Math / Numbers & Operations

QuestionCOMPLETING A RATIO TABLE Find the missing values in the ratio table. Then write the equivalent ratios. 15. \begin{tabular}{|l|c|c|c|c|} \hline Calories & 20 & & 10 & 90 \\ \hline Miles & $\frac{1}{6}$ & $\frac{2}{3}$ & & \\ \hline \end{tabular} 16. \begin{tabular}{|l|c|c|c|c|} \hline Meters & 8 & 4 & & \\ \hline Minutes & $\frac{1}{3}$ & & $\frac{1}{4}$ & $\frac{5}{12}$ \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The tables represent ratios between two quantities.
2. The missing values can be determined using equivalent ratios.
3. The ratios in each row are consistent across the table.

STEP 2

1. Solve for missing values in the first table (Calories and Miles).
2. Write equivalent ratios for the first table.
3. Solve for missing values in the second table (Meters and Minutes).
4. Write equivalent ratios for the second table.

STEP 3

For the first table, identify the known ratio between Calories and Miles using the first column.
$\frac{20 \text{ Calories}}{\frac{1}{6} \text{ Miles}} = \frac{20}{\frac{1}{6}} = 20 \times 6 = 120$
This means $120$ Calories per Mile.

STEP 4

Use the known ratio to find the missing values:
- For $10$ Calories: $ \frac{10 \text{ Calories}}{x \text{ Miles}} = 120 \Rightarrow x = \frac{10}{120} = \frac{1}{12} \]
- For $90$ Calories: $ \frac{90 \text{ Calories}}{y \text{ Miles}} = 120 \Rightarrow y = \frac{90}{120} = \frac{3}{4} \]

STEP 5

Write the equivalent ratios for the first table:
$\frac{20}{\frac{1}{6}}, \frac{\frac{2}{3}}{8}, \frac{10}{\frac{1}{12}}, \frac{90}{\frac{3}{4}}$

STEP 6

For the second table, identify the known ratio between Meters and Minutes using the first column.
$\frac{8 \text{ Meters}}{\frac{1}{3} \text{ Minutes}} = \frac{8}{\frac{1}{3}} = 8 \times 3 = 24$
This means $24$ Meters per Minute.

STEP 7

Use the known ratio to find the missing values:
- For $4$ Meters: $ \frac{4 \text{ Meters}}{x \text{ Minutes}} = 24 \Rightarrow x = \frac{4}{24} = \frac{1}{6} \]
- For $\frac{1}{4}$ Minutes: $ \frac{z \text{ Meters}}{\frac{1}{4} \text{ Minutes}} = 24 \Rightarrow z = 24 \times \frac{1}{4} = 6 \]

STEP 8

Write the equivalent ratios for the second table:
$\frac{8}{\frac{1}{3}}, \frac{4}{\frac{1}{6}}, \frac{6}{\frac{1}{4}}, \frac{10}{\frac{5}{12}}$
The completed tables with equivalent ratios are:
First Table: \begin{tabular}{|l|c|c|c|c|} \hline \text{Calories} & 20 & 30 & 10 & 90 \\ \hline \text{Miles} & \frac{1}{6} & \frac{2}{3} & \frac{1}{12} & \frac{3}{4} \\ \hline \end{tabular}
Second Table: \begin{tabular}{|l|c|c|c|c|} \hline \text{Meters} & 8 & 4 & 6 & 10 \\ \hline \text{Minutes} & \frac{1}{3} & \frac{1}{6} & \frac{1}{4} & \frac{5}{12} \\ \hline \end{tabular}

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Studdy Solution

STEP 1

1. The tables represent ratios between two quantities.
2. The missing values can be determined using equivalent ratios.
3. The ratios in each row are consistent across the table.

STEP 2

1. Solve for missing values in the first table (Calories and Miles).
2. Write equivalent ratios for the first table.
3. Solve for missing values in the second table (Meters and Minutes).
4. Write equivalent ratios for the second table.

