Adding and Subtracting Integers

Adding and Subtracting Integers

Integers are whole numbers and their opposites and zero. Here you can learn how to add and subtract integers.

Step by step guide to add and subtract integers

  • Integers include: zero, counting numbers, and the negative of the counting numbers. \(\{… , – \ 3, – \ 2, – \ 1, 0, 1, 2, 3 , …\} \)
  • Add a positive integer by moving to the right on the number line.
  • Add a negative integer by moving to the left on the number line.
  • Subtract an integer by adding its opposite.

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: \((- \ 2) \ \color{blue}{+} \ 6=4\)

Example 2:

Solve. \( 8 \ + \ (12 \ – \ 20)=\)

Solution:

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

Example 3:

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

Solution:

Keep the first number and convert the sign of the second number to it’s opposite. (change subtraction into addition. Then: \((-8)+5= \ -3\)

Example 4:

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

Solution:

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

Exercises

Find the sum and the difference.

  • \(\color{blue}{(– 12) + (– 4)}\)
  • \(\color{blue}{5 + (– 24)}\)
  • \(\color{blue}{4 + (– 30) + (45 – 34)}\)
  • \(\color{blue}{( – 14) – (– 9) – (18)}\)
  • \(\color{blue}{( – 9) – (– 25)}\)
  • \(\color{blue}{(55) – (– 5) + (– 4)}\)

Download Adding and Subtracting Integers Worksheet

Answers

  • \(\color{blue}{-16}\)
  • \(\color{blue}{-19}\)
  • \(\color{blue}{-15}\)
  • \(\color{blue}{-23}\)
  • \(\color{blue}{16}\)
  • \(\color{blue}{56}\)

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