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:
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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.
-
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.
-
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.
-
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.
1 answer