Solve the Fraction Subtraction: 5/8 minus 3/10

To solve the subtraction problem $\frac{5}{8} - \frac{3}{10}$, we first need to find a common denominator for the fractions.

• Step 1: Determine the least common multiple (LCM) of the denominators 8 and 10.

To find the LCM of 8 and 10, list their multiples:

Multiples of 8: $8, 16, 24, 32, 40, \ldots$
Multiples of 10: $10, 20, 30, 40, 50, \ldots$

The smallest common multiple is 40. Therefore, the common denominator is 40.

• Step 2: Adjust each fraction to the common denominator of 40.

Convert $\frac{5}{8}$ to a fraction with a denominator of 40:

$\frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40}$

Convert $\frac{3}{10}$ to a fraction with a denominator of 40:

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

• Step 3: Subtract the fractions.

Subtract the numerators and place the result over the common denominator:

$\frac{25}{40} - \frac{12}{40} = \frac{25 - 12}{40} = \frac{13}{40}$

The result is $\frac{13}{40}$, which is already in its simplest form.

The solution to the problem is $\frac{13}{40}$.