Math Background

Lesson: Multiplying and Dividing Decimals
Introducing the Concept

Multiplication of decimals is one of the most frequently used operations in our daily lives. Working with money and using calculators makes understanding decimals an essential skill.

Prerequisite Skills and Concepts: Students should be familiar with multiplication of whole numbers.

  • Say: You have learned how to multiply two whole numbers. Now you will learn how to multiply two decimals. First, let's begin by reviewing how to multiply two whole numbers.
  • Ask: There are 26 books in the astronomy section of the library. They average 175 pages each. How many total pages are there? Who can show on the board how to solve this problem?
    Students should show the correct whole number multiplication.
    multiplication problem

    There are 4,550 pages.

  • Say: Multiplying decimals is very similar to multiplying whole numbers.
  • Ask: Marilyn needs 2.6 yards of fabric for her sewing project. The fabric costs $1.75 per yard. What is the cost of the fabric? Who can show us on the board how to solve this problem?
    Students should respond by writing the following.
    multiplication problem

    Have students multiply the numbers, disregarding the decimal points, just as if they were whole numbers.

  • Ask: Who can tell us how many decimal places are in the first factor?
    Students may answer “two places.” Write this next to the first factor. Underline the two decimal places in 1.75.
    multiplication problem
  • Ask: How many decimal places are in the second factor?
    Students may answer “one place.” Write this next to the second factor. Underline the decimal place in 2.6.
    multiplication problem
  • Ask: What is the total number of decimal places in the factors?
    Students should answer “three places.” Show the following.
    multiplication problem
  • Say: There is one important rule to remember when multiplying decimals. The number of decimal places in the product must equal the total number of decimal places in the factors.
    You can write this rule and display it in a prominent place in the classroom.
  • Ask: Who can show us where the decimal point should be placed in this product?
    Students should respond by placing the decimal point between the 4 and 5.
    multiplication problem

    Remind students that the product has 3 decimal places because the total number of decimal places in the factors is 3. Point out the similarities between the whole number example and the final example.

  • Ask: How much did Marilyn's fabric cost?
    Students may answer $4.55
    Have students practice multiplying decimals.

    Have them label the number of decimal places in each factor and the total number of decimal places in the product. Have them underline the decimal places just as they did in the lesson examples.

    multiplication problems

Houghton Mifflin Math Grade 5