Solved on Jan 26, 2024

Determine if the ratios $10: 16 = 5: 8$ form a proportion. Are these ratios a proportion? No/Yes

STEP 1

Assumptions
1. We are given two ratios, $10:16$ and $5:8$ .
2. To determine if these ratios form a proportion, we need to check if the cross products of the ratios are equal.

STEP 2

A proportion exists when two ratios are equal, which can be expressed as:
$\frac{a}{b} = \frac{c}{d}$

STEP 3

For the given ratios $10:16$ and $5:8$ , we can write them as fractions:
$\frac{10}{16} \quad \text{and} \quad \frac{5}{8}$

STEP 4

To check if these two fractions are equal, we can cross-multiply and compare the products:
$a \cdot d = b \cdot c$

STEP 5

Substitute the values from the given ratios into the cross-multiplication formula:
$10 \cdot 8 = 16 \cdot 5$

STEP 6

Calculate the cross products:
$10 \cdot 8 = 80$ $16 \cdot 5 = 80$

STEP 7

Compare the results of the cross products:
$80 = 80$

STEP 8

Since the cross products are equal, the two ratios form a proportion:
$\frac{10}{16} = \frac{5}{8}$
Therefore, the answer is "Yes", the ratios $10:16$ and $5:8$ are a proportion.

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Determine if the ratios $10: 16 = 5: 8$ form a proportion. Are these ratios a proportion? No/Yes

STEP 1

Assumptions
1. We are given two ratios, $10:16$ and $5:8$ .
2. To determine if these ratios form a proportion, we need to check if the cross products of the ratios are equal.

STEP 2

A proportion exists when two ratios are equal, which can be expressed as:
$\frac{a}{b} = \frac{c}{d}$

STEP 3

For the given ratios $10:16$ and $5:8$ , we can write them as fractions:
$\frac{10}{16} \quad \text{and} \quad \frac{5}{8}$

STEP 4

To check if these two fractions are equal, we can cross-multiply and compare the products:
$a \cdot d = b \cdot c$

STEP 5

Substitute the values from the given ratios into the cross-multiplication formula:
$10 \cdot 8 = 16 \cdot 5$

STEP 6

Calculate the cross products:
$10 \cdot 8 = 80$ $16 \cdot 5 = 80$

STEP 7

Compare the results of the cross products:
$80 = 80$

STEP 8

Since the cross products are equal, the two ratios form a proportion:
$\frac{10}{16} = \frac{5}{8}$
Therefore, the answer is "Yes", the ratios $10:16$ and $5:8$ are a proportion.

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Determine if the ratios 10:16=5:810: 16 = 5: 810:16=5:8 form a proportion. Are these ratios a proportion? No/Yes

STEP 1

Assumptions1. We are given two ratios, 10:1610:1610:16 and 5:85:85:8.2. To determine if these ratios form a proportion, we need to check if the cross products of the ratios are equal.

STEP 2

A proportion exists when two ratios are equal, which can be expressed as:ab=cd\frac{a}{b} = \frac{c}{d}ba​=dc​

STEP 3

For the given ratios 10:1610:1610:16 and 5:85:85:8, we can write them as fractions:1016and58\frac{10}{16} \quad \text{and} \quad \frac{5}{8}1610​and85​

STEP 4

To check if these two fractions are equal, we can cross-multiply and compare the products:a⋅d=b⋅ca \cdot d = b \cdot ca⋅d=b⋅c

STEP 5

Substitute the values from the given ratios into the cross-multiplication formula:10⋅8=16⋅510 \cdot 8 = 16 \cdot 510⋅8=16⋅5

STEP 6

Calculate the cross products:10⋅8=8010 \cdot 8 = 8010⋅8=80 16⋅5=8016 \cdot 5 = 8016⋅5=80

STEP 7

Compare the results of the cross products:80=8080 = 8080=80

STEP 8

Since the cross products are equal, the two ratios form a proportion:1016=58\frac{10}{16} = \frac{5}{8}1610​=85​Therefore, the answer is "Yes", the ratios 10:1610:1610:16 and 5:85:85:8 are a proportion.

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

Determine if the ratios $10: 16 = 5: 8$ form a proportion. Are these ratios a proportion? No/Yes

Assumptions
1. We are given two ratios, $10:16$ and $5:8$ .
2. To determine if these ratios form a proportion, we need to check if the cross products of the ratios are equal.

A proportion exists when two ratios are equal, which can be expressed as:
$\frac{a}{b} = \frac{c}{d}$

For the given ratios $10:16$ and $5:8$ , we can write them as fractions:
$\frac{10}{16} \quad \text{and} \quad \frac{5}{8}$

To check if these two fractions are equal, we can cross-multiply and compare the products:
$a \cdot d = b \cdot c$

Substitute the values from the given ratios into the cross-multiplication formula:
$10 \cdot 8 = 16 \cdot 5$

Calculate the cross products:
$10 \cdot 8 = 80$ $16 \cdot 5 = 80$

Compare the results of the cross products:
$80 = 80$

Since the cross products are equal, the two ratios form a proportion:
$\frac{10}{16} = \frac{5}{8}$
Therefore, the answer is "Yes", the ratios $10:16$ and $5:8$ are a proportion.