Learn on PengiEureka Math, Grade 5Chapter 23: Multiplication of a Fraction by a Fraction

Lesson 1: Multiply unit fractions by unit fractions.

In this Grade 5 Eureka Math lesson from Chapter 23, students learn to multiply unit fractions by unit fractions, building on prior work with multiplying fractions and whole numbers. Using paper folding, area models, and tape diagrams, students develop conceptual understanding of why multiplying two unit fractions like one-half by one-half yields one-fourth. The lesson connects pictorial and numerical representations to help students generalize the procedure for fraction-by-fraction multiplication.

Section 1

Multiply Unit Fractions Using an Area Model

Property

To find the product of two unit fractions, such as finding a fraction 'of' another fraction, you can multiply the denominators. The resulting product is a new unit fraction.

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

Examples

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Chapter 23: Multiplication of a Fraction by a Fraction

  1. Lesson 1Current

    Lesson 1: Multiply unit fractions by unit fractions.

  2. Lesson 2

    Lesson 2: Multiply unit fractions by non-unit fractions.

  3. Lesson 3

    Lesson 3: Multiply non-unit fractions by non-unit fractions.

  4. Lesson 4

    Lesson 4: Solve word problems using tape diagrams and fraction-by-fraction multiplication.

  5. Lesson 5

    Lesson 5: Relate decimal and fraction multiplication.

  6. Lesson 6

    Lesson 6: Relate decimal and fraction multiplication.

  7. Lesson 7

    Lesson 7: Convert measures involving whole numbers, and solve multi-step word problems.

  8. Lesson 8

    Lesson 8: Convert mixed unit measurements, and solve multi-step word problems.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Multiply Unit Fractions Using an Area Model

Property

To find the product of two unit fractions, such as finding a fraction 'of' another fraction, you can multiply the denominators. The resulting product is a new unit fraction.

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

Examples

Book overview

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

Continue this chapter

Chapter 23: Multiplication of a Fraction by a Fraction

  1. Lesson 1Current

    Lesson 1: Multiply unit fractions by unit fractions.

  2. Lesson 2

    Lesson 2: Multiply unit fractions by non-unit fractions.

  3. Lesson 3

    Lesson 3: Multiply non-unit fractions by non-unit fractions.

  4. Lesson 4

    Lesson 4: Solve word problems using tape diagrams and fraction-by-fraction multiplication.

  5. Lesson 5

    Lesson 5: Relate decimal and fraction multiplication.

  6. Lesson 6

    Lesson 6: Relate decimal and fraction multiplication.

  7. Lesson 7

    Lesson 7: Convert measures involving whole numbers, and solve multi-step word problems.

  8. Lesson 8

    Lesson 8: Convert mixed unit measurements, and solve multi-step word problems.