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Solving rationale equation by cross multiplication 

To solve the equation \( \frac{1}{3} + \frac{4}{5} = \frac{x}{9} \), we will follow these steps:

### Step 1: Find a common denominator for the left-hand side
We need to add \( \frac{1}{3} \) and \( \frac{4}{5} \). To do this, we first find the least common denominator (LCD) of 3 and 5, which is 15.

Now rewrite the fractions:
\[
\frac{1}{3} = \frac{5}{15}, \quad \frac{4}{5} = \frac{12}{15}
\]

Now, add the two fractions:
\[
\frac{1}{3} + \frac{4}{5} = \frac{5}{15} + \frac{12}{15} = \frac{17}{15}
\]

### Step 2: Set up the equation
Now the equation becomes:
\[
\frac{17}{15} = \frac{x}{9}
\]

### Step 3: Cross-multiply
To solve for \( x \), we cross-multiply:
\[
17 \times 9 = 15 \times x
\]
This simplifies to:
\[
153 = 15x
\]

### Step 4: Solve for \( x \)
Now, divide both sides by 15 to isolate \( x \):
\[
x = \frac{153}{15} = 10.2
\]

Thus, \( x = 10.2 \).

Would you like further details on any part of the process, or have any questions?

Here are 5 related questions for further exploration:
1. How do you add fractions with different denominators?
2. What are some methods to find the least common denominator of two numbers?
3. Can you apply cross-multiplication in any type of equation, or just rational ones?
4. How would you solve if the equation had multiple variables instead of just \( x \)?
5. What if the denominator on the right-hand side was a variable—how would you handle that?

**Tip**: Always simplify fractions before proceeding with further operations to reduce the chance of calculation errors.

Solve the equation 1/3 + 4/5 = x/9 using cross multiplication.

Learn how to solve the equation 1/3 + 4/5 = x/9 step by step using cross multiplication. This example demonstrates how to add fractions with different denominators and use cross multiplication to find the value of x. Suitable for students in Grades 6-8.

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