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:
8.4 ÷ 3 = 2.1 because 84 ÷ 3 = 21 and the decimal goes after the first digit.
Corrected: 8.4 ÷ 3 = 2.8 because 84 ÷ 3 = 28 and the decimal point stays directly above its position in the dividend.
The corrected sentence is: "8.4 ÷ 3 = 2.8 because 84 ÷ 3 = 28 and the decimal point stays directly above its position in the dividend." The error was wrong division result: the original sentence "8.4 ÷ 3 = 2.1 because 84 ÷ 3 = 21 and the decimal goes after the first digit." needed to be fixed.
2. Fix the sentence:
6.5 ÷ 5 = 1.5 because 5 goes into 65 thirteen times.
Corrected: 6.5 ÷ 5 = 1.3 because 5 goes into 65 thirteen times, giving 1.3.
The corrected sentence is: "6.5 ÷ 5 = 1.3 because 5 goes into 65 thirteen times, giving 1.3." The error was digit transposition in quotient: the original sentence "6.5 ÷ 5 = 1.5 because 5 goes into 65 thirteen times." needed to be fixed.
3. Fix the sentence:
9.24 ÷ 4 = 2.36 because 924 ÷ 4 = 236.
Corrected: 9.24 ÷ 4 = 2.31 because 924 ÷ 4 = 231, so the quotient is 2.31.
The corrected sentence is: "9.24 ÷ 4 = 2.31 because 924 ÷ 4 = 231, so the quotient is 2.31." The error was wrong division computation: the original sentence "9.24 ÷ 4 = 2.36 because 924 ÷ 4 = 236." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 7.2 ÷ 6 = 1.2
The answer is 1.2. Think of 7.2 as 72 tenths: 72 ÷ 6 = 12 tenths, which equals 1.2.
2. 14.4 ÷ 8 = 1.8
The answer is 1.8. Divide 144 tenths by 8 to get 18 tenths, then place the decimal to get 1.8.
3. When dividing a decimal by a whole number, the decimal point in the quotient goes directly above the decimal point in the dividend.
The answer is "above." Placing the decimal point directly above its position in the dividend ensures every digit in the quotient has the correct place value.
4. 25.5 ÷ 5 = 5.1
The answer is 5.1. Since 255 ÷ 5 = 51, placing the decimal back gives 5.1, and you can check: 5.1 × 5 = 25.5.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A pack of 4 erasers costs $3.48. How much does one eraser cost? Show your reasoning.
Sample answer: Divide $3.48 by 4: 348 ÷ 4 = 87, so one eraser costs $0.87.
A good answer includes: Divide $3.48 by 4: 348 ÷ 4 = 87, so one eraser costs $0.87.
2. Why is it helpful to think of 6.5 ÷ 5 as 65 tenths ÷ 5 when dividing?
Sample answer: Thinking in tenths turns the decimal into a whole-number division (65 ÷ 5 = 13 tenths = 1.3), which is easier to compute.
A good answer includes: Thinking in tenths turns the decimal into a whole-number division (65 ÷ 5 = 13 tenths = 1.3), which is easier to compute.