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

Lesson 6: Multiply Decimals Using Partial Products

In this Grade 5 lesson from enVision Mathematics Chapter 4, students learn to multiply two decimals using the partial products method, applying their understanding of place value and area models to break multiplication problems into smaller parts. Students practice estimating products first, then use area models to organize partial products before finding the final answer. The lesson connects decimal multiplication to strategies students already know from multiplying whole numbers.

Section 1

Decomposing Decimals into Expanded Form

Property

To write a decimal in expanded form, you express it as the sum of the values of each digit. This process is called decomposition.

3.45=3+0.4+0.053.45 = 3 + 0.4 + 0.05

Section 2

Solving Decimal Multiplication with Partial Products

Property

To multiply two decimals using partial products, decompose each factor, multiply each part of the first factor by each part of the second, and sum the results. For decimals a.ba.b and c.dc.d:

(a+0.b)×(c+0.d)=(a×c)+(a×0.d)+(0.b×c)+(0.b×0.d)(a + 0.b) \times (c + 0.d) = (a \times c) + (a \times 0.d) + (0.b \times c) + (0.b \times 0.d)

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 6Current

    Lesson 6: Multiply Decimals Using Partial Products

  7. Lesson 7

    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

Decomposing Decimals into Expanded Form

Property

To write a decimal in expanded form, you express it as the sum of the values of each digit. This process is called decomposition.

3.45=3+0.4+0.053.45 = 3 + 0.4 + 0.05

Section 2

Solving Decimal Multiplication with Partial Products

Property

To multiply two decimals using partial products, decompose each factor, multiply each part of the first factor by each part of the second, and sum the results. For decimals a.ba.b and c.dc.d:

(a+0.b)×(c+0.d)=(a×c)+(a×0.d)+(0.b×c)+(0.b×0.d)(a + 0.b) \times (c + 0.d) = (a \times c) + (a \times 0.d) + (0.b \times c) + (0.b \times 0.d)

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 6Current

    Lesson 6: Multiply Decimals Using Partial Products

  7. Lesson 7

    Lesson 7: Use Properties to Multiply Decimals

  8. Lesson 8

    Lesson 8: Use Number Sense to Multiply Decimals