are the ratios 80/96 and 77/84 proportional?
Yes, the ratios 80/96 and 77/84 are proportional.
the canned answer is wrong again
80/96 = 5/6
77/84 = 11/12
so they are not proportional
so, @coolbeans007, how cool was that robo-answer?
You will find that many of the auto-responses in the math area are either just wrong or even ridiculous.
To determine if two ratios are proportional, we need to compare their cross products.
The cross product of the first ratio (80/96) is calculated by multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. So, the cross product is (80 * 84) / (96 * 1).
The cross product of the second ratio (77/84) is calculated by multiplying the numerator of the second ratio by the denominator of the first ratio, and vice versa. So, the cross product is (77 * 96) / (84 * 1).
Now, we compare the two cross products. If they are equal, the ratios are proportional. Otherwise, they are not proportional.
Calculating the cross products gives us (80 * 84) / (96 * 1) = 6720 / 96 = 70 and (77 * 96) / (84 * 1) = 7392 / 84 = 88.
Since the cross products are not equal (70 ≠ 88), we can conclude that the ratios 80/96 and 77/84 are not proportional.