5m/12 - m/8 = 1/3

To solve the equation \( \frac{5m}{12} - \frac{m}{8} = \frac{1}{3} \), we first need to find a common denominator for the fractions involved. The denominators are 12, 8, and 3. The least common multiple of these numbers is 24.

Next, we will rewrite each term with a denominator of 24:

1. Convert \( \frac{5m}{12} \): \[ \frac{5m}{12} = \frac{5m \times 2}{12 \times 2} = \frac{10m}{24} \]

2. Convert \( \frac{m}{8} \): \[ \frac{m}{8} = \frac{m \times 3}{8 \times 3} = \frac{3m}{24} \]

3. Convert \( \frac{1}{3} \): \[ \frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24} \]

Now we can rewrite the original equation: \[ \frac{10m}{24} - \frac{3m}{24} = \frac{8}{24} \]

Combine the left-hand side: \[ \frac{10m - 3m}{24} = \frac{8}{24} \] \[ \frac{7m}{24} = \frac{8}{24} \]

Since the denominators are the same, we can set the numerators equal to each other: \[ 7m = 8 \]

Now, solve for \( m \): \[ m = \frac{8}{7} \]

Thus, the solution to the equation \( \frac{5m}{12} - \frac{m}{8} = \frac{1}{3} \) is: \[ m = \frac{8}{7} \]