Final answer:
No, the ratios 5:37 and 7:53 are not proportional because the cross products are not equal (265 ≠ 259). This is determined by the method of cross-multiplication.
Step-by-step explanation:
To determine if the ratios 5:37 and 7:53 are proportional, one could set them up as fractions and see if they are equivalent by cross-multiplying. Proportionality between two ratios means that one ratio is a scaled version of the other, maintaining the same relationship between the numbers. If the product of the means equals the product of the extremes, the ratios are proportional.
Checking Proportionality
For the ratios 5:37 and 7:53, we can write two fractions as 5/37 and 7/53 and perform the cross-multiplication to check for proportionality.
Using cross-multiplication, compare 5 \(\times\) 53 to 37 \(\times\) 7:
5 \(\times\) 53 = 265
37 \(\times\) 7 = 259
Since 265 does not equal 259, the ratios 5:37 and 7:53 are not proportional.
This demonstrates an important concept in mathematics that involves setting up and solving proportions to compare ratios.