INTEGERS - How To Subtract?

So far in our INTEGERS learning series we have explored the basic introduction to integers and how to add integers. This presentation is about the rule on how to subtract (take away) integers. 

Recall from the previous presentations on integers;

1. Integers are signed numbers and they have their signs only and only at their left front.
2. Positive sign at front of an integer is not shown and is obvious.
3. Same signs add and keep, ADD and KEEP.   
4. The next line to the above line is,  Opposite signs, you subtract, keep the bigger number sign then you are perfect!   

So, if two numbers have the opposite signs, subtract the smaller number from the larger number to get the answer. Write the sign of the bigger number in front of the answer and you done.   

Let’s do the following examples to understand the above concept. 

1. 8 – 5    
2. – 8 + 5 

In problem number (1), both the numbers have opposite signs, as 8 got plus sign (didn’t show at its front) and 5 got negative sign at its front. Because of opposite signs take away the smaller number from the larger. Subtract 5 from 8 to get 3. Now decide the sign of 3. As you already know, the answer takes the bigger number sign, and 8 is bigger than 5 and is positive, so the answer 3 takes the positive sign.  So the answer is +3. You already know that, in mathematics, positive integers are written without the plus sign, so leave answer as 3. Therefore 8 – 5 = 3   

In problem number (2), again both numbers got the opposite signs (as 8 got negative sign and 5 got positive sign).  Opposite signs ask you to subtract the smaller number from the larger.  So, subtract 5 from 8 to get 3. Now, 3 will take the bigger number sign and 8 is bigger than five and is negative, so the answer 3 is negative. Therefore  - 8 + 5 = - 3   

More examples: 1) 9 – 11 = -2 

Explanation:  As 9 is positive and 11 is negative, so both numbers got the opposite signs. Opposite signs ask you to subtract the smaller number from the larger, so subtract 9 from 11 to get 2. The sign of 2 is negative as 11 is larger than 9 and got the negative sign.   

2) – 4 + 10 = 6 

Explanation: Again both the numbers got opposite signs. Opposite signs means, subtract the smaller number from the larger number. So subtract 4 from 10 to get 6. The sign of 6 is positive, as 10 is larger than 4 and is positive.  Notice that the positive sign at front of 6 is not shown as it is understood in mathematics. 

Let's do the same addition and subtraction of integers on a number line

God Bless

Manjit Singh