Solve: Adding Fractions 4/8 + 3/10 with Unlike Denominators

To solve the problem of adding the fractions $\frac{4}{8} + \frac{3}{10}$, we follow these steps:

• Step 1: Determine the least common denominator (LCD) for the fractions.
• Step 2: Convert each fraction to have the LCD.
• Step 3: Add the numerators of these converted fractions.

Let's go through each step in detail:

Step 1: Find the least common denominator for the fractions.

The denominators are 8 and 10. The least common multiple of 8 and 10 is 40. So, the LCD is 40.

Step 2: Convert each fraction to an equivalent fraction with a denominator of 40.

For $\frac{4}{8}$: Multiply both the numerator and denominator by 5 to convert it:

$\frac{4 \times 5}{8 \times 5} = \frac{20}{40}$.

For $\frac{3}{10}$: Multiply both the numerator and denominator by 4 to convert it:

$\frac{3 \times 4}{10 \times 4} = \frac{12}{40}$.

Step 3: Add the two fractions with the common denominator:

$\frac{20}{40} + \frac{12}{40} = \frac{20 + 12}{40} = \frac{32}{40}$.

Thus, the sum of the fractions is $\frac{32}{40}$.

Therefore, the solution to the problem is $\frac{32}{40}$.