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Percent Increase and Decrease

Question 5 • DAEP - Math 7 A (20 DAY TERM)

Why is the percent increase from 45 to 75 not equal to the percent decrease from 75 to 45? Select three options.

Answer
A
The amount of change is different for the percent increase and the percent decrease.
B
The ratio of the percent increase is not the same as the percent decrease.
C
The ratio for the percent increase has a smaller denominator than the percent decrease.
D
The ratio for the percent increase has a different numerator than the percent decrease.
E
The original amount for the percent increase is different from the original amount for the percent decrease.

Explanation

Both changes are 30, but percent change is measured relative to the starting amount. The increase is 30 ÷ 45 = 2/3, while the decrease is 30 ÷ 75 = 2/5, so the ratios differ. The increase uses the smaller denominator, and the original amounts are different; the numerators are the same, so A and D do not apply.

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