Learn on PengiPengi Math (Grade 5)Chapter 4: Decimal Multiplication and Division

Lesson 2: Multiplying Decimals by Whole Numbers Using Models

In this Grade 5 Pengi Math lesson from Chapter 4, students learn to multiply decimals by whole numbers by interpreting the operation as repeated addition and modeling products with base-ten blocks. They use place value charts to regroup units and connect their visual models to numerical results, building a concrete understanding of 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

Representing Decimal Multiplication with Grids and Blocks

Property

Base ten blocks can model decimal multiplication by arranging blocks in rectangular arrays, where the area represents the product.
On hundredths grids, decimal multiplication is shown by creating overlapping shaded regions where the intersection area equals the product: 0.3×0.40.3 \times 0.4 creates a 3×43 \times 4 rectangle covering 1212 squares out of 100100.

Examples

Section 3

Model Decimal Multiplication on a Place Value Chart

Property

To multiply a decimal by a whole number nn, you can represent the decimal on a place value chart nn times. Sum the units in each place value, regrouping (bundling) any groups of 10 and moving them to the next larger place value to find the product.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

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

Representing Decimal Multiplication with Grids and Blocks

Property

Base ten blocks can model decimal multiplication by arranging blocks in rectangular arrays, where the area represents the product.
On hundredths grids, decimal multiplication is shown by creating overlapping shaded regions where the intersection area equals the product: 0.3×0.40.3 \times 0.4 creates a 3×43 \times 4 rectangle covering 1212 squares out of 100100.

Examples

Section 3

Model Decimal Multiplication on a Place Value Chart

Property

To multiply a decimal by a whole number nn, you can represent the decimal on a place value chart nn times. Sum the units in each place value, regrouping (bundling) any groups of 10 and moving them to the next larger place value to find the product.

Examples