Add and subtract rational numbers

Key notes:

Adding Rational Numbers

  • If the rational numbers have the same sign, add their absolute values and keep the sign.
    • Example: 3/4 + 5/4 = 8/4 = 2
    • Example: −2/3+(−1/3)=−3/3= −1
  • If the rational numbers have different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger number.
    • Example: 5/6 + (−1/6) = 4/6 = 2/3
    • Example: −7/5 + 2/5 = (−5/5) = −1

Subtracting Rational Numbers

Use the addition rules to solve the problem after changing the sign.

To subtract a rational number, add its opposite.

Example: 3/5 − 2/ 5= 3/5 + (−2/5) =1/5

Example: −4/7 −1/7 = −4/7 + (−1/7)= −5/7

Use the addition rules to solve the problem after changing the sign.

Learn with an example

🎯 Add. 3 1/2 + -1/2 = _________

  • You are adding two numbers with different signs, so subtract the lesser absolute value from the greater absolute value:
  • 3 1/2 – 1/2 = 3
  • Since the number with the greater absolute value is positive, the result must also be positive.
  • So: 3 1/2 + – 1/2 = 3

👉 Add. -4 + 1/2 = _____

  • You are adding two numbers with different signs, so subtract the lesser absolute value from the greater absolute value:
  • 4 – 1/2
  • 3 1/2
  • Since the number with the greater absolute value is negative, the result must also be negative:
  • 3 1/2 —-> – 3 1/2
  • So: – 4 + 1/2 = -3 1/2

🎯 Add. – 8 + 9 / 10 ____

  • You are adding two numbers with different signs, so subtract the lesser absolute value from the greater absolute value:
  • 8 – 9/10 = 7 1/10
  • Since the number with the greater absolute value is negative, the result must also be negative:
  • 7 1/10 —-> – 7 1/10
  • So: – 8 + 9/10 = – 7 1/10

Let’s practice!🖊️