Learn on PengiPengi Math (Grade 5)Chapter 4: Decimal Multiplication and Division

Lesson 3: Multiplying Two Decimals Using Area and Partial Products

In this Grade 5 Pengi Math lesson from Chapter 4, students learn how to multiply two decimals by modeling products on 10×10 area grids and decomposing each decimal into expanded form. They apply the partial products method to calculate exact values and use the area model to verify correct decimal placement in the final answer.

Section 1

Model Multiplying Two Decimals Less Than One

Property

To multiply two decimals less than one, you can use a 10x10 grid to model the area of a rectangle. The product of the two decimals is represented by the overlapping shaded area.

Examples

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: Decimal Multiplication and Division

  1. Lesson 1

    Lesson 1: Estimating Decimal Products to Check Reasonableness

  2. Lesson 2

    Lesson 2: Multiplying Decimals by Whole Numbers Using Models

  3. Lesson 3Current

    Lesson 3: Multiplying Two Decimals Using Area and Partial Products

  4. Lesson 4

    Lesson 4: Decimal Multiplication Algorithms and Decimal Placement

  5. Lesson 5

    Lesson 5: Dividing Decimals Using Models and Algorithms

  6. Lesson 6

    Lesson 6: Dividing Decimals by Decimals

  7. Lesson 7

    Lesson 7: Solving Multi-Step Problems with Decimal Operations

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Model Multiplying Two Decimals Less Than One

Property

To multiply two decimals less than one, you can use a 10x10 grid to model the area of a rectangle. The product of the two decimals is represented by the overlapping shaded area.

Examples

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: Decimal Multiplication and Division

  1. Lesson 1

    Lesson 1: Estimating Decimal Products to Check Reasonableness

  2. Lesson 2

    Lesson 2: Multiplying Decimals by Whole Numbers Using Models

  3. Lesson 3Current

    Lesson 3: Multiplying Two Decimals Using Area and Partial Products

  4. Lesson 4

    Lesson 4: Decimal Multiplication Algorithms and Decimal Placement

  5. Lesson 5

    Lesson 5: Dividing Decimals Using Models and Algorithms

  6. Lesson 6

    Lesson 6: Dividing Decimals by Decimals

  7. Lesson 7

    Lesson 7: Solving Multi-Step Problems with Decimal Operations