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