1. (a) 4a + b = 4 × 3 + 5 = 12 + 5 = 17
2. (b) 2ab = 2 × 3 × 5 = 30
3. (c) 5b − 3c = 5 × 5 − 3 × 2 = 25 − 6 = 19
4. (d) a(b + c) = 3 × (5 + 2) = 3 × 7 = 21 (brackets first)
5. (e) (a + b) ÷ c = (3 + 5) ÷ 2 = 8 ÷ 2 = 4 (the fraction line acts like brackets)
6. (f) a² + b = 3 × 3 + 5 = 9 + 5 = 14

Answer: 17, 30, 19, 21, 4, 14.

Example 2: An expression from a real situation

Question: A taxi charges a $5 pick-up fee plus $3 for every kilometre. Write an expression for the fare for k km, and find the fare for a 7 km ride.

1. Cost of the kilometres: 3 × k = 3k dollars. Add the fixed fee: 5 + 3k.
2. Here 5 is a constant and k is the variable.
3. Substitute k = 7: 5 + 3 × 7 = 5 + 21 = 26.

Answer: Fare = $(5 + 3k); a 7 km ride costs $26.

Example 3: Writing an expression

Question: Phone credit starts at $100 and $15 is used each week. Write an expression for the credit left after k weeks. How much is left after 4 weeks?

1. Credit used after k weeks: 15k. Credit left: 100 − 15k.
2. Substitute k = 4: 100 − 15 × 4 = 100 − 60 = 40.

Answer: 100 − 15k dollars; $40 after 4 weeks.

Common mistakes

• Treating 3a as a two-digit number. If a = 4, then 3a = 3 × 4 = 12, not 34.
• Reversing “less than”. “7 less than y” is y − 7, not 7 − y.
• Ignoring the order of operations. With b = 5 and c = 2, 5b − 3c = 25 − 6 = 19. Working left to right without care gives wrong answers.
• Calling an equation an expression. If there is an = sign, it is an equation.
• Thinking a letter is an object. In 3a + 2b, the letters stand for numbers (such as the cost of an apple), not for “apples” and “bananas”.

Practice questions

Try these yourself first, then open each answer to check your working.

Quick check

Next: Simplifying Algebraic Expressions: Like Terms and the Distributive Law

Curriculum link: This post is relevant to the Trinidad and Tobago National Lower Secondary (NCSE) Mathematics Curriculum – Form 1, Term 1, Strand 1.6 Algebra, Topic 1.6.1 Introducing Algebra – Learning Outcomes 1.6.1.1 (investigating varying quantities), 1.6.1.2 (constants and variables), 1.6.1.3 (using symbols for unknown quantities), 1.6.1.4 (translating word statements into expressions), 1.6.1.5 (identifying an expression) and 1.6.1.6 (substituting whole numbers for variables).

Updates

2026/10/25

– Put each lettered part of the questions and answers on its own line.

© 2026 Vedesh Kungebeharry. All rights reserved.