Grade 5 · Number & Operations in Base Ten · MAT-05-NBT-008
Subtract Decimals to Hundredths
Represent and solve subtract decimals to hundredths problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve subtract decimals to hundredths problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for subtract decimals to hundredths works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Subtract Decimals to Hundredths extends base-ten place value to positions right of the decimal point. Tenths, hundredths, and thousandths are powers-of-ten units, so digit position—not visual length—determines value.
Represent the idea
The Math Box uses base ten blocks as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
Estimate before calculating, then use the inverse operation or an equivalent representation to confirm the exact result.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Decimal Place-Value Lab
Change one place at a time and watch how its value contributes to the complete decimal.
- Build one example of subtract decimals to hundredths in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
Subtract 2.75 − 1.25.
2.75 − 1.25 = 1.50Align decimal points and regroup across place values when necessary.
Subtract 2.84 − 1.30.
2.84 − 1.30 = 1.54Align decimal points and regroup across place values when necessary.
Subtract 2.93 − 1.35.
2.93 − 1.35 = 1.58Align decimal points and regroup across place values when necessary.
Subtract 3.02 − 1.40.
3.02 − 1.40 = 1.62Align decimal points and regroup across place values when necessary.
Subtract 3.11 − 1.45.
3.11 − 1.45 = 1.66Align decimal points and regroup across place values when necessary.
Subtract 3.20 − 1.50.
3.20 − 1.50 = 1.70Align decimal points and regroup across place values when necessary.
Subtract 3.29 − 1.55.
3.29 − 1.55 = 1.74Align decimal points and regroup across place values when necessary.
Subtract 3.38 − 1.60.
3.38 − 1.60 = 1.78Align decimal points and regroup across place values when necessary.
Subtract 3.47 − 1.65.
3.47 − 1.65 = 1.82Align decimal points and regroup across place values when necessary.
Subtract 3.56 − 1.70.
3.56 − 1.70 = 1.86Align decimal points and regroup across place values when necessary.
Subtract 3.65 − 1.75.
3.65 − 1.75 = 1.90Align decimal points and regroup across place values when necessary.
Subtract 3.74 − 1.80.
3.74 − 1.80 = 1.94Align decimal points and regroup across place values when necessary.
Subtract 3.83 − 1.85.
3.83 − 1.85 = 1.98Align decimal points and regroup across place values when necessary.
Subtract 3.92 − 1.90.
3.92 − 1.90 = 2.02Align decimal points and regroup across place values when necessary.
Subtract 4.01 − 1.95.
4.01 − 1.95 = 2.06Align decimal points and regroup across place values when necessary.
Subtract 4.10 − 2.00.
4.10 − 2.00 = 2.10Align decimal points and regroup across place values when necessary.
Subtract 4.19 − 2.05.
4.19 − 2.05 = 2.14Align decimal points and regroup across place values when necessary.
Subtract 4.28 − 2.10.
4.28 − 2.10 = 2.18Align decimal points and regroup across place values when necessary.
Subtract 4.37 − 2.15.
4.37 − 2.15 = 2.22Align decimal points and regroup across place values when necessary.
Subtract 4.46 − 2.20.
4.46 − 2.20 = 2.26Align decimal points and regroup across place values when necessary.
Practice
Guided practice with hints
01Subtract 4.55 − 2.25.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4.55 − 2.25 = 2.30
02Subtract 4.64 − 2.30.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4.64 − 2.30 = 2.34
03Subtract 4.73 − 2.35.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4.73 − 2.35 = 2.38
04Subtract 4.82 − 2.40.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4.82 − 2.40 = 2.42
05Subtract 4.91 − 2.45.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4.91 − 2.45 = 2.46
06Subtract 5.00 − 2.50.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 5.00 − 2.50 = 2.50
Practice
Independent practice
01Subtract 5.09 − 2.55.
Answer: 5.09 − 2.55 = 2.54
02Subtract 5.18 − 2.60.
Answer: 5.18 − 2.60 = 2.58
03Subtract 5.27 − 2.65.
Answer: 5.27 − 2.65 = 2.62
04Subtract 5.36 − 2.70.
Answer: 5.36 − 2.70 = 2.66
05Subtract 2.75 − 1.25.
Answer: 2.75 − 1.25 = 1.50
06Subtract 2.84 − 1.30.
Answer: 2.84 − 1.30 = 1.54
07Subtract 2.93 − 1.35.
Answer: 2.93 − 1.35 = 1.58
08Subtract 3.02 − 1.40.
Answer: 3.02 − 1.40 = 1.62
Common mistakes
Learn to catch the error, not just the answer.
Compare corresponding place values; trailing zeros do not change a decimal's value.
Align place values vertically before combining digits.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Scale recipes, measurements, money, and data while preserving the meaning of the unit.
- Compare quantities that are not whole numbers in science, construction, shopping, and measurement.
Challenge problems
Subtract 3.11 − 1.45.
3.11 − 1.45 = 1.66
Subtract 3.20 − 1.50.
3.20 − 1.50 = 1.70
Subtract 3.29 − 1.55.
3.29 − 1.55 = 1.74
Subtract 3.38 − 1.60.
3.38 − 1.60 = 1.78
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 5 Math Strategy Sprint
Solve and explain subtract decimals to hundredths problems accurately, then check each result with a second method.
Practice
Mastery check
01Subtract 3.47 − 1.65.
Answer: 3.47 − 1.65 = 1.82
02Subtract 3.56 − 1.70.
Answer: 3.56 − 1.70 = 1.86
03Subtract 3.65 − 1.75.
Answer: 3.65 − 1.75 = 1.90
04Subtract 3.74 − 1.80.
Answer: 3.74 − 1.80 = 1.94
05Subtract 3.83 − 1.85.
Answer: 3.83 − 1.85 = 1.98
06Subtract 3.92 − 1.90.
Answer: 3.92 − 1.90 = 2.02
07Subtract 4.01 − 1.95.
Answer: 4.01 − 1.95 = 2.06
08Subtract 4.10 − 2.00.
Answer: 4.10 − 2.00 = 2.10
Terminology
Words to know
- decimal point
- The symbol separating whole-number places from fractional base-ten places.
- tenth
- One of ten equal parts of a whole.
- hundredth
- One of one hundred equal parts of a whole.
- place value
- The value a digit has because of its position in a numeral.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.