Learn on PengiEureka Math, Grade 5Chapter 21: Multiplication of a Whole Number by a Fraction

Lesson 2: Multiply any whole number by a fraction using tape diagrams.

In this Grade 5 Eureka Math lesson from Chapter 21, students learn to multiply any whole number by a fraction using tape diagrams, building on their understanding of fractions as division. They work through problems such as finding 3/5 of 35 by partitioning a bar model into equal units, determining the value of one unit, and then scaling up to the required number of units. Fluency activities reinforce related skills including reading tape diagrams, finding fractions of whole numbers, and expressing fractions as division sentences.

Section 1

Find a Fractional Part of a Whole Number

Property

To find a fraction of a whole number, ab of W\frac{a}{b} \text{ of } W, using a tape diagram, the value is calculated by first finding the value of one unit (W÷bW \div b) and then multiplying by the numerator (aa).

ab×W=(Wb)×a \frac{a}{b} \times W = (\frac{W}{b}) \times a

Examples

Section 2

Find the Whole Given a Fractional Part

Property

If ab\frac{a}{b} of a whole is equal to a value VV, then the whole can be found by first calculating the value of one unit (V÷aV \div a) and then multiplying by the total number of units (bb).

Whole=(V÷a)×b\text{Whole} = (V \div a) \times b

Examples

Book overview

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Chapter 21: Multiplication of a Whole Number by a Fraction

  1. Lesson 1

    Lesson 1: Relate fractions as division to fraction of a set.

  2. Lesson 2Current

    Lesson 2: Multiply any whole number by a fraction using tape diagrams.

  3. Lesson 3

    Lesson 3: Relate a fraction of a set to the repeated addition interpretation of fraction multiplication.

  4. Lesson 4

    Lesson 4: Find a fraction of a measurement, and solve word problems.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Find a Fractional Part of a Whole Number

Property

To find a fraction of a whole number, ab of W\frac{a}{b} \text{ of } W, using a tape diagram, the value is calculated by first finding the value of one unit (W÷bW \div b) and then multiplying by the numerator (aa).

ab×W=(Wb)×a \frac{a}{b} \times W = (\frac{W}{b}) \times a

Examples

Section 2

Find the Whole Given a Fractional Part

Property

If ab\frac{a}{b} of a whole is equal to a value VV, then the whole can be found by first calculating the value of one unit (V÷aV \div a) and then multiplying by the total number of units (bb).

Whole=(V÷a)×b\text{Whole} = (V \div a) \times b

Examples

Book overview

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

Continue this chapter

Chapter 21: Multiplication of a Whole Number by a Fraction

  1. Lesson 1

    Lesson 1: Relate fractions as division to fraction of a set.

  2. Lesson 2Current

    Lesson 2: Multiply any whole number by a fraction using tape diagrams.

  3. Lesson 3

    Lesson 3: Relate a fraction of a set to the repeated addition interpretation of fraction multiplication.

  4. Lesson 4

    Lesson 4: Find a fraction of a measurement, and solve word problems.