Question

use reasoning to choose the closest estimate of the product. 1. circle the best estimate: 23 × 48 a. 80 b. 800 c. 100 d. 1,000 e. 20 f. 200 explain your reasoning

Explanation:

Step1: Round the numbers

Round 23 to 20 and 48 to 50.

Step2: Calculate the estimated product

Multiply the rounded numbers: \(20\times50 = 1000\)? Wait, no, wait. Wait, 23 is closer to 20 or 25? Wait, maybe a better rounding: 23 ≈ 20, 48 ≈ 50, but also, 23 ≈ 25, 48 ≈ 50? Wait, no, let's do proper estimation. 23 is about 20, 48 is about 50, so 20×50=1000? But wait, 23×48: let's calculate the actual product: 23×48 = 1104. Wait, but the options are 80, 800, 100, 1000, 20, 200. Wait, maybe I rounded wrong. Let's try 23≈20, 48≈50: 20×50=1000. But 23×48=1104, which is close to 1000? Wait, no, 23×48: 20×48=960, 3×48=144, so 960+144=1104. So the closest estimate among the options: 800, 1000, 200. 1104 is closest to 1000? Wait, no, 23×48: let's round 23 to 25 and 48 to 50: 25×50=1250, but that's not an option. Wait, the options are a.80, b.800, c.100, d.1000, e.20, f.200. So 23×48: 20×50=1000, 25×40=1000. Wait, 23×48: 23×48 = (20 + 3)×(50 - 2) = 20×50 - 20×2 + 3×50 - 3×2 = 1000 - 40 + 150 - 6 = 1000 + 110 - 6 = 1104. So the closest estimate is 1000? Wait, but 800: 20×40=800. 23×48: 23 is 20+3, 48 is 40+8. So 20×40=800, 20×8=160, 3×40=120, 3×8=24. So 800+160+120+24=1104. So the actual product is 1104, which is closer to 1000 than 800? Wait, 1104 - 1000 = 104, 1104 - 800 = 304. So 1000 is closer. Wait, but maybe the problem expects rounding to the nearest ten: 23≈20, 48≈50, so 20×50=1000. So the best estimate is d. 1000? Wait, no, wait, maybe I made a mistake. Let's check again. 23×48: 23×48. Let's do 23×50=1150, then subtract 23×2=46, so 1150-46=1104. So 1104 is the actual product. Among the options, 1000 is the closest (1104-1000=104), 800 is 304 away, 200 is 904 away. So the closest is 1000.

Answer:

d. 1,000