Decimal Deduction Worksheet
Math Practice Standard 5.NBT.B.7
Decimal Deduction
Subtracting whole numbers, tenths, hundredths, and thousandths
Name:
Date: Score:
Subtraction Protocol:
1. Align decimal points 2. Annex zeros \( (52 = 52.000) \) 3. Regroup & subtract
1 Whole Numbers Only
\( 600 - 274 \)
Answer:
2 Whole − Tenths
\( 85 - 39.4 \)
Answer:
3 Tenths Only
\( 73.2 - 28.7 \)
Answer:
4 Whole − Hundredths
\( 90 - 46.38 \)
Answer:
5 Budget Application
Whole − Hundredths
A school robotics team begins the term with an equipment budget of \( \$150 \). During their initial supply order, they purchase motor controllers costing exactly \( \$64.85 \). Exactly how much money remains in their budget?
Remaining Budget
$
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Decimal Deduction • Page 2
Name:
Inverse Check Tip: Verify your answer using addition: \( \text{Difference} + \text{Subtrahend} = \text{Minuend} \).
6 Hundredths Only
\( 82.15 - 37.68 \)
Answer:
7 Tenths − Hundredths
\( 64.3 - 28.75 \)
Answer:
8 Whole − Thousandths
\( 70 - 24.582 \)
Answer:
9 Hundredths − Thousandths
\( 91.04 - 43.627 \)
Answer:
10 Precision Lab Measurement
Tenths − Thousandths
A digital laboratory balance measures the combined mass of a glass beaker and a salt solution at \( 142.5 \) grams. When empty, the dry glass beaker weighs exactly \( 38.865 \) grams. What is the exact mass of the salt solution?
Solution Mass
grams
Self-Assessment: How confident are you borrowing across zeros?
Need Practice Getting There Confident Master
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Decimal Deduction Answer Key
Teacher Resource Complete Solutions & Key
Decimal Deduction — Answer Key
Worked vertical algorithms, regrouping pathways, and quick-grade reference
Max Points 10 Pts
Quick Key (1–5):
1: 326 2: 45.6 3: 44.5 4: 43.62 5: $85.15
1 Whole Numbers Only
Problem: \( 600 - 274 \)
5 9 10 (regroup)
6 0 0
- 2 7 4
3 2 6
Watch: Students must borrow across the tens zero to the hundreds.
Correct Answer: 326
2 Whole − Tenths
Problem: \( 85 - 39.4 \)
7 14 10
8 5.0
- 3 9.4
4 5.6
Annex 0: Annex \( .0 \) to 85. Cannot simply "bring down" the 4.
Correct Answer: 45.6
3 Tenths Only
Problem: \( 73.2 - 28.7 \)
6 12 12
7 3.2
- 2 8.7
4 4.5
Regrouping: Two regroupings required: tenths from ones, ones from tens.
Correct Answer: 44.5
4 Whole − Hundredths
Problem: \( 90 - 46.38 \)
8 9.9 10
9 0.00
- 4 6.38
4 3.62
Annex 2 Zeros: Rewrite 90 as \( 90.00 \). Regroup across 3 digits.
Correct Answer: 43.62
5 Robotics Budget Application Solution
Contextual Subtraction
0 14 9. 9 10
1 5 0.00
- 6 4.85
8 5.15
Key Grading Criteria:
- Annexed \( .00 \) to \( \$150 \)
- Correct regrouping from hundreds
- Includes dollar symbol \( (\$) \) in answer
Full Sentence Response: The team has $85.15 remaining.
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Decimal Deduction — Answer Key • Page 2
Problems 6–10
Quick Key (6–10):
6: 44.47 7: 35.55 8: 45.418 9: 47.413 10: 103.635 g
6 Hundredths Only
Problem: \( 82.15 - 37.68 \)
7 11.10 15
8 2.15
- 3 7.68
4 4.47
Check: \( 44.47 + 37.68 = 82.15 \). Regrouping across every column.
Correct Answer: 44.47
7 Tenths − Hundredths
Problem: \( 64.3 - 28.75 \)
5 13.12 10
6 4.30
- 2 8.75
3 5.55
Common Error: Writing 5 in hundredths without borrowing (0 - 5 = 5 error).
Correct Answer: 35.55
8 Whole − Thousandths
Problem: \( 70 - 24.582 \)
6 9.9 9 10
7 0.000
- 2 4.582
4 5.418
Triple Zero: Requires cascading ungroup from the 7 tens.
Correct Answer: 45.418
9 Hundredths − Thousandths
Problem: \( 91.04 - 43.627 \)
8 10.10 3 10
9 1.040
- 4 3.627
4 7.413
Internal Zero: Note \( 0 \) tenths becomes 10, then provides regrouping.
Correct Answer: 47.413
10 Lab Balance Measurement Solution
Thousandths Precision
0 13 11.14 9 10
1 4 2.500
- 3 8.865
1 0 3.635
Scoring Breakdown:
- Annexed two zeros to tenths: \( 142.500 \)
- Correct regrouping pathway
- Unit label: grams (g)
Full Sentence Response: The mass of the salt solution is 103.635 g.
Diagnostic Check: If student answers 45.428 on #8, they subtracted \( 2 - 0 \) instead of regrouping \( 10 - 2 \).
Target: 8/10 for Mastery
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