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

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.