13/3=26/y solve it using fraction busting

To solve the equation \( \frac{13}{3} = \frac{26}{y} \) using fraction busting, follow these steps:

### Step-by-Step Solution:

1. **Start with the equation:**
   \[
   \frac{13}{3} = \frac{26}{y}
   \]

2. **Multiply both sides by the least common denominator (LCD):**
   The LCD here is \( 3y \), which will eliminate the denominators.

   \[
   3y \cdot \frac{13}{3} = 3y \cdot \frac{26}{y}
   \]

3. **Simplify both sides:**
   On the left-hand side, the \( 3 \)'s cancel out, leaving \( 13y \).
   On the right-hand side, the \( y \)'s cancel out, leaving \( 26 \times 3 \).

   So, the equation becomes:
   \[
   13y = 78
   \]

4. **Solve for \( y \):**
   Divide both sides by 13 to isolate \( y \).

   \[
   y = \frac{78}{13}
   \]

   \[
   y = 6
   \]

### Final Answer:
The solution is \( y = 6 \).

Would you like more details or have any questions?

Here are 5 related questions to extend your understanding:
1. How would you solve \( \frac{5}{x} = \frac{10}{12} \)?
2. Can you solve \( \frac{a}{b} = \frac{c}{d} \) for \( b \)?
3. What is the general approach for solving proportions?
4. How can cross-multiplying help solve fractional equations?
5. What happens if both sides of the equation have more complex expressions?

**Tip:** When solving equations with fractions, it's often useful to multiply by the least common denominator (LCD) to simplify the equation quickly.

Learn how to solve the equation 13/3 = 26/y using the fraction busting method. This tutorial provides a step-by-step solution to find the value of y, emphasizing key algebraic concepts such as cross-multiplication and proportionality. Suitable for students in Grades 6-8.

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