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The problem asks to find the value of \( m \) from the equation:

\[
\frac{m}{9} + \frac{m - 3}{10} = 0.56
\]

Let's solve it step by step:

### Step 1: Eliminate the fractions by multiplying the entire equation by the least common denominator (LCD) of 9 and 10, which is 90.

\[
90 \times \left( \frac{m}{9} + \frac{m - 3}{10} \right) = 90 \times 0.56
\]

This gives:

\[
10m + 9(m - 3) = 50.4
\]

### Step 2: Expand the terms:

\[
10m + 9m - 27 = 50.4
\]

This simplifies to:

\[
19m - 27 = 50.4
\]

### Step 3: Add 27 to both sides:

\[
19m = 50.4 + 27
\]

\[
19m = 77.4
\]

### Step 4: Solve for \( m \) by dividing both sides by 19:

\[
m = \frac{77.4}{19}
\]

\[
m = 4.074
\]

Thus, the value of \( m \) is approximately **4.074**.

Would you like more details or have any other questions?

Here are five related questions to consider:
1. What is the general method for solving linear equations with fractions?
2. How can you verify the solution of an equation by substituting back into the original equation?
3. What are other techniques for solving equations with multiple fractions?
4. How does multiplying both sides by the least common denominator simplify an equation?
5. Why is it important to balance both sides of an equation when performing operations?

**Tip:** When solving equations with fractions, clearing the denominators early on by multiplying by the least common denominator (LCD) can simplify the process.

Hallar el valor de m en la ecuación: m/9 + (m-3)/10 = 0.56

Learn how to solve the equation m/9 + (m-3)/10 = 0.56 by eliminating fractions and solving for m. This step-by-step explanation is ideal for students in Grades 8-10 who are learning to handle algebraic equations with fractions.

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