How to Add and Subtract Integers? (+FREE Worksheet!)

Any number that can be displayed without a fraction is called an integer. For example, the numbers \(-10, -5, 0, 1, 2\) are integers because we can specify them without having to display a regular fraction.

It can be said that integers consist of three categories:

1. Positive integers
2. Zero
3. Negative integers

Related Topics

• How to Multiply and Divide Integers
• How to Order Integers and Numbers
• How to Use Order of Operations
• How to Solve Integers and Absolute Value Problems

Step by step guide to add and subtract integers

Integers include: zero, counting numbers, and the negative of the counting numbers. \(\{… , – \ 3, – \ 2, – \ 1, 0, 1, 2, 3 , …\} \)

Addition of integers:

In the addition of integers, two cases occur:

• Case 1: Both numbers have the same sign. That is, both are negative or both are positive, in which case we add them together and then put the sign of one of the two numbers.
• Case 2: in this case, two numbers don’t have the same sign. That is, one is negative and the other is positive, which we must subtract and then put the bigger number sign.

• Note 1: Add a positive integer by moving to the right on the number line.
• Note 2: Add a negative integer by moving to the left on the number line.

Subtraction of integers:

In subtraction of integers, we have to convert the subtraction mode to the addition mode, but how?

How to convert subtraction to addition:

We write the first number and put the addition sign instead of the subtraction sign. Then we make the second number opposite. Then we solve the obtained sum with the help of the two mentioned cases in the addition of integers.

Adding and Subtracting Integers – Example 1:

Solve. \( (- \ 2) \ – \ (- \ 6)=\)

Solution:

Keep the first number, and convert the sign of the second number to it’s opposite. (change subtraction into addition). Then: \((- \ 2) \ \color{blue}{+} \ 6=4\)

Adding and Subtracting Integers – Example 2:

Solve. \( 8 \ + \ (12 \ – \ 20)=\)

Solution:

First subtract the numbers in brackets, \(12 \ – \ 20= \ – 8\)
Then: \(8 \ + \ (- \ 8)= \ → \) change addition into subtraction: \(8 \ \color{blue}{-} \ 8=0\)

Adding and Subtracting Integers – Example 3:

Solve. \((-8)-(-5)=\)

Solution:

Keep the first number and convert the sign of the second number to its opposite. (change subtraction into addition). Then: \((-8) \color{blue}{+} 5= \ -3\)

Adding and Subtracting Integers – Example 4:

Solve. \(10+(4-8)=\)

Solution:

First subtract the numbers in brackets, \(4-8= \ -4\)
Then: \(10+(-4)= →\) change addition into subtraction: \(10 \color{blue}{-} 4=6\)

Exercises for Adding and Subtracting Integers

Find the sum and the difference.

1. \(\color{blue}{(– 12) + (– 4)}\)
2. \(\color{blue}{5 + (– 24)}\)
3. \(\color{blue}{4 + (– 30) + (45 – 34)}\)
4. \(\color{blue}{( – 14) – (– 9) – (18)}\)
5. \(\color{blue}{( – 9) – (– 25)}\)
6. \(\color{blue}{(55) – (– 5) + (– 4)}\)

Download Adding and Subtracting Integers Worksheet

1. \(\color{blue}{-16}\)
2. \(\color{blue}{-19}\)
3. \(\color{blue}{-15}\)
4. \(\color{blue}{-23}\)
5. \(\color{blue}{16}\)
6. \(\color{blue}{56}\)