Solve the Fraction Addition: 4/6 + 1/8 Step-by-Step

To solve the addition of the fractions $\frac{4}{6} + \frac{1}{8}$, we will first find the least common denominator.

• The denominators of the fractions are 6 and 8. To add these fractions, we need a common denominator.
• Calculate the least common multiple (LCM) of 6 and 8:
• Prime factorization of 6: $6 = 2 \times 3$.
• Prime factorization of 8: $8 = 2^3$.
• The LCM will take the highest power of each prime that appears in these factorizations: $2^3 \times 3 = 24$.
• Convert each fraction to an equivalent fraction with 24 as the denominator:
• Convert $\frac{4}{6}$: Multiply both the numerator and denominator by 4 (since $\frac{24}{6} = 4$): $\frac{4 \times 4}{6 \times 4} = \frac{16}{24}$.
• Convert $\frac{1}{8}$: Multiply both the numerator and denominator by 3 (since $\frac{24}{8} = 3$): $\frac{1 \times 3}{8 \times 3} = \frac{3}{24}$.
• Now, add these two fractions:
• $\frac{16}{24} + \frac{3}{24} = \frac{16 + 3}{24} = \frac{19}{24}$.

Thus, the sum of the fractions $\frac{4}{6}$ and $\frac{1}{8}$ is $\frac{19}{24}$.

The correct choice from the available options is $\frac{19}{24}$.

Therefore, the solution to the problem is $\frac{19}{24}$.