We are given the equation:

\[
\frac{20}{8} = \frac{4k}{32}
\]

### Step 1: Simplify both fractions
Simplify each fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

For \( \frac{20}{8} \), the GCD of 20 and 8 is 4, so:

\[
\frac{20}{8} = \frac{20 \div 4}{8 \div 4} = \frac{5}{2}
\]

For \( \frac{4k}{32} \), the GCD of 4 and 32 is 4, so:

\[
\frac{4k}{32} = \frac{4k \div 4}{32 \div 4} = \frac{k}{8}
\]

Now, the equation becomes:

\[
\frac{5}{2} = \frac{k}{8}
\]

### Step 2: Use fraction busting (cross-multiplication)
To eliminate the fractions, cross-multiply:

\[
5 \cdot 8 = 2 \cdot k
\]

This simplifies to:

\[
40 = 2k
\]

### Step 3: Solve for \( k \)
To solve for \( k \), divide both sides of the equation by 2:

\[
k = \frac{40}{2} = 20
\]

### Final Answer:
\[
k = 20
\]

Would you like a detailed explanation of any step, or do you have any questions?

Here are some related questions you could explore:

1. What is fraction busting, and how is it used in solving equations?
2. How do you simplify fractions?
3. Can you solve an equation involving more than one variable?
4. What are the methods to find the GCD of two numbers?
5. How does cross-multiplication help solve proportions?

**Tip:** Always simplify fractions at the start—it makes the math easier later!

20/8 = 4k/32 solve using fraction busting

Learn how to solve the proportion 20/8 = 4k/32 using fraction busting and cross-multiplication. This step-by-step solution simplifies fractions, uses the GCD, and demonstrates cross-multiplication to find k = 20. Ideal for students in Grades 6-8.

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