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

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

In this Grade 5 Eureka Math lesson from Chapter 21, students learn to relate fractions as division to finding a fraction of a set, working with expressions such as 1/3 of 6 and 1/4 of 12. Using counters and arrays, students practice rewriting division sentences as fractions and determine the value of unit and non-unit fractions of a given whole number. This lesson builds the conceptual foundation for multiplying whole numbers by fractions.

Section 1

Finding a Unit Fraction of a Set

Property

Finding a unit fraction of a set is equivalent to dividing the total number in the set (NN) by the denominator (bb). This calculation finds the size of one equal part.

1b of N=N÷b\frac{1}{b} \text{ of } N = N \div b

Examples

Section 2

Using Tape Diagrams to Find a Fraction of a Set

Property

A tape diagram can model finding a fraction of a set, ab\frac{a}{b} of NN.
The tape represents the total number, NN, and is divided into bb equal units (the denominator).
The value of aa units (the numerator) is the answer.

Examples

Book overview

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Chapter 21: Multiplication of a Whole Number by a Fraction

  1. Lesson 1Current

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

  2. Lesson 2

    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

Finding a Unit Fraction of a Set

Property

Finding a unit fraction of a set is equivalent to dividing the total number in the set (NN) by the denominator (bb). This calculation finds the size of one equal part.

1b of N=N÷b\frac{1}{b} \text{ of } N = N \div b

Examples

Section 2

Using Tape Diagrams to Find a Fraction of a Set

Property

A tape diagram can model finding a fraction of a set, ab\frac{a}{b} of NN.
The tape represents the total number, NN, and is divided into bb equal units (the denominator).
The value of aa units (the numerator) is the answer.

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 1Current

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

  2. Lesson 2

    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.