Multiply by Tenths Using an Area Model
To multiply a whole number by a decimal with tenths using an area model, rename the decimal as tenths (e.g., 2.4 becomes 24 tenths), multiply by the whole number using an area model, sum the partial products, then divide by 10 to convert back from tenths to a standard decimal. This Grade 5 math skill from Eureka Math Chapter 9 covers decimal multi-digit multiplication.
Key Concepts
To multiply a whole number by a decimal with tenths, you can rename the decimal as tenths, multiply the whole numbers using an area model, and then convert the product back to a standard decimal by dividing by 10. $$a \times b.c = \frac{{a \times (10 \times b.c)}}{{10}} = \frac{{a \times bc}}{{10}}$$.
Common Questions
How do you multiply a whole number by a decimal using an area model?
Rename the decimal as a number of tenths (e.g., 2.4 becomes 24 tenths), use the area model to multiply the whole number by that renamed value, sum the partial products, then divide the total by 10 to get the final decimal.
What is an example of 43 times 2.4 using the area model?
Rename 2.4 as 24 tenths. Use the area model to find 43 times 24 equals 1032. Since we multiplied by tenths, 1032 tenths equals 103.2.
Why do you divide by 10 at the end of this method?
Because you renamed the decimal as tenths and multiplied, the product is expressed in tenths. Dividing by 10 converts it back to a standard decimal value.
Why is the area model useful for decimal multiplication?
The area model converts an unfamiliar decimal multiplication into a familiar whole number multiplication with partial products, making the calculation easier to visualize and understand.