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

Lesson 10: Multiply Decimals by Whole Numbers

In this Grade 5 Illustrative Mathematics lesson from Chapter 5, students learn to multiply whole numbers by tenths and hundredths, such as finding the value of expressions like 2 × 0.4 and 4 × 0.03. Students apply their understanding of decimal place value and whole number multiplication, using strategies like hundredths grids, tape diagrams, and the distributive property to make sense of decimal products. The lesson builds on prior work with decimal addition and subtraction to help students see how place value patterns extend to multiplication.

Section 1

Procedure: How to Multiply a Decimal by a Whole Number

Property

To multiply a decimal by a whole number:

  1. Multiply the numbers as if they were whole numbers, ignoring the decimal point.
  2. Count the number of decimal places in the decimal factor.
  3. Place the decimal point in the product so it has the same number of decimal places as the decimal factor.

Examples

Section 2

Relating Decimal and Whole Number Multiplication

Property

To multiply a decimal by a whole number, first multiply the numbers as if they were whole numbers. Then, place the decimal point in the product so that it has the same number of decimal places as the decimal factor.

Examples

  • To solve 0.3×40.3 \times 4, first calculate the whole number fact 3×4=123 \times 4 = 12. Since 0.30.3 has one decimal place, the product will also have one decimal place: 1.21.2.
  • To solve 1.25×31.25 \times 3, first calculate the whole number fact 125×3=375125 \times 3 = 375. Since 1.251.25 has two decimal places, the product will also have two decimal places: 3.753.75.

Explanation

This skill helps you use your knowledge of whole number multiplication to solve decimal problems. By temporarily ignoring the decimal point, you can calculate the digits of the answer using familiar facts. Then, you simply place the decimal point correctly in the final product. The number of decimal places in your answer must match the number of decimal places in the decimal factor you started with.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Procedure: How to Multiply a Decimal by a Whole Number

Property

To multiply a decimal by a whole number:

  1. Multiply the numbers as if they were whole numbers, ignoring the decimal point.
  2. Count the number of decimal places in the decimal factor.
  3. Place the decimal point in the product so it has the same number of decimal places as the decimal factor.

Examples

Section 2

Relating Decimal and Whole Number Multiplication

Property

To multiply a decimal by a whole number, first multiply the numbers as if they were whole numbers. Then, place the decimal point in the product so that it has the same number of decimal places as the decimal factor.

Examples

  • To solve 0.3×40.3 \times 4, first calculate the whole number fact 3×4=123 \times 4 = 12. Since 0.30.3 has one decimal place, the product will also have one decimal place: 1.21.2.
  • To solve 1.25×31.25 \times 3, first calculate the whole number fact 125×3=375125 \times 3 = 375. Since 1.251.25 has two decimal places, the product will also have two decimal places: 3.753.75.

Explanation

This skill helps you use your knowledge of whole number multiplication to solve decimal problems. By temporarily ignoring the decimal point, you can calculate the digits of the answer using familiar facts. Then, you simply place the decimal point correctly in the final product. The number of decimal places in your answer must match the number of decimal places in the decimal factor you started with.