Rules of Addition/Sum and Subtraction/Difference of Integers
Let us understand it with the help of an example.
EXAMPLE 1: Add the integers – 5 and – 4.
In old math books, this addition/sum of integers is written as:
– 5 + (- 4)
and in new math books, this addition/sum is written as:
– 5 + – 4
Keep in mind both means the same.
Let us proceed with the new way of writing, that is
– 5 + – 4
STEP 1: Reduce the two operators/signs in the middle to ONE.
Remember,
(a) Same both operators/signs reduces to +
That is,
++ reduces to +
– – also reduces to +
(b) Different both operators/signs reduces to –
That is,
+ – reduces to –
– + also reduces to –
Now, we have to solve
– 5 + – 4
By applying STEP 1, part (b), it becomes – 5 – 4
STEP 2:
Remember
(a) If BOTH integers are POSITIVE,
ADD them
and the answer will be POSITIVE integer.
(b) If BOTH integers are NEGATIVE,
ADD them
and the answer will be negative integer.
(c) If first is POSITIVE and second is NEGATIVE integer,
OR
first is NEGATIVE and second is POSITIVE integer
SUBTRACT them
and the answer will have the sign of the bigger number.
In this example, both are negative integers, – 5 and – 4, so (b) will be applied here.
That is, add 5 and 4, and answer will be negative integer.
– 5 – 4 = – 9
Thus,
addition/sum of integers – 5 and – 4 = – 5 + – 4 = – 9.
EXAMPLE 2: Work out:
7 + – 3
SOLUTION:
7 + – 3 = 7 – 3 (By STEP 1, part (b))
For STEP 2, by part (c), as 7 is positive integer and -3 is negative integer, so subtract.
And as 7 is greater than 3, so apply the sign of 7. So
Thus,
7 + – 3 = 4
EXAMPLE 3: Work out:
– 6 – – 2
SOLUTION:
– 6 – – 2 = – 6 + 2 (By STEP 1, part (a))
For STEP 2, by part (c), as – 6 is negative integer and 2 is positive integer, so subtract.
And as 6 is greater than 2, so apply the sign of 6. So
Thus,
– 6 – – 2 = – 4
RELATED POST:
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MCQ-Quiz with Answers on Subtraction/Difference of Integers
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