Addition and Subtraction of Fractions Mathematics JSS 1 First Term Lesson Notes Week 8

Addition of Fractions with the Same Denominator

1. Keep the denominator the same.
2. Add the numerators.

   Example:
   $\frac{2}{5} + \frac{1}{5}$
   Keep the denominator (5) the same:
   $\frac{2 + 1}{5} = \frac{3}{5}$

2. Subtraction of Fractions with the Same Denominator

1. Keep the denominator the same.
2. Subtract the numerators.

   Example:
   $\frac{5}{8} – \frac{3}{8}$
   Keep the denominator (8) the same:
   $\frac{5 – 3}{8} = \frac{2}{8} = \frac{1}{4} \text{ (simplified)}$

3. Addition and Subtraction with Different Denominators

1. Find a common denominator.
   The common denominator is usually the least common multiple (LCM) of the two denominators.

   Example:
   To add $\frac{2}{3}$ and $\frac{1}{4}$, the LCM of 3 and 4 is 12.

2. Convert each fraction to an equivalent fraction with the common denominator.

   Example:
   $\frac{2}{3} = \frac{8}{12}$
   $\frac{1}{4} = \frac{3}{12}$

3. Add or subtract the numerators.

   Example:
   $\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$

4. Simplifying Fractions

1. Find the greatest common divisor (GCD) of the numerator and denominator.
2. Divide both by the GCD.

   Example:
   $\frac{8}{12} = \frac{2}{3}$ (GCD of 8 and 12 is 4)

Examples

1. Addition:
   $\frac{3}{4} + \frac{2}{5}$
   Common denominator: 20
   $\frac{15}{20} + \frac{8}{20} = \frac{23}{20} = 1 \frac{3}{20}$
2. Subtraction:
   $\frac{7}{10} – \frac{2}{5}$
   Common denominator: 10
   $\frac{7}{10} – \frac{4}{10} = \frac{3}{10}$

Practice Problems

1. $\frac{3}{8} + \frac{1}{4}$
2. $\frac{5}{6} – \frac{1}{3}$
3. $1 \frac{1}{2} + 2 \frac{1}{3}$