Mathematics 7th grade | UNIT 1: Integers 1.2 Adding and subtracting negative numbers
You have seen how to add or subtract a positive number by thinking of temperatures going up and down.
Examples:
$\begin{array}{l}
- 3 + 5 = 2\\
- 3 - 5 = - 8
\end{array}$
Suppose you want to add or subtract a negative number, for example, $ - 3 + - 5$ or $-3 - -5$.
How can you do that?
You need to think about these in a different way.
To work out $-5+-3$, start at 0 on a number line.
-5 means 'move 5 to the left and -3 means 'move 3 to the left'.
The result is 'move 8 to the left'.
$ - 5 + - 3 = - 8$
$-3--5=2$
To work out $-3--5$ you want the difference between -5 and -3.
To go from -5 to -3 on a number line, move 2 to the right.
$-3--5= 2$
Worked example 1.2
Work these out.
a: $2 + 6 - 6$
b: $2 - -6$
Exercise 1.2
1) Work these out.
a: $-3 + 4$
b: $3+-6$
c: $-5 + -5$
d: $-2 + 9$
2) Work these out.
a: $3-7$
b: $4 - -1$
c: $2- -4$
d: $-5 -8$
3) Work these out.
a: $3+5$
b: $-3+5$
c: $3+-5$
d: $-3+ -5$
4) Work these out.
a: $4-6$
b: $4 - -6$
c: $-4 -6$
d: $-4 - -6$
5) a: Work these out.
i- $3+-5$
ii- $-5+3$
iii- $-2 +-8$
iv- $-8+ -2$
b: If ....... and ........ are two integers, is it always true that ..... + ...... and ........ - ........?
Give a reason for your answer.
6) a: Work these out.
i- $5--2$
ii- $-2-5$
iii- $-4--3$
iv- $-3--4$
b: If ..... and ...... are two integers, what can you say about ....... - ....... and ....... - .......?