Numbers can be used to measure quantities that are found in everyday life, and in some situations we need to use negative numbers.
For example, if a company makes a profit of $\$5000$$5000 we can represent this as a positive number. But if a company makes a loss of $\$5000$$5000 we can represent this as a negative number.
We can represent positive and negative numbers on the number line:
Any number to the right of $0$0 is considered to be positive, and gets bigger as you move further to the right.
Any number to the left of $0$0 is considered negative, and gets smaller as you move further to the left.
The plus or minus sign in front of a number tells us whether it is to the right or left of $0$0.
a) $-2$−2 is $2$2 to the left of $0$0.
b) $+2$+2 is $2$2 to the right of $0$0, but we just write this as $2$2.
We use the term directed number to mean a number that has both direction and size.
For example, the number $-2$−2 is:
'To the left' is the direction.
Let's have a look at some words that represent directed numbers.
Words that indicate growth or getting bigger are represented by positive numbers in maths.
This includes words like:
For compass directions, North and East are typically represented by positive numbers.
Express the following statement as a directed number (i.e. positive or negative):
Driving $15$15km north.
We take North to be the "positive direction" so it can be represented by the number $+$+$15$15 which we can just write as $15$15.
Express the following statement as a directed number: Going up $4$4 flights of stairs.
"Going up" means "rising" so this can also be represented by the positive number $4$4.
Words that indicate a decrease or a decline are represented by negative numbers.
This includes words like
South and West directions on the compass are typically represented by negative numbers.
Express the following statement as a directed number: A weight loss of $2$2 kilograms.
"Loss" represents a decrease, so this would be represented by a negative number. Our answer would be $-2$−2.
Express the following statement as a directed number: Travelling west for $400$400 metres.
"West" is moving in a negative direction on our number line, so it would be represented by the number $-400$−400.
Express the following statement as a directed number: Losing $\$43$$43.
Understand addition and subtraction of fractions, decimals, and integers