Question
correct. pachel and Brian are trying to estimate this product \( 7 \times 538 \) computing \( 7 \times 500 \). (a) pachel esti-ates this pr What is her estimate? \[ 7 \times 500=3500 \] (b) Brian estimates this product by computing \( 7 \times 600 \). What is his estimate? \[ 7 \times 600=4000 \] (c) whose estinate is docer to \( 7 \times 5382 \) Rachells estimate is closer Briarl's estimate is doser Their estimates are equally cose
Ask by Schultz Martinez. in the United States
Feb 25,2025
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Answer
(a) Pachel's estimate is 3500.
(b) Brian's estimate is 4000.
(c) Brian's estimate is closer to the actual product.
Solution
We are given that the actual product is
7 × 538.
(a) Pachel’s method is to multiply 7 by 500. So her estimate is
7 × 500 = 3500.
(b) Brian’s method is to multiply 7 by 600. (According to the problem his multiplication is shown as 7 × 600 = 4000.) His estimate is 4000.
(c) To decide whose estimate is closer to the real product, we first compute the exact product:
7 × 538 = 7 × (500 + 38) = 7×500 + 7×38 = 3500 + 266 = 3766.
Now, find the errors:
Error for Pachel: |3766 – 3500| = 266
Error for Brian: |3766 – 4000| = 234
Since 234 is less than 266, Brian’s estimate is closer to the actual product.
Thus, the answers are:
(a) 3500
(b) 4000
(c) Brian’s estimate is closer.
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Simplify this solution Extra Insights
Rachell is estimating \( 7 \times 500 \) which gives her an estimate of 3500. On the other hand, Brian's estimate \( 7 \times 600 \) equals 4000. To determine whose estimate is closer to \( 7 \times 538 \), we can compare the distances of each estimate from the actual calculation. The actual product \( 7 \times 538 \) equals 3766. Calculating the distance: For Rachell: \( |3500 - 3766| = 266 \) For Brian: \( |4000 - 3766| = 234 \) So, Brian's estimate is closer to the actual product \( 7 \times 538 \). Brian's estimate is closer.
