Let's solve the equation step by step:

Given equation:

\[
\frac{3m}{4} - \frac{m}{12} = \frac{7}{8}
\]

### Step 1: Find a common denominator for the fractions on the left-hand side.

The denominators are 4 and 12. The least common denominator (LCD) is 12.

Convert \(\frac{3m}{4}\) to have a denominator of 12:

\[
\frac{3m}{4} = \frac{3m \times 3}{4 \times 3} = \frac{9m}{12}
\]

So the equation now becomes:

\[
\frac{9m}{12} - \frac{m}{12} = \frac{7}{8}
\]

### Step 2: Combine the fractions on the left-hand side.

\[
\frac{9m - m}{12} = \frac{8m}{12} = \frac{7}{8}
\]

### Step 3: Simplify the fraction on the left-hand side.

\[
\frac{8m}{12} = \frac{2m}{3}
\]

So the equation is now:

\[
\frac{2m}{3} = \frac{7}{8}
\]

### Step 4: Cross multiply to solve for \(m\).

\[
2m \times 8 = 3 \times 7
\]

\[
16m = 21
\]

### Step 5: Solve for \(m\).

\[
m = \frac{21}{16}
\]

So, the solution is:

\[
m = \frac{21}{16} \quad \text{or approximately } m = 1.3125
\]

Would you like more details or have any questions?

Here are some related questions to consider:
1. How do you find the least common denominator (LCD) for different fractions?
2. What steps would you take if the equation had variables on both sides?
3. How can you check if your solution for \(m\) is correct?
4. What is the process for solving equations that involve decimals instead of fractions?
5. How would you handle an equation with multiple variables?

**Tip:** Always simplify fractions early in the process to make calculations easier and reduce the risk of mistakes.

Learn how to solve the equation 3m/4 - m/12 = 7/8 step-by-step with detailed explanations. This problem involves equations with fractions and cross multiplication. Suitable for students in Grades 9-12.

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