Level 5

Mixed operations with algebraic terms (incl negatives)

Lesson

We've already learnt about the concept of negative numbers and how to simplify and evaluate expressions with directed numbers.

Now we are going to look at working with algebraic expressions that have positive and negative terms.

There are a few important things to remember when working with directed numbers:

	Example
Multiplying a positive term and a negative term gives a negative answer	$\left(-2f\right)\times5g=-10fg$(−2`f`)×5`g`=−10`fg`
Multiplying two negative terms gives a positive answer	$-6\times\left(-7c\right)=42c$−6×(−7`c`)=42`c`
Subtracting a negative term is the same as adding a positive term	$3-\left(-2a\right)$3−(−2`a`) is the same as $3+2a$3+2`a`
Adding a negative term is the same as subtracting the term	$h+\left(-3\right)$`h`+(−3) is the same as $h-3$`h`−3

Handy Hint

It may help to visualise a number line when you are working with directed numbers. Negatives go to the left down the number line and positives go up to the right down the number line.

Examples

Question 1

Simplify: $-2m-9m$−2m−9m

Question 2

Simplify the expression: $3x-\left(-4x\right)-2x$3x−(−4x)−2x

Question 3

Simplify the expression $\frac{10x}{3x}$10x3x

Outcomes

NA5-8

Generalise the properties of operations with fractional numbers and integers.