Expressions

In algebra, letters are used to stand for values that can change (variables) or for values that are not known (unknowns).

A term is a number or letter on its own, or numbers and letters multiplied together, such as - 2, 3x or 5a^2.

An expression is a set of terms combined using the operations +, – , x or  \div, for example 4x − 3 or x^2 – xy + 17.

An equation states that two expressions are equal in value, for example 4b − 2 = 6.

An identity is a statement that is true no matter what values are chosen, for example 4a \times a^2 = 4a^3.

Writing expressions

Example 1

Pens are sold in packs of 6 and rulers are sold in boxes of 10.

A teacher buys p packs of pens and r boxes of rulers. Write an expression for the total number of pens and rulers bought.

There are 6 pens in each pack, so the number of pens bought is 6 \times p which is 6p.

There are 10 rulers in each box, so the number of rulers bought is 10 \times r which is 10r.

The number of pens and rulers bought is 6p + 10r

Example 2

A rectangle has a width of x cm. The height is 3 cm less than the width. Write an expression for the perimeter of the rectangle.

Rectangle x cm long

The perimeter is found by adding together the lengths of the sides of a shape.

The width of the rectangle is given as x cm. The height of the rectangle is 3 less than the width: x - 3 cm

Perimeter = x + x + (x – 3) + (x – 3)

Perimeter = (4x - 6) cm

Question

John is n years old. Kim is three years younger than John. Vanessa is half Kim's age.

Write an expression for each person's age.

From the question, John is n years old.

Kim is three years younger than John, so Kim is ( n - 3) years old.

Vanessa is half Kim's age, so take Kim's age and divide by 2. This gives Vanessa's age as \frac{n - 3}{2}.