Lesson 10, Topic 3
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# Rules for Addition & Subtraction

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You can add and subtract direct numbers without drawing the number line using the rules below:

The rules for addition and subtraction are:

Replace the same signs that appear together with a positive sign:

e.g.    +5   +  ( + 3 )   =  5  +  3    =  8

Same sign gives  +

e.g.  + 7   ( 4 )   =    7   +  4   =  11

Same sign gives  +

In other words   $$\scriptsize + \; \times \; + = + \\ \scriptsize – \; \times \; – \; = +$$

Replace the different signs that appear together with a negative sign:

e.g.   +8  + ( 4) =   8     4    =   4

e.g.  +4     ( + 1)   =   4  1

In other words,    $$\scriptsize – \; \times \; + = \;- \\ \scriptsize + \; \times \; – \; =\; –$$

### Example

Find the values of the following:

i. (+5)    +   (+4)
ii. (+10)  –  (+5)
iii. (+12)  +  (-7)
iv. (+6)  –  (-5)
v. (-9)  –  (-6)

Solution

i. (+5)  +  (+4)

$$\scriptsize + \: \times \: + \: = +$$

= 5  +  4

=  9

Note: +5   =  5

ii. (+10)  –  (+5)

$$\scriptsize – \: \times \: + \: = \: –$$

= 10   –  5

=  5

iii. (+12)  +  (-7)

+  x   –  =   –

=    12  –  7

=  5

iv. (+6)  –  (-5)

$$\scriptsize – \: \times \: – \: = \: +$$

= 6   +    5

=  11

v. (-9)   – (-6)

$$\scriptsize – \: \times \: – \: = \: +$$

=   -9   +  6

=   -3

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