Final answer:
The ratios 3/4 and 27/36 are proportional because upon simplifying the second ratio, it equals the first, and the cross-multiplication of the ratios also shows they are equal. This implies that these ratios have the same scale factor.
Step-by-step explanation:
Are the Ratios Proportional?
To determine whether the ratios 3/4 and 27/36 are proportional, we need to compare them by simplifying one or both of the ratios or by applying cross-multiplication.
Simplification Method
Simplify the second ratio: 27/36 can be divided by 9 to get 3/4, which is the same as the first ratio. Thus, the ratios are proportional.
Cross-Multiplication Method
Cross-multiply the ratios: 3*36 should equal 4*27. Indeed, 108 equals 108, so the ratios are proportional.
Being proportional means that one ratio can be obtained from the other by multiplying or dividing both terms by the same number. These ratios represent the idea of scale factor, which is used in real-world applications like converting actual dimensions using a unit scale in mapping or constructing models.