In maths, an expression combines numbers, variables, and functions (such as addition, subtraction, multiplication, division, etc.)

Expressions can be thought of as similar to phrases. In language, a phrase may include an action but doesn’t make a complete sentence.

Here are some examples of expressions and how they relate to word phrases:

Expression: 3 + 7

Word Phrase: *The sum of three and seven*

or

Expression: *n*− 5

Word Phrase: *the difference between n and five*

These expressions express a mathematical operation, but they don’t tell us the outcome of the operation or what the operation is equal to.

**What is the difference between expressions and equations?**

The difference between expressions and equations is that an expression comprises a combination of numbers, variables, and operation symbols. In contrast, an equation is two different expressions connected by an equal sign in between. This indicates that each side of the expression is of the same value.

For example:

15 + 5 is an expression

But 15 + 5 = 20 is an equation

2*n* + 6 is an expression

But 2*n* + 6 = 14 – 2 is an equation

*y* + 9 is an expression

But *y* + 9 = 3*y* – 1 is an equation

Sometimes children are introduced to equations as ‘number sentences.’

Equations and expressions are often used in higher levels of mathematics and can require particular calculations to solve graphical problems and geometric figures. Sometimes they are used in explanations of lines, cartoons, and diagrams. They also have their place in computer software and are used for developing animations.

Children need to develop a sound understanding of equations and expressions and the difference between them, as they’ll likely encounter both throughout their time studying maths in school.

**Example questions about expressions**

**Example 1:**

Apples are sold in packs of 4 and oranges in bags of 8.

Emily buys *p* packs of apples and *r* bags of oranges. Write an expression for the total number of apples and oranges purchased.

There are four apples in each pack, so the number of apples bought is which is four x*p* or 4*p*

There are eight oranges in each bag, so the number of oranges bought is which is 6 x *r* or 6*r*

The total number of apples and oranges bought is 4*p +6r*

**Example 2:**

A rectangle has a width of *x *cm. The height is 4cm less than the width. Write an expression for the perimeter of the rectangle.

The perimeter is found by adding the lengths of a shape’s different sides.

The width of the rectangle is given as *x* cm. The height of the rectangle is four less than the width, which is *x* – 4 cm

Perimeter = *x* + *x* + (*x* – 4) + (*x* – 4)

Perimeter = (4*x* – 8) cm

**Example 3**

Some maths questions might ask you to take extended expressions with many of the same variables and simplify them into shorter, easier-to-read expressions.

3*b* + 11*b* + 7*b* – 9*b*

In this expression, all the terms are like terms, as the variable in each term is always* b*. This means we can simplify the expression like so:

3*b* + 11*b* + 7*b = *21*b*

21*b – 9b = 12b*