Grade 5 · Number & Operations in Base Ten · MAT-05-NBT-009
Multiply Decimals by Whole Numbers
Represent and solve multiply decimals by whole numbers problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve multiply decimals by whole numbers problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for multiply 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
Multiply 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 multiplication grid 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.
Array Builder
Build equal rows and columns, then connect the grid to repeated addition.
- Build one example of multiply 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.
Multiply 1.2 × 2.
1.2 × 2 = 2.4Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 1.3 × 3.
1.3 × 3 = 3.9Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 1.4 × 4.
1.4 × 4 = 5.6Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 1.5 × 5.
1.5 × 5 = 7.5Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 1.6 × 6.
1.6 × 6 = 9.6Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 1.7 × 7.
1.7 × 7 = 11.9Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 1.8 × 8.
1.8 × 8 = 14.4Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 1.9 × 2.
1.9 × 2 = 3.8Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 2.0 × 3.
2.0 × 3 = 6.0Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 2.1 × 4.
2.1 × 4 = 8.4Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 2.2 × 5.
2.2 × 5 = 11.0Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 2.3 × 6.
2.3 × 6 = 13.8Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 2.4 × 7.
2.4 × 7 = 16.8Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 2.5 × 8.
2.5 × 8 = 20.0Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 2.6 × 2.
2.6 × 2 = 5.2Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 2.7 × 3.
2.7 × 3 = 8.1Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 2.8 × 4.
2.8 × 4 = 11.2Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 2.9 × 5.
2.9 × 5 = 14.5Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 1.2 × 6.
1.2 × 6 = 7.2Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Multiply 1.3 × 7.
1.3 × 7 = 9.1Treat tenths as fractional units, multiply the count, then preserve the place-value scale.
Practice
Guided practice with hints
01Multiply 1.4 × 8.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1.4 × 8 = 11.2
02Multiply 1.5 × 2.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1.5 × 2 = 3.0
03Multiply 1.6 × 3.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1.6 × 3 = 4.8
04Multiply 1.7 × 4.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1.7 × 4 = 6.8
05Multiply 1.8 × 5.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1.8 × 5 = 9.0
06Multiply 1.9 × 6.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1.9 × 6 = 11.4
Practice
Independent practice
01Multiply 2.0 × 7.
Answer: 2.0 × 7 = 14.0
02Multiply 2.1 × 8.
Answer: 2.1 × 8 = 16.8
03Multiply 2.2 × 2.
Answer: 2.2 × 2 = 4.4
04Multiply 2.3 × 3.
Answer: 2.3 × 3 = 6.9
05Multiply 1.2 × 2.
Answer: 1.2 × 2 = 2.4
06Multiply 1.3 × 3.
Answer: 1.3 × 3 = 3.9
07Multiply 1.4 × 4.
Answer: 1.4 × 4 = 5.6
08Multiply 1.5 × 5.
Answer: 1.5 × 5 = 7.5
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
Multiply 1.6 × 6.
1.6 × 6 = 9.6
Multiply 1.7 × 7.
1.7 × 7 = 11.9
Multiply 1.8 × 8.
1.8 × 8 = 14.4
Multiply 1.9 × 2.
1.9 × 2 = 3.8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 5 Math Strategy Sprint
Solve and explain multiply decimals by whole numbers problems accurately, then check each result with a second method.
Practice
Mastery check
01Multiply 2.0 × 3.
Answer: 2.0 × 3 = 6.0
02Multiply 2.1 × 4.
Answer: 2.1 × 4 = 8.4
03Multiply 2.2 × 5.
Answer: 2.2 × 5 = 11.0
04Multiply 2.3 × 6.
Answer: 2.3 × 6 = 13.8
05Multiply 2.4 × 7.
Answer: 2.4 × 7 = 16.8
06Multiply 2.5 × 8.
Answer: 2.5 × 8 = 20.0
07Multiply 2.6 × 2.
Answer: 2.6 × 2 = 5.2
08Multiply 2.7 × 3.
Answer: 2.7 × 3 = 8.1
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.