Which two ratios form a proportion?(1 point)

Question

Responses

420
and 15
4 over 20 and 1 fifth

204
and 25
20 fourths and 2 fifths

420
and 25
4 over 20 and 2 fifths

204
and 15

Answer 1

To determine which two ratios form a proportion, we need to check if the cross-products of the two ratios are equal.

1. 420 and 15: The ratio is \( \frac{420}{15} \).
2. 4 over 20 and 1 fifth: The ratio is \( \frac{4}{20} \) and \( \frac{1}{5} \). We can simplify \( \frac{4}{20} = \frac{1}{5} \), so they are equal.

So, \( \frac{420}{15} \) does not equal \( \frac{1}{5} \), thus they do not form a proportion.

3. 204 and 25: The ratio is \( \frac{204}{25} \).

4. 20 fourths and 2 fifths: The ratio is \( \frac{20}{4} \) and \( \frac{2}{5} \). We can simplify \( \frac{20}{4} = 5 \) and \( 2/5 \) is not equal to \( \frac{5}{1} \), thus they do not form a proportion.

5. 420 and 25: The ratio is \( \frac{420}{25} \).

6. 4 over 20 and 2 fifths: \( \frac{4}{20} \) simplifies to \( \frac{1}{5} \). Therefore, this comparison is \( \frac{420}{25} \) and \( \frac{1}{5} \), which definitely does not hold.

7. 204 and 15: The ratio is \( \frac{204}{15} \).

After checking all options:

None of these pairs of ratios form a proportion that meets the criteria.

If I were to identify another pair, for completeness, it would be best to re-evaluate other options, but out of the options given, none obviously form matching proportions.

If you want correct proportions, please check the ratio notations and clarify if any modifications were incorrect in their simplifications.

Answer 2

a b c or d

Answer 3

Let's analyze the four given options to find the correct pair that forms a proportion:

1. (a) 420 and 15, 4 over 20 and 1 fifth

   • Ratios: \( \frac{420}{15} \) and \( \frac{4}{20} = \frac{1}{5} \)
   • Cross-multiply: \( 420 \times 5 \) vs. \( 1 \times 15 \)
   • \( 2100 \neq 15 \) (Not a proportion)

2. (b) 204 and 25, 20 fourths and 2 fifths

   • Ratios: \( \frac{204}{25} \) and \( \frac{20}{4} = 5 \) and \( \frac{2}{5} \)
   • Cross-multiply: \( 204 \times 5 \) vs. \( 25 \times 2 \)
   • \( 1020 \neq 50 \) (Not a proportion)

3. (c) 420 and 25, 4 over 20 and 2 fifths

   • Ratios: \( \frac{420}{25} \) and \( \frac{4}{20} = \frac{1}{5} \) and \( \frac{2}{5} \)
   • Cross-multiply: \( 420 \times 5 \) vs. \( 25 \times 2 \)
   • \( 2100 \neq 50 \) (Not a proportion)

4. (d) 204 and 15

   • We don't have a matching pair listed for comparison in this option.

After evaluating the four options, none of the choices listed clearly form a proportion when analyzed mathematically.

Please check for adjustments in your options or clarifications that might aid identification, as often proportions require careful arrangements that might not be apparent in verbal listings alone. However, (a) is closest, as it links to multiple fractions relatable, but technically produces no valid conclusion upon numeric checks.