https://file.aiquickdraw.com/mathbot/file/1727330877473cdq8vn4z.jpg

Let's solve each proportion presented in the image:

### a) \(\frac{6}{7} = \frac{9}{a}\)

To find the value of \(a\), we can use cross-multiplication:
\[6 \cdot a = 9 \cdot 7\]
\[6a = 63\]
\[a = \frac{63}{6}\]
\[a = 10.5\]

### b) \(\frac{v}{8} = \frac{7}{6}\)

Similarly, we use cross-multiplication to solve for \(v\):
\[v \cdot 6 = 7 \cdot 8\]
\[6v = 56\]
\[v = \frac{56}{6}\]
\[v = 9.\overline{3}\] (or \(\frac{28}{3}\) as a fraction)

So, the values are:
a) \(a = 10.5\)
b) \(v = 9.\overline{3}\) (or \(\frac{28}{3}\))

Would you like more details on any step of this solution or have any other questions? 

Here are five related questions you might consider:
1. How can you check if your solution to a proportion is correct?
2. What happens if you flip both ratios in a proportion?
3. Can proportions be solved using a method other than cross-multiplication?
4. What are the practical applications of solving proportions in real life?
5. How would you solve a proportion where both ratios include variables?

**Tip:** When solving proportions, ensure you cross-multiply correctly and simplify your fractions where possible to get the most accurate answers.

Solve each proportion: a) 6/7 = 9/a, b) v/8 = 7/6.

Learn how to solve proportions step-by-step using cross-multiplication. Example problems include 6/7 = 9/a and v/8 = 7/6. Ideal for students in Grades 6-8, this guide explains the core concepts of proportions and rational equations.

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