Learn on PengienVision, Mathematics, Grade 5Chapter 4: Use Models and Strategies to Multiply Decimals

Lesson 4: Multiply a Decimal and a Whole Number

In this Grade 5 enVision Mathematics lesson from Chapter 4, students learn how to multiply a decimal by a whole number using place-value patterns and standard multiplication algorithms. The lesson teaches students to first multiply as they would with whole numbers, then use number sense to correctly place the decimal point in the product. Real-world contexts, such as calculating distances traveled and charity donations from ticket sales, help students generalize the connection between whole-number multiplication and decimal multiplication.

Section 1

Repeated Addition

Property

Multiplication of a decimal by a whole number can be represented as repeated addition. The whole number, nn, tells you how many times to add the decimal, dd.

n×d=d+d+⋯+d⏟n timesn \times d = \underbrace{d + d + \dots + d}_{n \text{ times}}

Section 2

Multiplying Decimals by Whole Numbers

Property

When multiplying a decimal by a whole number, multiply as if both numbers were whole numbers, then place the decimal point in the product so it has the same number of decimal places as the original decimal factor.

decimal places in product=decimal places in decimal factor\text{decimal places in product} = \text{decimal places in decimal factor}

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Repeated Addition

Property

Multiplication of a decimal by a whole number can be represented as repeated addition. The whole number, nn, tells you how many times to add the decimal, dd.

n×d=d+d+⋯+d⏟n timesn \times d = \underbrace{d + d + \dots + d}_{n \text{ times}}

Section 2

Multiplying Decimals by Whole Numbers

Property

When multiplying a decimal by a whole number, multiply as if both numbers were whole numbers, then place the decimal point in the product so it has the same number of decimal places as the original decimal factor.

decimal places in product=decimal places in decimal factor\text{decimal places in product} = \text{decimal places in decimal factor}