Rules for Addition & Subtraction

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,    \( \scriptsize – \; \times \; + = \;- \\ \scriptsize + \; \times \; – \; =\; – \)

Worked Example 10.3.1:

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