Choose the best estimate for the multiplication problem below.
$\begin{array}{r}24 \\ \times \quad 55 \\ \hline\end{array}$
A. 1500
B. 1000
C. 1800
D. 1200
Answer (1)
Calculate the exact product: 24 × 55 = 1320 .
Compare the exact product to the given estimates: 1500, 1000, 1800, and 1200.
Find the differences between the exact product and each estimate: ∣1500 − 1320∣ = 180 , ∣1000 − 1320∣ = 320 , ∣1800 − 1320∣ = 480 , ∣1200 − 1320∣ = 120 .
Choose the estimate with the smallest difference: 1200 .
Explanation
Problem Analysis We are given the multiplication problem 24 × 55 and asked to choose the best estimate from the options: 1500, 1000, 1800, and 1200. To do this, we will first calculate the exact product and then compare it to the given estimates.
Calculating the Exact Product Let's calculate the exact product of 24 × 55 .
Exact Product The exact product is 24 × 55 = 1320 .
Comparing with Estimates Now, we compare the exact product, 1320, to the given estimates: 1500, 1000, 1800, and 1200. We want to find the estimate that is closest to 1320.
Calculating Differences
The difference between 1320 and 1500 is ∣1500 − 1320∣ = 180 .
The difference between 1320 and 1000 is ∣1000 − 1320∣ = 320 .
The difference between 1320 and 1800 is ∣1800 − 1320∣ = 480 .
The difference between 1320 and 1200 is ∣1200 − 1320∣ = 120 .
Identifying the Closest Estimate The estimate closest to 1320 is 1200, since the difference between them is the smallest (120).
Final Answer Therefore, the best estimate for the multiplication problem 24 × 55 is 1200 .
Examples
Estimating multiplication problems is useful in everyday situations, such as when you're shopping and want to quickly calculate the total cost of multiple items. For example, if you're buying 24 items that cost $55 each, you can estimate the total cost by rounding the numbers to 20 and 60, respectively, and then multiplying them to get an estimate of $1200. This helps you quickly determine if you have enough money or if the price is reasonable without needing to perform the exact calculation.
