Math Background

Lesson: Operations With Decimals
Introducing the Concept

Your students worked with addition, subtraction, multiplication, and division of decimals last year. Remind them of the importance of decimals in science, medicine, sports, and working with money.

Prerequisite Skills and Concepts: Students need to know how to add, subtract, multiply, and divide whole numbers.

  • Say: Last year, you learned to add, subtract, multiply, and divide with decimals. Today we'll review these operations.
  • Say: Aaron ran the first lap of his half-mile race in 1.08 minutes and the final lap in 1.13 minutes. What was his time for the race?
  • Ask: Who can show on the chalkboard how to solve this problem?
addition problem

Remind students that it's important to line up the decimal points.

  • Ask: Does it matter which number is written on top?
    Students should respond that the sum will be the same either way. Some students may remember that addition is commutative; if not, remind students of this property of addition, which states that the order of the addends doesn't change the sum.
  • Ask: Why is it important to line up the decimal points when adding or subtracting?
    Students should respond that when the decimal points are lined up, the place-value positions are also aligned correctly: ones with ones, tenths with tenths, hundredths with hundredths.

    Present this problem to the class.

  • Say: Tanya's batting average during the month of July was 0.342. Pat's batting average for July was 0.276. How much better was Tanya's batting average?
  • Ask: Who can show the class how to solve this decimal problem on the board?
    Students should reply with this solution.
    subtraction problem
  • Say: This difference shows that Tanya's batting average is sixty-six thousandths better than Pat's batting average.
  • Say: It is important to make sure the decimal points are lined up when subtracting. This keeps the place values correctly aligned.

    Present this problem to the class.

  • Say: Marvin telephoned his friend Carl in a neighboring city. The phone company charged $0.08 a minute for the toll call. If Marvin talked for 14.75 minutes, how much did the call cost?
  • Ask: Who can tell what operation to use to solve this problem?
    Students should respond that multiplying $0.08 x 14.75 min will give the total charge for the call.
    multiplication problem

    Have a student solve the problem on the board. If the decimal point is placed incorrectly in the answer, discuss the reasonableness of the solution. Some students may multiply and get $118.00. Discuss the idea that a reasonable estimate would be 15 x 8, or a little more than one dollar, so $118.00 would be unreasonable.

    Remind students of the rule for multiplying decimals: The sum of the number of decimal places in the factors equals the number of decimal places in the product. If necessary, write this rule on the board for review.

    multiplication problem

Present this problem to the class.

  • Say: Karen creates gift cards on her computer and sells them for $0.75 each. She earned $42.75 the last two weeks. How many cards did she sell?
  • Ask: Can anyone come to the board and show the class how to solve this decimal problem?
    Students should be able to write this division solution.
    division problem

    She sold 57 cards.

    If students forget the correct placement of the decimal point in the quotient, remind them that they should multiply the divisor and dividend by 100, which moves the decimal points 2 places to the right. This allows us to divide by a whole number, 75.


Houghton Mifflin Math Grade 6