Question

Estimate the sum.
7⅘ + 3.1
A) 5.9
B) 11
C) 8.0
D) 16

Answer 1

Rounding 7⅘ to 8, adding to 3.1 yields 11.1. Rounding to the nearest whole number, the correct answer is 8.0 (option C).

Step-by-step explanation:

To estimate the sum of 7⅘ and 3.1, we can round 7⅘ to 8 and then simply add it to 3.1. Thus, 8 + 3.1 equals 11.1. However, the provided options are in whole numbers, so we round 11.1 to the nearest whole number, which is 11. Therefore, the correct answer is option B) 11.

Now, let's delve into the detailed explanation. Firstly, we have the mixed number 7⅘. To add this to 3.1, we convert 7⅘ to an improper fraction, yielding
`\( (39)/(5) \)`. The sum of
`\( (39)/(5) + 3.1 \)` equals
`\( (39)/(5) + (31)/(10) \),`which, when finding a common denominator, becomes
`\( (78)/(10) + (31)/(10) \)`. Adding these fractions results in
`\( (109)/(10) \).` To simplify, we divide the numerator by the denominator, yielding 10 with a remainder of 9. Thus,
`\( (109)/(10) \) is equivalent to 10ⅉ9/10.`

Converting this back to a mixed number gives us 11ⅉ9/10. Rounding this to the nearest whole number, as per the provided options, results in 11. Therefore, the correct answer is B) 11. It's important to note that rounding is a crucial step in obtaining a whole number answer when estimating mathematical operations with mixed numbers and decimals.