STEP 3

For the first table, identify the known ratio between Calories and Miles using the first column.
$\frac{20 \text{ Calories}}{\frac{1}{6} \text{ Miles}} = \frac{20}{\frac{1}{6}} = 20 \times 6 = 120$
This means $120$ Calories per Mile.

STEP 4

Use the known ratio to find the missing values:
- For $10$ Calories: $ \frac{10 \text{ Calories}}{x \text{ Miles}} = 120 \Rightarrow x = \frac{10}{120} = \frac{1}{12} \]
- For $90$ Calories: $ \frac{90 \text{ Calories}}{y \text{ Miles}} = 120 \Rightarrow y = \frac{90}{120} = \frac{3}{4} \]

STEP 5

Write the equivalent ratios for the first table:
$\frac{20}{\frac{1}{6}}, \frac{\frac{2}{3}}{8}, \frac{10}{\frac{1}{12}}, \frac{90}{\frac{3}{4}}$

STEP 6

For the second table, identify the known ratio between Meters and Minutes using the first column.
$\frac{8 \text{ Meters}}{\frac{1}{3} \text{ Minutes}} = \frac{8}{\frac{1}{3}} = 8 \times 3 = 24$
This means $24$ Meters per Minute.

STEP 7

Use the known ratio to find the missing values:
- For $4$ Meters: $ \frac{4 \text{ Meters}}{x \text{ Minutes}} = 24 \Rightarrow x = \frac{4}{24} = \frac{1}{6} \]
- For $\frac{1}{4}$ Minutes: $ \frac{z \text{ Meters}}{\frac{1}{4} \text{ Minutes}} = 24 \Rightarrow z = 24 \times \frac{1}{4} = 6 \]

STEP 8

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Studdy Solution

STEP 1

1. The tables represent ratios between two quantities.2. The missing values can be determined using equivalent ratios.3. The ratios in each row are consistent across the table.

STEP 2

1. Solve for missing values in the first table (Calories and Miles).2. Write equivalent ratios for the first table.3. Solve for missing values in the second table (Meters and Minutes).4. Write equivalent ratios for the second table.

STEP 3

STEP 4

Use the known ratio to find the missing values:- For 10 10 10 Calories: $ \frac{10 \text{ Calories}}{x \text{ Miles}} = 120 \Rightarrow x = \frac{10}{120} = \frac{1}{12} \]- For 90 90 90 Calories: $ \frac{90 \text{ Calories}}{y \text{ Miles}} = 120 \Rightarrow y = \frac{90}{120} = \frac{3}{4} \]

STEP 5

Write the equivalent ratios for the first table:2016,238,10112,9034\frac{20}{\frac{1}{6}}, \frac{\frac{2}{3}}{8}, \frac{10}{\frac{1}{12}}, \frac{90}{\frac{3}{4}}61​20​,832​​,121​10​,43​90​

STEP 6

STEP 7

STEP 8

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The tables represent ratios between two quantities.
2. The missing values can be determined using equivalent ratios.
3. The ratios in each row are consistent across the table.

1. Solve for missing values in the first table (Calories and Miles).
2. Write equivalent ratios for the first table.
3. Solve for missing values in the second table (Meters and Minutes).
4. Write equivalent ratios for the second table.

Use the known ratio to find the missing values:
- For $10$ Calories: $ \frac{10 \text{ Calories}}{x \text{ Miles}} = 120 \Rightarrow x = \frac{10}{120} = \frac{1}{12} \]
- For $90$ Calories: $ \frac{90 \text{ Calories}}{y \text{ Miles}} = 120 \Rightarrow y = \frac{90}{120} = \frac{3}{4} \]

Write the equivalent ratios for the first table:
$\frac{20}{\frac{1}{6}}, \frac{\frac{2}{3}}{8}, \frac{10}{\frac{1}{12}}, \frac{90}{\frac{3}{4}}$