Understanding Rational Numbers

1. Definition:

1. Examples:

Addition of Rational Numbers

1. Same Denominator:
   • When adding rational numbers with the same denominator, add the numerators and keep the denominator the same.

1. Different Denominators:
   • Find a common denominator by finding the least common multiple (LCM) of the denominators.Convert each fraction to an equivalent fraction with the common denominator.Add the numerators of the equivalent fractions and keep the common denominator.
   Example:

Addition of Positive and Negative Rational Numbers

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

1. 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

1. Same Denominator:

• Different Denominators:

• Mixed Numbers:

• Positive and Negative Rational Numbers: