Solve the proportion.

*z*

21

 = 

8

14

To solve the proportion \(\frac{z}{21} = \frac{8}{14}\), you can use cross-multiplication. Here are the steps:

1. Cross multiply the terms:
   \[
   z \times 14 = 8 \times 21
   \]

2. Calculate the right side:
   \[
   14z = 168
   \]

3. Solve for \(z\) by dividing both sides by 14:
   \[
   z = \frac{168}{14}
   \]

4. Simplify the fraction:
   \[
   z = 12
   \]

So, the solution is \(z = 12\).

Would you like more details on any of the steps?

Here are five related questions to consider:

1. How would you solve \(\frac{a}{18} = \frac{9}{12}\)?
2. What is the value of \(x\) in \(\frac{x}{30} = \frac{15}{25}\)?
3. Can you solve \(\frac{y}{40} = \frac{20}{32}\)?
4. What does cross-multiplication help achieve in solving proportions?
5. How can you determine if a proportion is correct?

**Tip:** When working with proportions, always ensure the ratio comparisons are between like terms (e.g., lengths to lengths, weights to weights). This ensures accuracy in solving.

Learn how to solve the proportion z/21 = 8/14 with a detailed step-by-step solution. This problem covers key concepts in proportions and cross-multiplication. Suitable for students in Grades 7-9.

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