Math Background

Lesson: Multiplying and Dividing Decimals
Developing the Concept

Many problem-solving situations involve operations with decimals. Now that your students have learned to multiply decimals, it's time to show them how to divide a decimal by a decimal.

Prerequisite Skills and Concepts: Students need to be familiar with division of whole numbers and division by a decimal.

Present this problem to the class.

Aaron ties trout flies for the local fly-fishing shop. He earns $0.65 for each fly he ties. If he earned $9.75 before his lunch break, how many trout flies did he tie?

  • Ask: Can anyone come to the board and show what operation is needed to solve this problem?
    A volunteer should show the following.
    division problem
  • Say: Remember that when we divide by a decimal we can multiply by a power of 10 to change the divisor to a whole number.
  • Ask: What power of 10 must we use to change the divisor to 65?
    Students should answer 10², or 100. Remind students that if you multiply the divisor by a power of 10, you must also multiply the dividend by the same power of 10. This does not change the quotient. Show students how the decimal points move to the right when we mentally multiply by 100. Show this before completing the division.
    division problem
  • Ask: Why did we multiply by 10²?
    Students should respond that in order to change 0.65 to a whole number, we must multiply it by 10², or 100.
  • Say: Once we multiply both the divisor and the dividend by a power of 10, we can divide as with whole numbers.

    Have the volunteer complete the division.

    division problem

    Aaron tied 15 trout flies.

Wrap-Up and Assessment Hints
Provide the following practice exercises to check students' mastery of dividing a decimal by a decimal. Remind students that when multiplying by (positive) powers of ten, we move the decimal to the right as many places as designated by the exponent (or the number of zeros in the standard form).

  1. 4.85 ÷ 0.5 = (9.7)
  2. 0.938 ÷ 0.7 = (1.34)
  3. 0.315 ÷ 0.35 = (0.9)
  4. 0.184 ÷ 0.8 = (0.23)
  5. 0.824 ÷ 0.24 = (3.43)

Houghton Mifflin Math Grade 5