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I see the math worksheet you’ve provided. The task asks to solve for \( x \) in several proportion-based equations. Let’s go through each one step-by-step:

### a) \[ \frac{x}{10} = \frac{40}{50} \]

This has already been solved with \( x = 8 \) based on the cross-multiplication.

### b) \[ \frac{x}{42} = \frac{36}{72} \]

Cross-multiply:
\[
x \cdot 72 = 42 \cdot 36
\]
Simplify and solve for \( x \).

### c) \[ \frac{56}{64} = \frac{x}{8} \]

Cross-multiply:
\[
56 \cdot 8 = 64 \cdot x
\]
Solve for \( x \).

### d) \[ \frac{36}{81} = \frac{x}{9} \]

Cross-multiply:
\[
36 \cdot 9 = 81 \cdot x
\]
Solve for \( x \).

### e) \[ \frac{x}{2056} = \frac{3}{4} \]

Cross-multiply:
\[
x \cdot 4 = 2056 \cdot 3
\]
Solve for \( x \).

### f) \[ \frac{x}{15} = \frac{288}{360} \]

Cross-multiply:
\[
x \cdot 360 = 15 \cdot 288
\]
Solve for \( x \).

### g) \[ \frac{3}{5} = \frac{x}{460} \]

Cross-multiply:
\[
3 \cdot 460 = 5 \cdot x
\]
Solve for \( x \).

### h) \[ \frac{x}{594} = \frac{11}{99} \]

Cross-multiply:
\[
x \cdot 99 = 11 \cdot 594
\]
Solve for \( x \).

Would you like me to go through the specific solutions for each equation? Let me know if you'd like the detailed steps.

Here are 5 related questions that expand on proportion and cross-multiplication:
1. How do you simplify a ratio before solving for \( x \) in proportion problems?
2. What is the role of cross-multiplication in solving ratios and fractions?
3. Can proportion problems be solved using decimals instead of fractions? Why or why not?
4. How do you check your answer after solving for \( x \) in a proportion equation?
5. How do proportions relate to similar triangles in geometry?

**Tip:** Always check if the fractions in proportion problems can be simplified before cross-multiplying to make calculations easier!

Solve for x in the provided proportion-based equations, such as x/42 = 36/72 and x/15 = 288/360.

Explore how to solve proportion problems such as x/42 = 36/72 using cross-multiplication. This lesson covers proportion concepts and the steps to solve for x in basic algebraic equations. Ideal for students in Grades 7-9.

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