SUBTRACTING INTEGERS BY ADDING THE OPPOSITE
About "Subtracting integers by adding the opposite"
Subtracting integers by adding the opposite :
We can use the fact that subtracting an integer is the same as adding its opposite to solve problems.
Subtracting integers by adding the opposite - Examples
Problem 1 :
Subtract -4 from 7.
Solution :
Step 1 :
7 - (-4)
Rewrite the above subtraction as addition by taking opposite of -4, that is "+4"
7 + (+4)
Step 2 :
In the above addition, the integers 7 and 4 are having same sign, that is positive.
So, find the absolute values of 7 & 4 and add the absolute values.
|7| = 7 and |4| = 4
Sum of the absolute values :
7 + 4 = 11
Step 3 :
Since both the integers 7 and 4 are having the same positive sign, we have to take positive sign to the result.
So, we have 7 + (+4) = 11
Hence, 7 - (-4) = 11
Problem 2 :
Subtract -2 from -5.
Solution :
Step 1 :
-5 - (-2)
Rewrite the above subtraction as addition by taking opposite of -2, that is "+2"
-5 + (+2)
Step 2 :
In the above addition, the integers 5 and 2 are having different signs.
So, find the absolute difference of the integers without the actual signs.
|5 - 2| = |3| = 3
Step 3 :
In the two integers 5 and 2, the sign of the bigger integer is negative. So, we have to take negative sign to the answer. That is -3
Hence, -5 - (-2) = -3
Problem 3 :
Subtract 4 from -9.
Solution :
Step 1 :
-9 - (4)
Rewrite the above subtraction as addition by taking opposite of 4, that is "-4"
-9 + (-4)
Step 2 :
In the above addition, the integers 9 and 4 are having same sign, that is negative.
So, find the absolute values of -9 & -4 and add the absolute values.
|-9| = 9 and |-4| = 4
Sum of the absolute values :
9 + 4 = 13
Step 3 :
Since both the integers -9 and -4 are having the same negative sign, we have to take negative sign to the result.
So, we have -9 + (-4) = -13
Hence, -9 + (-4) = 13
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