Learn on PengiEureka Math, Grade 5Chapter 24: Multiplication with Fractions and Decimals as Scaling and Word Problems

Lesson 1: Explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1.

In this Grade 5 Eureka Math lesson from Chapter 24, students learn to explain why multiplying a fraction by a fraction equal to 1 (such as 2/2 or 3/3) produces a product that is equivalent in size to the original fraction. Using area models and multiplication expressions, students explore how fractions like 6/8 and 3/4 represent the same quantity, deepening their understanding of fraction equivalence. The lesson also connects this concept to decimal equivalence and includes unit conversion practice with mixed numbers.

Section 1

Convert Fractions to Decimals Using Equivalent Fractions

Property

To convert a fraction ab\frac{a}{b} to a decimal, find a number nn such that the denominator b×nb \times n is a power of 10 (e.g., 10, 100, 1000). Multiplying the original fraction by nn\frac{n}{n} (a form of 1) creates an equivalent fraction that is easy to write as a decimal.

ab=ab×nn=a×nb×n\frac{a}{b} = \frac{a}{b} \times \frac{n}{n} = \frac{a \times n}{b \times n}

Examples

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Chapter 24: Multiplication with Fractions and Decimals as Scaling and Word Problems

  1. Lesson 1Current

    Lesson 1: Explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1.

  2. Lesson 2

    Lesson 2: Compare the size of the product to the size of the factors.

  3. Lesson 3

    Lesson 3: Compare the size of the product to the size of the factors.

  4. Lesson 4

    Lesson 4: Solve word problems using fraction and decimal multiplication.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Convert Fractions to Decimals Using Equivalent Fractions

Property

To convert a fraction ab\frac{a}{b} to a decimal, find a number nn such that the denominator b×nb \times n is a power of 10 (e.g., 10, 100, 1000). Multiplying the original fraction by nn\frac{n}{n} (a form of 1) creates an equivalent fraction that is easy to write as a decimal.

ab=ab×nn=a×nb×n\frac{a}{b} = \frac{a}{b} \times \frac{n}{n} = \frac{a \times n}{b \times n}

Examples

Book overview

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

Continue this chapter

Chapter 24: Multiplication with Fractions and Decimals as Scaling and Word Problems

  1. Lesson 1Current

    Lesson 1: Explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1.

  2. Lesson 2

    Lesson 2: Compare the size of the product to the size of the factors.

  3. Lesson 3

    Lesson 3: Compare the size of the product to the size of the factors.

  4. Lesson 4

    Lesson 4: Solve word problems using fraction and decimal multiplication.