 Expressions vs equations

Lesson

Solving problems

When we work with number problems, we may not know the mathematical names for the things we are working with. In fact, why do we even need to know them? Well, in some cases, it can help you find missing values, or solve problems.

The terms we're looking at today are:

• expressions
• equations (Can you see a clue in that word?)
• numeric (another clue!), and
• algebraic

expressions and equations

An expression is a statement of something, and does not have an equal sign. If I have $5$5 Mb of data left on my internet plan, and you have $2$2 Mb of data left on your internet plan, we could write an expression showing the data we both have left:

$5+2$5+2

Once we include an equal sign, it becomes an equation, that is, both sides are equal:

$5+2=7$5+2=7

There are times where our expression or equation might include letters of the alphabet, called pronumerals, or variables. In this case they are called algebraic expressions or algebraic equations. You may like to refresh your memory of writing equations with variables (where we don't know the value), using pronumerals.

If I don't know how much data you have left, I might use y in place of the number for your data. I could write an expression showing my data, and yours, like this:

$5+y$5+y

We could also write an equation, with an equal sign, showing the total (let's call that t), like this:

$5+y=t$5+y=t

Let's go and explore expressions and equations in more detail, in Video 1.

Phew! Now we have sorted out what an expression and equation is, we can use them for problem solving. Let's imagine you set up a fund-raising stall, and buy the ingredients to make pancakes. When you add up all the costs, your pancakes may cost $\$11 each to make. How can we set our selling price, to make sure we make a profit? Let's work through this example in Video 2.

Remember!

To have an equation, we must have two expressions, with an equal sign in the middle.

Worked examples

Question 1

Is $6x$6x an expression or an equation?

1. It is an expression.

A

It is an equation.

B

It is an expression.

A

It is an equation.

B

Question 2

Is $r=4$r=4 an expression or an equation?

1. It is an expression.

A

It is an equation.

B

It is an expression.

A

It is an equation.

B

Question 3

Consider the expression $x+6$x+6.

1. What is the value of the expression when $x=4$x=4?

2. What is the value of the expression when $x=9$x=9?

3. What happens to the value of $x+6$x+6 as we substitute in different values of $x$x?

The value of the expression stays the same.

A

The value of the expression changes depending on the value of $x$x.

B

The value of the expression stays the same.

A

The value of the expression changes depending on the value of $x$x.

B

Outcomes

NA5-8

Generalise the properties of operations with fractional numbers and integers.