Fractions Math Example 5

Solution

1. 1
   Find the least common denominator (LCD) of $3$ and $4$: $\text{LCD} = 12$.
2. 2
   Convert each fraction: $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$ and $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$.
3. 3
   Add the numerators: $\frac{8}{12} + \frac{9}{12} = \frac{17}{12}$.
4. 4
   Convert to a mixed number: $\frac{17}{12} = 1\frac{5}{12}$. Since $\gcd(5, 12) = 1$, this is already in simplest form.