Addition of Rational Numbers

key notes :

Understanding Rational Numbers

Definition:

Examples:

Addition of Rational Numbers

Same Denominator:

  • When adding rational numbers with the same denominator, add the numerators and keep the denominator the same.

Different Denominators:

Addition of Positive and Negative Rational Numbers

Same Sign:

  • When adding rational numbers with the same sign, add their absolute values and keep the common sign.

Diffearent Signs:

  • When adding rational numbers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.
Simplifying Rational Numbers
  • After adding the rational numbers, simplify the result if possible by dividing the numerator and the denominator by their greatest common divisor (GCD).Example:
Practice Problems

Same Denominator:

  • Different Denominators:
  • Mixed Numbers:
  • Positive and Negative Rational Numbers:

Learn with an example

🔮 Add. 2/5 + 3/5 = ____

Add:

2/5 + 3/5 =

= 1

Since the numbers being added are positive, the result must also be positive.

So:

2/5 + 3/5 = 1

🔮 Add. 2/5 + 2/5

Add:

2/5 + 2/5

= 4/5

Since the numbers being added are positive, the result must also be positive.

So:

2/5 + 2/5 = 4/5

🔮 Subtract. 4/5 – 1/5 =

Subtract:

4/5 – 1/5

= 3/5

Since you are subtracting a smaller number from a larger number, the result must be positive.

So:

4/5 – 1/5 = 3/5

Let’s Practice!