Do the ratios 3/12 and 7/21 form a proportion?
Understand the Problem
The question is asking whether two ratios, 3/12 and 7/21, form a proportion. To determine this, we need to check if the cross-products of the ratios are equal.
Answer
No, they do not form a proportion.
Answer for screen readers
No, they do not form a proportion.
Steps to Solve
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Identify the ratios The two ratios given are $\frac{3}{12}$ and $\frac{7}{21}$.
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Set up the cross-products To determine if they form a proportion, we need to check if the cross-products are equal: $$ 3 \times 21 \quad \text{and} \quad 7 \times 12 $$
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Calculate the cross-products Calculating the cross-products gives: $$ 3 \times 21 = 63 $$ and $$ 7 \times 12 = 84 $$
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Compare the results Now, compare the two results: $$ 63 \neq 84 $$
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Conclusion about proportions Since the cross-products are not equal, the ratios do not form a proportion.
No, they do not form a proportion.
More Information
A proportion is an equation that states that two ratios are equal. In this case, since the cross-products were not equal, the two ratios don't form a proportion.
Tips
- Forgetting to multiply correctly when finding cross-products.
- Assuming that two ratios are proportional simply because they seem similar. Always check the cross-products.
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