Algebraic expressions

What is an algebraic expression?

An algebraic expression uses numbers, variables and operations to describe a quantity:

• n + 5
• 3x − 2
• 4a² + b
• (y + 1)/2

There’s no equals sign. (With an equals sign, it becomes an equation.)

Terms

Terms are separated by + or − signs.

• 3x − 2y + 7 has three terms: 3x, −2y and 7.

Translating words into expressions

To translate words into algebra, look for operation words.

Careful: "5 less than n" is n − 5, not 5 − n.

Translating expressions into words

• 4x − 1 → "one less than four times a number"
• (x + 3)/2 → "half of the sum of a number and three"

Expressions from situations

Example: Movie tickets cost $12 each, plus a $3 booking fee. Write an expression for the cost of t tickets.

12t + 3

Example: Sara is 4 years older than her brother, who is b years old. Sara’s age: b + 4.

Example: The perimeter of a rectangle with length l and width w: 2l + 2w.

Evaluating

To evaluate, substitute the value and calculate.

3n + 2 when n = 5 → 3 × 5 + 2 = 17.

Patterns lead to expressions

The pattern grows by 3, starting at 5, so the nth figure has 3n + 2 tiles.

Worked examples

Example 1: Write "9 fewer than twice a number".

2n − 9.

Example 2: Write in words: 5(x − 1).

"Five times the difference of a number and one."

Example 3: Pizza costs $15 plus $2 per topping. Expression for t toppings?

15 + 2t.

Common mistakes

• Reversing subtraction for "less than".
• Forgetting brackets for "the sum of … times".
• Writing an equation when only an expression is asked.

Try it yourself

1. A number decreased by 8
2. The product of 6 and a number, plus 1
3. The quotient of a number and 4
4. Write in words: 2x + 10
5. Pens cost $1.50 each. Write the cost of p pens.

Answers: 1) n − 8 2) 6n + 1 3) n/4 4) ten more than twice a number 5) 1.5p

Quick recap

• An algebraic expression combines variables, numbers and operations.
• Translate carefully, especially "less than" and "the sum of".
• Evaluate by substituting values.