Let's solve the given equation step by step:

The equation is:

\[
3m \cdot \frac{3}{7} = \frac{3}{7} \cdot 10
\]

### Step 1: Simplify both sides

On the left-hand side, you have:

\[
3m \cdot \frac{3}{7} = \frac{9m}{7}
\]

On the right-hand side, simplify:

\[
\frac{3}{7} \cdot 10 = \frac{30}{7}
\]

### Step 2: Set up the equation

Now, you have the equation:

\[
\frac{9m}{7} = \frac{30}{7}
\]

### Step 3: Multiply both sides by 7 to eliminate the denominator:

\[
9m = 30
\]

### Step 4: Solve for \(m\)

Divide both sides by 9:

\[
m = \frac{30}{9} = \frac{10}{3}
\]

Thus, the value of \(m\) is:

\[
m = \frac{10}{3}
\]

Would you like further details on any step?

### Related Questions:
1. What happens if the equation involves subtraction or addition instead of multiplication?
2. How do you handle variables in the denominator?
3. How can you solve a system of equations like this?
4. What if the equation involves fractions with different denominators?
5. How do you apply this method to equations with more variables?

**Tip:** Always simplify both sides of the equation before isolating the variable.

3m \cdot \frac{3}{7} = \frac{3}{7} \cdot 10

Learn how to solve the linear equation 3m * 3/7 = 3/7 * 10 with a step-by-step approach. This problem demonstrates key algebraic techniques for handling fractions, simplifying equations, and solving for variables. Suitable for students in Grades 6-8.

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