https://file.aiquickdraw.com/mathbot/file/1728598783677ic6ty0kj.jpg

To solve the ratio table, let's first observe the given ratios:

\[
\frac{54}{63}, \frac{72}{84}, \frac{78}{91}
\]

We can reduce these ratios to their simplest forms:

1. \(\frac{54}{63}\) simplifies by dividing both the numerator and denominator by 9:
   \[
   \frac{54}{63} = \frac{6}{7}
   \]
   
2. \(\frac{72}{84}\) simplifies by dividing both the numerator and denominator by 12:
   \[
   \frac{72}{84} = \frac{6}{7}
   \]

3. \(\frac{78}{91}\) simplifies by dividing both the numerator and denominator by 13:
   \[
   \frac{78}{91} = \frac{6}{7}
   \]

All these simplified ratios are equal to \(\frac{6}{7}\), which means that the constant ratio is \(\frac{6}{7}\).

Now, to find the missing values:

1. In the first row, we know that the ratio is also \(\frac{6}{7}\), so if the second column is 7, the corresponding first column value must be 6:
   \[
   \frac{\text{Missing value}}{7} = \frac{6}{7} \implies \text{Missing value} = 6
   \]

2. In the second row, where the second column is 14, we can similarly apply the same ratio:
   \[
   \frac{\text{Missing value}}{14} = \frac{6}{7} \implies \text{Missing value} = 12
   \]

So, the completed table is:

\[
\begin{array}{|c|c|}
\hline
6 & 7 \\
12 & 14 \\
54 & 63 \\
72 & 84 \\
78 & 91 \\
\hline
\end{array}
\]

Would you like further explanation or have any questions?

Here are 5 related questions to deepen understanding:
1. How can you use cross-multiplication to verify if two ratios are equivalent?
2. What happens to the ratio if you multiply both terms by the same number?
3. How do you simplify ratios with larger numbers?
4. Can you create a ratio table for \(\frac{5}{8}\)?
5. Why is it important to simplify ratios when solving problems?

**Tip:** Always check if a ratio can be simplified by dividing both terms by their greatest common divisor (GCD).

Learn how to complete a ratio table by simplifying ratios and applying proportionality. This exercise focuses on filling in missing values and understanding the concept of equivalent ratios. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation