Question

Which pair of ratios are proportional?

Select the two pairs of ratios that are proportional.

Get Help Here
Responses

34
and 914

3 fourths and 9 over 14

15
and 315

1 fifth and 3 over 15

621
and 27

6 over 21 and 2 sevenths

1945
and 615

19 over 45 and 6 over 15
R

Answer 1

To determine which pairs of ratios are proportional, we can cross-multiply the fractions and check if the products are equal. A pair of ratios \( \frac{a}{b} \) and \( \frac{c}{d} \) are proportional if \( a \times d = b \times c \).

Let’s evaluate the provided pairs one by one:

1. **34 and 914** and **3/4 and 9/14**
- Cross multiply: \( 34 \times 14 \) and \( 3 \times 914 \)
- \( 34 \times 14 = 476 \)
- \( 3 \times 914 = 2742 \)
- Not proportional.

2. **15 and 315** and **1/5 and 3/15**
- Cross multiply: \( 15 \times 15 \) and \( 1 \times 315 \)
- \( 15 \times 15 = 225 \)
- \( 1 \times 315 = 315 \)
- Not proportional.

3. **621 and 27** and **6/21 and 2/7**
- Cross multiply: \( 621 \times 7 \) and \( 27 \times 6 \)
- \( 621 \times 7 = 4347 \)
- \( 27 \times 6 = 162 \)
- Not proportional.

4. **1945 and 615** and **19/45 and 6/15**
- Cross multiply: \( 1945 \times 15 \) and \( 615 \times 19 \)
- \( 1945 \times 15 = 29175 \)
- \( 615 \times 19 = 11685 \)
- Not proportional.

It looks like none of the pairs provided are proportional. However, to find out which pairs are proportional, let's check using decimal or direct division approach for 3/4 and 9/14:

- \( 3/4 = 0.75 \)
- \( 9/14 \approx 0.642857 \)
- Not equal, thus not proportional.

Similarly for:
- \( 1/5 = 0.2 \)
- \( 3/15 = 0.2 \)
- Equal, hence proportional.

Continuing with our checks, it appears only **1/5 and 3/15** are proportional.

In conclusion, the correct answer, among the presented pairs, would be:

- \(1/5\) and \(3/15\) are proportional.
- There are no other pairs that are proportional in the options provided.