Learn on PengienVision, Mathematics, Grade 5Chapter 4: Use Models and Strategies to Multiply Decimals

Lesson 7: Use Properties to Multiply Decimals

In this Grade 5 lesson from enVision Mathematics Chapter 4, students learn how to multiply decimals using the Associative and Commutative Properties by decomposing factors into whole numbers and powers of 0.1. They practice applying the rule that a tenth times a tenth equals a hundredth to find products like 0.6 × 0.9 and 1.25 × 1.5. The lesson builds understanding of decimal place value relationships through real-world problems involving measurement and multi-step calculations.

Section 1

Regrouping Decimal Factors

Property

After decomposing decimals, you can use the Commutative and Associative Properties to regroup the factors. This allows you to group the whole numbers together and the decimal units together.

(a×0.1)×(b×0.1)=(a×b)×(0.1×0.1)(a \times 0.1) \times (b \times 0.1) = (a \times b) \times (0.1 \times 0.1)

Section 2

Multiplying Decimal Units

Property

Multiplying tenths by tenths results in hundredths, and multiplying tenths by hundredths results in thousandths.

0.1×0.1=0.010.1 \times 0.1 = 0.01
0.1×0.01=0.0010.1 \times 0.01 = 0.001

Examples

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Chapter 4: Use Models and Strategies to Multiply Decimals

  1. Lesson 1

    Lesson 1: Multiply Decimals by Powers of 10

  2. Lesson 2

    Lesson 2: Estimate the Product of a Decimal and a Whole Number

  3. Lesson 3

    Lesson 3: Use Models to Multiply a Decimal and a Whole Number

  4. Lesson 4

    Lesson 4: Multiply a Decimal and a Whole Number

  5. Lesson 5

    Lesson 5: Use Models to Multiply a Decimal and a Decimal

  6. Lesson 6

    Lesson 6: Multiply Decimals Using Partial Products

  7. Lesson 7Current

    Lesson 7: Use Properties to Multiply Decimals

  8. Lesson 8

    Lesson 8: Use Number Sense to Multiply Decimals

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Regrouping Decimal Factors

Property

After decomposing decimals, you can use the Commutative and Associative Properties to regroup the factors. This allows you to group the whole numbers together and the decimal units together.

(a×0.1)×(b×0.1)=(a×b)×(0.1×0.1)(a \times 0.1) \times (b \times 0.1) = (a \times b) \times (0.1 \times 0.1)

Section 2

Multiplying Decimal Units

Property

Multiplying tenths by tenths results in hundredths, and multiplying tenths by hundredths results in thousandths.

0.1×0.1=0.010.1 \times 0.1 = 0.01
0.1×0.01=0.0010.1 \times 0.01 = 0.001

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 4: Use Models and Strategies to Multiply Decimals

  1. Lesson 1

    Lesson 1: Multiply Decimals by Powers of 10

  2. Lesson 2

    Lesson 2: Estimate the Product of a Decimal and a Whole Number

  3. Lesson 3

    Lesson 3: Use Models to Multiply a Decimal and a Whole Number

  4. Lesson 4

    Lesson 4: Multiply a Decimal and a Whole Number

  5. Lesson 5

    Lesson 5: Use Models to Multiply a Decimal and a Decimal

  6. Lesson 6

    Lesson 6: Multiply Decimals Using Partial Products

  7. Lesson 7Current

    Lesson 7: Use Properties to Multiply Decimals

  8. Lesson 8

    Lesson 8: Use Number Sense to Multiply Decimals