Which expression has an estimated product of 45?
A. $44.7 \times 2.1$
B. $7.5 \times 8.4$
C. $8.7 \times 5.28$
D. $38.1 \times 7.3$
Answer (2)
After estimating the products of the given expressions by rounding, the expression 8.7 × 5.28 is the only one that has an estimated product of 45. The other options yield products that are significantly different from 45. Thus, the correct answer is option C.
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Round each number in the expressions to the nearest whole number.
Multiply the rounded numbers to estimate the product.
44.7 × 2.1 estimates to 45 × 2 = 90 .
7.5 × 8.4 estimates to 8 × 8 = 64 .
8.7 × 5.28 estimates to 9 × 5 = 45 .
38.1 × 7.3 estimates to 38 × 7 = 266 .
The expression with an estimated product of 45 is 8.7 × 5.28 .
Explanation
Problem Analysis We are given four multiplication expressions and asked to identify the one with an estimated product of 45. To do this, we will estimate each product by rounding each number in the expression to the nearest whole number and then multiplying.
Estimating the First Product First, let's estimate the product of 44.7 × 2.1 . Rounding each number to the nearest whole number, we get 45 × 2 = 90 .
Estimating the Second Product Next, let's estimate the product of 7.5 × 8.4 . Rounding each number to the nearest whole number, we get 8 × 8 = 64 .
Estimating the Third Product Now, let's estimate the product of 8.7 × 5.28 . Rounding each number to the nearest whole number, we get 9 × 5 = 45 .
Estimating the Fourth Product Finally, let's estimate the product of 38.1 × 7.3 . Rounding each number to the nearest whole number, we get 38 × 7 = 266 .
Finding the Expression with Estimated Product of 45 Comparing the estimated products, we see that 8.7 × 5.28 has an estimated product of 45.
Examples
Estimating products is useful in everyday situations, such as when you are grocery shopping and want to quickly estimate the total cost of your items. By rounding the prices of the items to the nearest dollar and then multiplying, you can get a rough estimate of the total cost before you get to the checkout. This can help you stay within your budget and avoid any surprises at the register. For example, if you are buying 5 items that cost $2.95, $4.05, $1.98, $6.10, and $3.02, you can estimate the total cost by rounding each price to the nearest dollar: $3 + $4 + $2 + $6 + $3 = $18. So, you know that your total bill will be around $18.
