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

Lesson overview

Expand to review the lesson summary and core properties.

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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