Grade 5 · Number & Operations in Base Ten · MAT-05-NBT-010
Divide Decimals by Whole Numbers
Represent and solve divide decimals by whole numbers problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve divide decimals by whole numbers problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for divide decimals by whole numbers 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.
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
Divide Decimals by Whole Numbers 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 equation balance 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
Check multiplication with an inverse division or a second model; check division by multiplying the quotient by the divisor and accounting for any remainder.
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.
Equation Balance
Adjust both sides. Equality means both expressions have the same value.
Balanced: both sides have equal value.
- Build one example of divide decimals by whole numbers 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.
Divide 2.4 ÷ 2.
2.4 ÷ 2 = 1.2Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 3.9 ÷ 3.
3.9 ÷ 3 = 1.3Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 5.6 ÷ 4.
5.6 ÷ 4 = 1.4Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 7.5 ÷ 5.
7.5 ÷ 5 = 1.5Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 9.6 ÷ 6.
9.6 ÷ 6 = 1.6Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 3.4 ÷ 2.
3.4 ÷ 2 = 1.7Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 5.4 ÷ 3.
5.4 ÷ 3 = 1.8Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 7.6 ÷ 4.
7.6 ÷ 4 = 1.9Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 10.0 ÷ 5.
10.0 ÷ 5 = 2.0Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 12.6 ÷ 6.
12.6 ÷ 6 = 2.1Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 4.4 ÷ 2.
4.4 ÷ 2 = 2.2Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 6.9 ÷ 3.
6.9 ÷ 3 = 2.3Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 9.6 ÷ 4.
9.6 ÷ 4 = 2.4Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 12.5 ÷ 5.
12.5 ÷ 5 = 2.5Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 15.6 ÷ 6.
15.6 ÷ 6 = 2.6Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 5.4 ÷ 2.
5.4 ÷ 2 = 2.7Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 8.4 ÷ 3.
8.4 ÷ 3 = 2.8Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 11.6 ÷ 4.
11.6 ÷ 4 = 2.9Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 6.0 ÷ 5.
6.0 ÷ 5 = 1.2Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Divide 7.8 ÷ 6.
7.8 ÷ 6 = 1.3Division asks how much belongs in each equal group; multiplication by the quotient checks the result.
Practice
Guided practice with hints
01Divide 2.8 ÷ 2.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 2.8 ÷ 2 = 1.4
02Divide 4.5 ÷ 3.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4.5 ÷ 3 = 1.5
03Divide 6.4 ÷ 4.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 6.4 ÷ 4 = 1.6
04Divide 8.5 ÷ 5.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 8.5 ÷ 5 = 1.7
05Divide 10.8 ÷ 6.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 10.8 ÷ 6 = 1.8
06Divide 3.8 ÷ 2.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3.8 ÷ 2 = 1.9
Practice
Independent practice
01Divide 6.0 ÷ 3.
Answer: 6.0 ÷ 3 = 2.0
02Divide 8.4 ÷ 4.
Answer: 8.4 ÷ 4 = 2.1
03Divide 11.0 ÷ 5.
Answer: 11.0 ÷ 5 = 2.2
04Divide 13.8 ÷ 6.
Answer: 13.8 ÷ 6 = 2.3
05Divide 2.4 ÷ 2.
Answer: 2.4 ÷ 2 = 1.2
06Divide 3.9 ÷ 3.
Answer: 3.9 ÷ 3 = 1.3
07Divide 5.6 ÷ 4.
Answer: 5.6 ÷ 4 = 1.4
08Divide 7.5 ÷ 5.
Answer: 7.5 ÷ 5 = 1.5
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
Divide 9.6 ÷ 6.
9.6 ÷ 6 = 1.6
Divide 3.4 ÷ 2.
3.4 ÷ 2 = 1.7
Divide 5.4 ÷ 3.
5.4 ÷ 3 = 1.8
Divide 7.6 ÷ 4.
7.6 ÷ 4 = 1.9
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 5 Math Strategy Sprint
Solve and explain divide decimals by whole numbers problems accurately, then check each result with a second method.
Practice
Mastery check
01Divide 10.0 ÷ 5.
Answer: 10.0 ÷ 5 = 2.0
02Divide 12.6 ÷ 6.
Answer: 12.6 ÷ 6 = 2.1
03Divide 4.4 ÷ 2.
Answer: 4.4 ÷ 2 = 2.2
04Divide 6.9 ÷ 3.
Answer: 6.9 ÷ 3 = 2.3
05Divide 9.6 ÷ 4.
Answer: 9.6 ÷ 4 = 2.4
06Divide 12.5 ÷ 5.
Answer: 12.5 ÷ 5 = 2.5
07Divide 15.6 ÷ 6.
Answer: 15.6 ÷ 6 = 2.6
08Divide 5.4 ÷ 2.
Answer: 5.4 ÷ 2 = 2.7
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.