Complete the Ratio Tables with Missing Values

Math Problem Statement

Complete the ratio tables provided in the image by filling in the missing values based on proportional reasoning.

I see that you've uploaded a ratio table worksheet. Let me solve the problems in the image step by step.

The given ratios are $12:11$ .

The multiplier to move from $12$ to $24$ is $\times 2$ , so the second number is $11 \times 2 = 22$ .
The multiplier to move from $11$ to $33$ is $\times 3$ , so the first number is $12 \times 3 = 36$ .
For $12$ to $60$ , the multiplier is $\times 5$ , so the second number is $11 \times 5 = 55$ .

Completed table for (1):

\hline 12 & 11 \\ 24 & 22 \\ 36 & 33 \\ 60 & 55 \\ \hline \end{array}$$ --- ### Problem (3): The given ratios are $$1:9$$. - $$1$$ to $$2$$: multiplier $$\times 2$$, so $$9 \times 2 = 18$$. - $$9$$ to $$27$$: multiplier $$\times 3$$, so $$1 \times 3 = 3$$. - $$1$$ to $$5$$: multiplier $$\times 5$$, so $$9 \times 5 = 45$$. **Completed table for (3):** $$\begin{array}{|c|c|} \hline 1 & 9 \\ 2 & 18 \\ 3 & 27 \\ 5 & 45 \\ \hline \end{array}$$ --- ### Problem (5): The given ratios are $$6:8$$. - $$6$$ to $$8$$: multiplier $$\times \frac{4}{3}$$, so $$8$$ to the next entry is $$8 \times \frac{4}{3} = 28$$. - $$8$$ to $$35$$: multiplier equivalentContinuing from where I left off for **Problem (5)**: The given ratio is $$6:8$$. 1. **Row 1** (6:8) is already provided. 2. To find the missing number when $$8 \to 28$$: - Multiplier is $$28 / 8 = 3.5$$. - Thus, $$6 \times 3.5 = 21$$. 3. To find the missing number when $$6 \to 12$$: - Multiplier is $$12 / 6 = 2$$. - Thus, $$8 \times 2 = 16$$. 4. For $$35$$ in the second column: - Multiplier from $$8 \to 35$$ is $$35 / 8 = 4.375$$. - $$6 \times 4.375 = 26.25$$. **Completed table for (5):** $$\begin{array}{|c|c|} \hline 6 & 8 \\ 21 & 28 \\ 26.25 & 35 \\ 12 & 16 \\ \hline \end{array}$$ --- If you need clarifications or more explanations, let me know. Would you like me to complete the other parts of the worksheet or assist further?

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