Learn on PengiIllustrative Mathematics, Grade 5Chapter 3: Multiplying and Dividing Fractions

Lesson 2: Multiply Unit Fractions

In this Grade 5 Illustrative Mathematics lesson from Chapter 3: Multiplying and Dividing Fractions, students learn to multiply unit fractions by applying the concept that multiplying by a unit fraction is the same as finding a fractional part of a quantity. Students use visual models and equations to develop fluency with expressions such as 1/2 × 1/3, building foundational understanding of fraction multiplication.

Section 1

Writing Expressions from Area Models

Property

An area model divided into aa horizontal parts (rows) and bb vertical parts (columns) represents the multiplication of two unit fractions, 1a×1b\frac{1}{a} \times \frac{1}{b}. The product is 1a×b\frac{1}{a \times b}.

Examples

Section 2

Commutative Property with Unit Fractions

Property

The commutative property of multiplication states that changing the order of the fractions does not change the product. For any two unit fractions:

1a×1b=1b×1a\frac{1}{a} \times \frac{1}{b} = \frac{1}{b} \times \frac{1}{a}

Examples

Book overview

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Chapter 3: Multiplying and Dividing Fractions

  1. Lesson 1

    Lesson 1: Represent Unit Fraction Multiplication

  2. Lesson 2Current

    Lesson 2: Multiply Unit Fractions

  3. Lesson 3

    Lesson 3: Multiply Unit and Non-unit Fractions

  4. Lesson 4

    Lesson 4: Generalize Fraction Multiplication

  5. Lesson 5

    Lesson 5: Apply Fraction Multiplication

  6. Lesson 6

    Lesson 6: My Own Flag (Optional)

  7. Lesson 7

    Lesson 7: Concepts of Division (Optional)

  8. Lesson 8

    Lesson 8: Divide Unit Fractions by Whole Numbers

  9. Lesson 9

    Lesson 9: Divide Whole Numbers by Unit Fractions

  10. Lesson 10

    Lesson 10: Fraction Division Situations

  11. Lesson 11

    Lesson 11: Reason About Quotients

  12. Lesson 12

    Lesson 12: Represent Multiplication and Division Situations

  13. Lesson 13

    Lesson 13: Fraction Games

Lesson overview

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Section 1

Writing Expressions from Area Models

Property

An area model divided into aa horizontal parts (rows) and bb vertical parts (columns) represents the multiplication of two unit fractions, 1a×1b\frac{1}{a} \times \frac{1}{b}. The product is 1a×b\frac{1}{a \times b}.

Examples

Section 2

Commutative Property with Unit Fractions

Property

The commutative property of multiplication states that changing the order of the fractions does not change the product. For any two unit fractions:

1a×1b=1b×1a\frac{1}{a} \times \frac{1}{b} = \frac{1}{b} \times \frac{1}{a}

Examples

Book overview

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

Continue this chapter

Chapter 3: Multiplying and Dividing Fractions

  1. Lesson 1

    Lesson 1: Represent Unit Fraction Multiplication

  2. Lesson 2Current

    Lesson 2: Multiply Unit Fractions

  3. Lesson 3

    Lesson 3: Multiply Unit and Non-unit Fractions

  4. Lesson 4

    Lesson 4: Generalize Fraction Multiplication

  5. Lesson 5

    Lesson 5: Apply Fraction Multiplication

  6. Lesson 6

    Lesson 6: My Own Flag (Optional)

  7. Lesson 7

    Lesson 7: Concepts of Division (Optional)

  8. Lesson 8

    Lesson 8: Divide Unit Fractions by Whole Numbers

  9. Lesson 9

    Lesson 9: Divide Whole Numbers by Unit Fractions

  10. Lesson 10

    Lesson 10: Fraction Division Situations

  11. Lesson 11

    Lesson 11: Reason About Quotients

  12. Lesson 12

    Lesson 12: Represent Multiplication and Division Situations

  13. Lesson 13

    Lesson 13: Fraction Games