Learn on PengiEureka Math, Grade 5Chapter 9: Decimal Multi-Digit Multiplication

Lesson 1: Multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products.

In this Grade 5 Eureka Math lesson from Chapter 9, students learn to multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products. Students rename decimal factors as tenths, then apply expanded form and the area model to find partial products before combining them into a final decimal answer. The lesson builds directly on prior whole number multiplication strategies, helping students see how the distributive property and partial products work the same way with decimals.

Section 1

Multiply by Tenths Using an Area Model

Property

To multiply a whole number by a decimal with tenths, you can rename the decimal as tenths, multiply the whole numbers using an area model, and then convert the product back to a standard decimal by dividing by 10.

a×b.c=a×(10×b.c)10=a×bc10a \times b.c = \frac{{a \times (10 \times b.c)}}{{10}} = \frac{{a \times bc}}{{10}}

Examples

Book overview

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

Continue this chapter

Chapter 9: Decimal Multi-Digit Multiplication

  1. Lesson 1Current

    Lesson 1: Multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products.

  2. Lesson 2

    Lesson 2: Multiply decimal fractions by multi-digit whole numbers through conversion to a whole number problem and reasoning about the placement of the decimal.

  3. Lesson 3

    Lesson 3: Reason about the product of a whole number and a decimal with hundredths using place value understanding and estimation.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Multiply by Tenths Using an Area Model

Property

To multiply a whole number by a decimal with tenths, you can rename the decimal as tenths, multiply the whole numbers using an area model, and then convert the product back to a standard decimal by dividing by 10.

a×b.c=a×(10×b.c)10=a×bc10a \times b.c = \frac{{a \times (10 \times b.c)}}{{10}} = \frac{{a \times bc}}{{10}}

Examples

Book overview

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

Continue this chapter

Chapter 9: Decimal Multi-Digit Multiplication

  1. Lesson 1Current

    Lesson 1: Multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products.

  2. Lesson 2

    Lesson 2: Multiply decimal fractions by multi-digit whole numbers through conversion to a whole number problem and reasoning about the placement of the decimal.

  3. Lesson 3

    Lesson 3: Reason about the product of a whole number and a decimal with hundredths using place value understanding and estimation.