Decimal Operations: Add, Subtract, Multiply, Divide — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
To estimate 4.87 + 3.14, round both to the nearest ten: 0 + 0 = 0.
Corrected: To estimate 4.87 + 3.14, round both to the nearest whole number: 5 + 3 = 8.
The corrected sentence is: "To estimate 4.87 + 3.14, round both to the nearest whole number: 5 + 3 = 8." The error was rounded to wrong place value: the original sentence "To estimate 4.87 + 3.14, round both to the nearest ten: 0 + 0 = 0." needed to be fixed.
2. Fix the sentence:
9.52 rounded to the nearest whole number is 9 because the tenths digit is 5.
Corrected: 9.52 rounded to the nearest whole number is 10 because the tenths digit 5 means you round up.
The corrected sentence is: "9.52 rounded to the nearest whole number is 10 because the tenths digit 5 means you round up." The error was incorrect rounding rule application: the original sentence "9.52 rounded to the nearest whole number is 9 because the tenths digit is 5." needed to be fixed.
3. Fix the sentence:
Estimating 7.8 × 4.2 gives about 28 because 7 × 4 = 28.
Corrected: Estimating 7.8 × 4.2 gives about 32 because 8 × 4 = 32 when you round 7.8 up to 8.
The corrected sentence is: "Estimating 7.8 × 4.2 gives about 32 because 8 × 4 = 32 when you round 7.8 up to 8." The error was rounded 7.8 down instead of up: the original sentence "Estimating 7.8 × 4.2 gives about 28 because 7 × 4 = 28." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 6.49 rounded to the nearest whole number is 6.
The answer is 6. The tenths digit is 4, which is less than 5, so 6.49 rounds down to 6.
2. To estimate 11.7 − 4.3, round each to get 12 − 4 = 8.
The answer is 12 − 4 = 8. Rounding 11.7 up to 12 and 4.3 down to 4 gives a quick estimate of 8, which is close to the exact answer of 7.4.
3. 3.45 rounded to the nearest tenth is 3.5.
The answer is 3.5. The hundredths digit is 5, so by the "5 or more, round up" rule the tenths digit increases from 4 to 5.
4. An estimate for 5.1 × 7.9 using rounding is about 40.
The answer is 40. Rounding 5.1 to 5 and 7.9 to 8 gives 5 × 8 = 40, a quick estimate near the exact product of 40.29.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A shirt costs $14.89 and socks cost $6.25. Estimate the total. Is $20 enough to buy both?
Sample answer: Round to $15 + $6 = $21, so $20 is probably not enough. The exact total is $21.14.
A good answer includes: Round to $15 + $6 = $21, so $20 is probably not enough. The exact total is $21.14.
2. Why is estimation useful before computing an exact decimal answer?
Sample answer: Estimation gives a rough answer first, so you can check whether your exact calculation is reasonable and catch mistakes.
A good answer includes: Estimation gives a rough answer first, so you can check whether your exact calculation is reasonable and catch mistakes.