In this Grade 5 Eureka Math lesson from Chapter 5, students learn to multiply decimal fractions by single-digit whole numbers using place value understanding and the area model. They practice multiplying tenths and hundredths by whole numbers, bundling units when products exceed one whole, and connecting visual models to written algorithms. The lesson builds on prior work with decimal addition and subtraction to develop fluency with decimal multiplication expressions such as 4 × 0.423.
Section 1
Model Decimal Multiplication on a Place Value Chart
To multiply a decimal by a whole number , you can represent the decimal on a place value chart 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.
Section 2
Using an Area Model for Decimal Multiplication
The area model for decimal multiplication visually represents the distributive property. To multiply a whole number by a decimal, you can break the decimal into its place value components (addends), multiply each component by the whole number, and then sum the resulting partial products.
Section 3
Multiplying Decimals by Whole Numbers Using Place Value
When multiplying a whole number by a decimal, you can treat the decimal as a whole number of its smallest place value unit (e.g., tenths, hundredths, or thousandths). Multiply the whole numbers, and then express the product using that same place value unit. For example, is the same as , which equals or .
Expand to review the lesson summary and core properties.
Section 1
Model Decimal Multiplication on a Place Value Chart
To multiply a decimal by a whole number , you can represent the decimal on a place value chart 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.
Section 2
Using an Area Model for Decimal Multiplication
The area model for decimal multiplication visually represents the distributive property. To multiply a whole number by a decimal, you can break the decimal into its place value components (addends), multiply each component by the whole number, and then sum the resulting partial products.
Section 3
Multiplying Decimals by Whole Numbers Using Place Value
When multiplying a whole number by a decimal, you can treat the decimal as a whole number of its smallest place value unit (e.g., tenths, hundredths, or thousandths). Multiply the whole numbers, and then express the product using that same place value unit. For example, is the same as , which equals or .