Question

"Emily estimated 163% of 32 using the distributive property, as shown.

Emily’s work:
(100 percent) (30) + (60 percent) (30) = (1.0) (30) + (0.60) (30) = 30 + 18 = 48.
Which of the following statements is true?
a The estimate is greater than the actual answer because both values were rounded down.
b The estimate is greater than the actual answer because both values were rounded up.
c The estimate is less than the actual answer because both values were rounded down.
d The estimate is less than the actual answer because both values were rounded up."

Answer 1

Emily's estimate of 48 is less than the actual answer because she rounded both the percentage (163% to 160%) and the number (32 to 30) down. Therefore, the correct answer is that the estimate is less than the actual answer because both values were rounded down.

Step-by-step explanation:

The student question presents a scenario where Emily estimated 163% of 32 using the distributive property. By breaking down the percentage into 100% and 60% of 30 (instead of 32), she reached an estimate of 48. To determine whether the estimate is greater than or less than the actual answer and why, let's first calculate the actual answer. We do this by converting the percentage to a decimal and multiplying by the given number: 1.63 × 32 = 52.16. Comparing the estimate (48) with the actual answer (52.16), we can see that the estimate is less than the actual value.

Emily rounded both values, 163% to 160% (or 1.63 to 1.60) and 32 to 30, down to make the mental calculation easier. Therefore, the correct statement about Emily's estimate is that it is less than the actual answer because both values were rounded down. Hence, the correct answer is option (c).