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

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

In this Grade 5 Eureka Math lesson from Chapter 23, students learn to multiply unit fractions by non-unit fractions, such as finding 1/3 of 3/5, by drawing rectangular fraction models and writing multiplication sentences. The lesson builds on prior knowledge of unit fraction multiplication to help students understand how multiplying a unit fraction by a non-unit fraction produces a simplified product. Students also practice simplifying results like 3/15 to equivalent fractions such as 1/5.

Section 1

Connecting Area Models to the Multiplication Algorithm

Property

When multiplying a unit fraction by a non-unit fraction, the area model shows that the product can be found by multiplying the numerators to find the number of double-shaded parts and multiplying the denominators to find the total number of parts in the whole.

1a×bc=1×ba×c\frac{1}{a} \times \frac{b}{c} = \frac{1 \times b}{a \times c}

Examples

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Chapter 23: Multiplication of a Fraction by a Fraction

  1. Lesson 1

    Lesson 1: Multiply unit fractions by unit fractions.

  2. Lesson 2Current

    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.

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Section 1

Connecting Area Models to the Multiplication Algorithm

Property

When multiplying a unit fraction by a non-unit fraction, the area model shows that the product can be found by multiplying the numerators to find the number of double-shaded parts and multiplying the denominators to find the total number of parts in the whole.

1a×bc=1×ba×c\frac{1}{a} \times \frac{b}{c} = \frac{1 \times b}{a \times c}

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 1

    Lesson 1: Multiply unit fractions by unit fractions.

  2. Lesson 2Current

    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.