Certainly! To determine which of the given ratios is equivalent to the ratio 13:15, we can use the principle of cross-multiplication. Two ratios \(\(\frac{a}{b}\)\) and \(\(\frac{c}{d}\)\) are equivalent if \(\(a \times d = b \times c\)\).
Let's analyze each option step by step:
1. Option A: 39 to 30
We need to check if \(\(\frac{13}{15}\)\) is equivalent to \(\(\frac{39}{30}\)\).
Cross-multiply:
\(\[
13 \times 30 \quad \text{and} \quad 15 \times 39
\]\)
Calculate both sides:
\(\[
13 \times 30 = 390
\]\)
\(\[
15 \times 39 = 585
\]\)
Since 390 does not equal 585, the ratios are not equivalent.
2. Option B: 45 to 26
We need to check if \(\(\frac{13}{15}\)\) is equivalent to \(\(\frac{45}{26}\)\).
Cross-multiply:
\(\[
13 \times 26 \quad \text{and} \quad 15 \times 45
\]\)
Calculate both sides:
\(\[
13 \times 26 = 338
\]\)
\(\[
15 \times 45 = 675
\]\)
Since 338 does not equal 675, the ratios are not equivalent.
3. Option C: 26 to 45
We need to check if \(\(\frac{13}{15}\)\) is equivalent to \(\(\frac{26}{45}\)\).
Cross-multiply:
\(\[
13 \times 45 \quad \text{and} \quad 15 \times 26
\]\)
Calculate both sides:
\(\[
13 \times 45 = 585
\]\)
\(\[
15 \times 26 = 390
\]\)
Since 585 does not equal 390, the ratios are not equivalent.
4. Option D: 39 to 45
We need to check if \(\(\frac{13}{15}\)\) is equivalent to \(\(\frac{39}{45}\)\).
Cross-multiply:
\(\[
13 \times 45 \quad \text{and} \quad 15 \times 39
\]\)
Calculate both sides:
\(\[
13 \times 45 = 585
\]\)
\(\[
15 \times 39 = 585
\]\)
Since 585 equals 585, the ratios are equivalent.
Therefore, the ratio equivalent to 13:15 is found in Option D: 39 to 45.
