How to Add and Subtract Integers

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The term integers represent the meaning “intact” or “whole”. So, you can generally refer an integer as a whole number, except integers can be negative also!

What is an Integer?

An integer is a whole number (not any decimal or fraction numbers) which can be zero, positive or negative numbers. Some examples of integers can be \(7 \ , \ 3 \ , \ 0 \ , \ -5 \ , \ -15 \), etc. Moreover, we can represent integers by the denotation \(Z\) which comprises of:
Positive Integers: As the name suggests, any integer that is greater than zero is termed as a positive integer.
Negative Integer: As from the name, any integer that is less than zero is termed as a negative integer.
Zero: Zero is neither a positive integer or a negative integer. It is just a whole number.
So, we can write \(Z = \{…… -5 \ , \ -4 \ , \ -3 \ , \ -2 \ , \ -1 \ , \ 0 \ , \ 1 \ , \ 2 \ , \ 3 \ , \ 4 \ , \ 5 \ , \ ……\}\)
Also, we can place all integers on a number line where the negative ones are placed on the left of “\(0\)” and the positive ones on the right. Moreover, we can perform the \(4\) basic mathematic properties with integers. They are:

Addition
Subtraction
Multiplication
Division

We often see that negative integers are always written as \(-5 \ , \ -9\), and so on. But it is not generally considered necessary to write positive integers like \(+5 \ , \ +9\), and so on. So, when we write just \(5\), we mean \(+5\).
Another thing to note is, that an absolute value of any integer is always positive. So, \( \lvert -6 \rvert = 6\) and \(\lvert 6 \rvert\) is also \(6\).

How to Add and Subtract Integers

To add or subtract two integers, follow these steps:

In the first case, if two integers have the same sign (either both are positive or both are negative), add up those integers and put the common sign.
In the second case, if two integers have an opposite sign (one is positive and the other one negative), then subtract them and put the sign of the bigger number.

Example:

\(-12 +13 = +1\)
\(-12 -13 = -25\)
\(12 – 13 = -1\) and so on.

Free printable Worksheets

Exercises for Adding and Subtracting Integers

1) \((-48) \ + \ (-27) \ =\)

2) \((-34) \ + \ (-27) \ = \)

3) \(10 \ + \ (-26) \ = \)

4) \((-19) \ + \ (3) \ = \)

5) \((-26) \ + \ (-27) \ = \)

6) \((-12) \ + \ (-13) \ = \)

7) \((-41) \ + \ (-23) \ = \)

8) \(3 \ + \ (-22) \ = \)

9) \(25 \ + \ (-21) \ = \)

10) \(32 \ + \ (-20) \ = \)

Answers

1) \((-48) \ + \ (-27) \ = \color{red}{-75} \)

Solution
Both numbers have the same sign (both are negative ), therefore add them together: \(48 + 27=75\),
and then put the negative sign:\(-75 \)

2) \((-34) \ + \ (-27) \ = \color{red}{-61} \)

Solution
Both numbers have the same sign (both are negative ), therefore add them together: \(34 + 27=61\),
and then put the negative sign:\(-61 \)

3) \(10 \ + \ (-26) \ = \color{red}{-16} \)

Solution
Two numbers don’t have the same sign (one is negative and the other is positive), you must subtract them \(26 - 10=16\),
and then put the bigger number sign, \(-16 \)

4) \((-19) \ + \ (3) \ = \color{red}{-16} \)

Two numbers don’t have the same sign (one is negative and the other is positive), you must subtract them \(19 - 3=16\),
and then put the bigger number sign, \(-16 \)

5) \((-26) \ + \ (-27) \ = \color{red}{-53} \)

6) \((-12) \ + \ (-13) \ = \color{red}{-25} \)

7) \((-41) \ + \ (-23) \ = \color{red}{-64} \)

8) \(3 \ + \ (-22) \ = \color{red}{-19} \)

9) \(25 \ + \ (-21) \ = \color{red}{4} \)

10) \(32 \ + \ (-20) \ = \color{red}{12} \)

How to Add and Subtract Integers