Question

completing a ratio table find the missing values in the ratio table. then write the equivalent ratios.
15.
calories 20 10 90
miles $\frac{1}{6}$ $\frac{2}{3}$

16.
meters 8 4
minutes $\frac{1}{3}$ $\frac{1}{4}$ $\frac{5}{12}$

17.
feet $\frac{1}{24}$ $\frac{1}{8}$
inches $\frac{1}{2}$ 1 $\frac{1}{4}$

18.
tea (cups) 3.75
milk (cups) 1.5 1 3.5 2.5

Explanation:

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Problem 15

Step1: Find unit ratio (cal/mile)

First, calculate the ratio of calories to miles using the first row:
$\frac{20}{\frac{1}{6}} = 20 \times 6 = 120$ calories per mile.

Step2: Find missing calories

Multiply miles by 120:
$\frac{2}{3} \times 120 = 80$

Step3: Find missing miles (row3)

Divide calories by 120:
$\frac{10}{120} = \frac{1}{12}$

Step4: Find missing miles (row4)

Divide calories by 120:
$\frac{90}{120} = \frac{3}{4}$

Step5: List equivalent ratios

$20:\frac{1}{6}$, $80:\frac{2}{3}$, $10:\frac{1}{12}$, $90:\frac{3}{4}$

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Problem 16

Step1: Find unit ratio (meters/minute)

Calculate meters per minute using the first row:
$\frac{8}{\frac{1}{3}} = 8 \times 3 = 24$ meters per minute.

Step2: Find missing minutes (row2)

Divide meters by 24:
$\frac{4}{24} = \frac{1}{6}$

Step3: Find missing meters (row3)

Multiply minutes by 24:
$\frac{1}{4} \times 24 = 6$

Step4: Find missing meters (row4)

Multiply minutes by 24:
$\frac{5}{12} \times 24 = 10$

Step5: List equivalent ratios

$8:\frac{1}{3}$, $4:\frac{1}{6}$, $6:\frac{1}{4}$, $10:\frac{5}{12}$

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Problem 17

Step1: Confirm unit conversion (ft to in)

Since 1 foot = 12 inches, verify the ratio:
$\frac{\frac{1}{2}}{\frac{1}{24}} = \frac{1}{2} \times 24 = 12$ inches per foot.

Step2: Find missing feet (row2)

Divide inches by 12:
$\frac{1}{12}$

Step3: Find missing inches (row3)

Multiply feet by 12:
$\frac{1}{8} \times 12 = \frac{3}{2}$

Step4: Find missing feet (row4)

Divide inches by 12:
$\frac{\frac{1}{4}}{12} = \frac{1}{48}$

Step5: List equivalent ratios

$\frac{1}{24}:\frac{1}{2}$, $\frac{1}{12}:1$, $\frac{1}{8}:\frac{3}{2}$, $\frac{1}{48}:\frac{1}{4}$

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Problem 18

Step1: Find unit ratio (tea/milk)

Calculate tea per cup of milk using the first row:
$\frac{3.75}{1.5} = 2.5$ cups of tea per cup of milk.

Step2: Find missing tea (row2)

Multiply milk by 2.5:
$1 \times 2.5 = 2.5$

Step3: Find missing tea (row3)

Multiply milk by 2.5:
$3.5 \times 2.5 = 8.75$

Step4: Find missing tea (row4)

Multiply milk by 2.5:
$2.5 \times 2.5 = 6.25$

Step5: List equivalent ratios

$3.75:1.5$, $2.5:1$, $8.75:3.5$, $6.25:2.5$

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Answer:

Problem 15

Missing values: Calories = 80, Miles = $\frac{1}{12}$, $\frac{3}{4}$
Equivalent ratios: $20:\frac{1}{6}$, $80:\frac{2}{3}$, $10:\frac{1}{12}$, $90:\frac{3}{4}$

Problem 16

Missing values: Minutes = $\frac{1}{6}$, Meters = 6, 10
Equivalent ratios: $8:\frac{1}{3}$, $4:\frac{1}{6}$, $6:\frac{1}{4}$, $10:\frac{5}{12}$

Problem 17

Missing values: Feet = $\frac{1}{12}$, $\frac{1}{48}$, Inches = $\frac{3}{2}$
Equivalent ratios: $\frac{1}{24}:\frac{1}{2}$, $\frac{1}{12}:1$, $\frac{1}{8}:\frac{3}{2}$, $\frac{1}{48}:\frac{1}{4}$

Problem 18

Missing values: Tea = 2.5, 8.75, 6.25
Equivalent ratios: $3.75:1.5$, $2.5:1$, $8.75:3.5$, $6.25:2.5$