Learn on PengiIllustrative Mathematics, Grade 5Chapter 5: Place Value Patterns and Decimal Operations

Lesson 12: Multiply More Decimals

In this Grade 5 Illustrative Mathematics lesson, students use place value understanding to multiply multi-digit decimals, including products of two decimals to the tenths and products of a whole number and a decimal to the hundredths. Students learn to relate decimal products to whole number products, for example recognizing that 2.5 × 6.4 equals (25 × 64) × 0.01 using place value reasoning. The lesson is part of Chapter 5: Place Value Patterns and Decimal Operations and addresses standards 5.NBT.A.1 and 5.NBT.B.7.

Section 1

Placing the Decimal Point in a Product

Property

To multiply decimals, first multiply the numbers as if they were whole numbers. The total number of decimal places in the product is the sum of the number of decimal places in the factors being multiplied.

Examples

To solve $0.3 \times 0.07$ : First, find the product of the whole numbers, $3 \times 7 = 21$ . The factors have one and two decimal places, respectively, for a total of three ( $1+2=3$ ). So, the product is $0.021$ .
To solve $1.2 \times 0.5$ : First, find the product of the whole numbers, $12 \times 5 = 60$ . Each factor has one decimal place, for a total of two ( $1+1=2$ ). So, the product is $0.60$ or $0.6$ .

Explanation

This rule works because multiplying by decimals is like multiplying by fractions with denominators of 10, 100, etc. When you multiply the numbers, you are also multiplying their place values. Counting the decimal places is a shortcut for determining the correct place value of the final product. This method allows you to use whole number multiplication skills and then correctly place the decimal point.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Placing the Decimal Point in a Product

Property

Examples

To solve $0.3 \times 0.07$ : First, find the product of the whole numbers, $3 \times 7 = 21$ . The factors have one and two decimal places, respectively, for a total of three ( $1+2=3$ ). So, the product is $0.021$ .
To solve $1.2 \times 0.5$ : First, find the product of the whole numbers, $12 \times 5 = 60$ . Each factor has one decimal place, for a total of two ( $1+1=2$ ). So, the product is $0.60$ or $0.6$ .

Explanation

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Placing the Decimal Point in a Product

Property

Examples

To solve $0.3 \times 0.07$ : First, find the product of the whole numbers, $3 \times 7 = 21$ . The factors have one and two decimal places, respectively, for a total of three ( $1+2=3$ ). So, the product is $0.021$ .
To solve $1.2 \times 0.5$ : First, find the product of the whole numbers, $12 \times 5 = 60$ . Each factor has one decimal place, for a total of two ( $1+1=2$ ). So, the product is $0.60$ or $0.6$ .