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:
3.5 + 2.14 = 5.19 because you just add left to right.
Corrected: 3.50 + 2.14 = 5.64 because you must align decimal points and add by place value.
The corrected sentence is: "3.50 + 2.14 = 5.64 because you must align decimal points and add by place value.". The original sentence "3.5 + 2.14 = 5.19 because you just add left to right." contained an error that needed to be fixed.
2. Fix the sentence:
7.8 − 3.25 = 4.45 since 80 minus 25 is 45.
Corrected: 7.80 − 3.25 = 4.55 since 80 hundredths minus 25 hundredths is 55 hundredths.
The corrected sentence is: "7.80 − 3.25 = 4.55 since 80 hundredths minus 25 hundredths is 55 hundredths.". The original sentence "7.8 − 3.25 = 4.45 since 80 minus 25 is 45." contained an error that needed to be fixed.
3. Fix the sentence:
12.6 + 9.47 = 21.07 because 6 + 47 = 107.
Corrected: 12.60 + 9.47 = 22.07 because 60 + 47 = 107 hundredths, carry 1 to the ones place.
The corrected sentence is: "12.60 + 9.47 = 22.07 because 60 + 47 = 107 hundredths, carry 1 to the ones place.". The original sentence "12.6 + 9.47 = 21.07 because 6 + 47 = 107." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 4.32 + 1.57 = 5.89
Align decimal points: 4.32 + 1.57. Add hundredths: 2+7=9; tenths: 3+5=8; ones: 4+1=5. Answer: 5.89.
2. 9.05 − 3.72 = 5.33
Align decimal points. 9.05 − 3.72. Hundredths: 5−2=3; tenths: 0−7 requires regrouping → 10−7=3, carry; ones: 9−1−3=5. Answer: 5.33.
3. When adding 6.3 + 2.48, rewrite 6.3 as 6.30 so both have the same decimal places.
Adding a zero to 6.3 to get 6.30 does not change its value but gives both numbers the same number of decimal places, making column alignment easier.
4. 15.00 − 7.63 = 7.37
15.00 − 7.63. Regroup to subtract: hundredths 0−3 → borrow; tenths 0−6 → borrow; 15.00 − 7.63 = 7.37.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why is it important to align decimal points before adding or subtracting?
Sample answer: Aligning decimal points ensures you add digits with the same place value, like tenths with tenths.
Place value alignment is essential. The decimal point marks the boundary between whole and fractional parts, and digits must be combined with their matching place value.
2. Explain how to subtract 4.7 from 10.25.
Sample answer: Rewrite 4.7 as 4.70, then subtract: 10.25 − 4.70 = 5.55, regrouping as needed.
Step 1: Add a trailing zero to 4.7 → 4.70. Step 2: Align decimals and subtract: 10.25 − 4.70 = 5.55.