ADDING THE OPPOSITE

We can use the fact that subtracting a number is the same as adding its opposite to solve problems.

Problem 1 : 

Subtract -5 from 7.

Solution : 

Step 1 :

7 - (-5)

Rewrite the above subtraction as addition by taking opposite of -5, that is "+5" 

7 + (+5)

Step 2 : 

In the above addition, the numbers 7 and 5 are having same sign, that is positive. 

So, find the absolute values of 7 & 5 and add the absolute values. 

|7|  =  7 and  |5|  =  5

Sum of the absolute values :

7 + 5  =  12

Step 3 : 

Since both the numbers 7 and 5 are having the same positive sign, we have to take positive sign to the result. 

So, we have 7 + (+5)  =  12

Therefore, 

7 - (-5)  =  12

Problem 2 : 

Find the value of 3.5 - 5.8.

Solution : 

Step 1 :

3.5 - 5.8

Rewrite the above subtraction as addition by taking opposite of 5.8, that is "-5.8" 

3.5 + (-5.8)

Step 2 : 

In the above addition, the numbers 3.5 and 5.8 are having different signs.  

So, find the absolute difference between 3.5 & 5.8.

|3.5 - 5.8|  =  |-2.3|  =  2.3

Step 3 : 

In 3.5 + (-5.8), the sign of the bigger number is negative. So, we have to take negative sign to the answer. That is -2.3

So,

3.5 + (-5.8)  =  -2.3

Problem 3 : 

Joe is diving 7 feet below sea level. He decides to ascend descend 2 more feet. How many feet below sea level is he ?

Solution : 

Step 1 :

Use negative numbers to represent the number of feet below sea level.

So, we have to find -7 + (- 2). 

Step 2 :

In "-7 + (- 2)", the numbers 7 and 2 are having same sign, that is negative. 

So, find the absolute values of -7 & -2 and add the absolute values. 

|-7|  =  7 and  |-2|  =  2

Sum of the absolute values :

7 + 2  =  9

Step 3 : 

Since both the numbers -7 and -2 are having negative sign, we have to take negative sign to the result. 

So, we have -7 + (- 2)  =  - 9

Therefore, Joe is 9 feet below sea level.

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