What you should learn

To add and subtract rational numbers

To simplify expressions that contain rational numbers

NCTM Curriculm Standards 2, 4, 6 - 10

 

Introduction: In 1982, the average number of weekly overtime hours worked by a U.S. worker was 2 1/4 hours. This average increased 1 1/4 hours by 1989 and then decreased 1/2 hour by 1991. What was the average number of weekly overtime hours worked in 1991?

To answer this question, you need to find the following sum.

To add rational numbers such as these, use the same rules you used to add integers. When adding three or more rational numbers, you can use the commutative and associative properties to rearrange the addends.

Method 1: Use the rules

Method 2: Use a number line.

Exercise 1: Find each sum.

a. 4 1/8 + (-1 1/2)

4 1/8 + (-1 1/2) = 4 1/8 + (-1 4/8)

= +(|4 1/8| - |-1 4/8|)

= + (4 1/8 - 1 4/8)

= + (3 9/8 - 1 4/8)

= 2 5/8

b. -1.34 + (-0.458)

c. -2/5 + 1 1/2 + (-2/3)

 

 

To subtract rational numbers, use the same process you used to subtract integers.

Exercise 2: Find each difference

a. -6.24 - 8.52

-6.24 - 8.52 = -6.24 + (-8.52) = -14.76

b. -3/5 - (-4/7)

Exercise 3: A corporation produces a high-speed processor for computers. In November, 1994, the corporation announced that there was a flaw in the processor tha tcould cause errors in mathematical calculations. In one week, the corporation's stock dropped 2 1/4 points. By December 13, the stock had dropped another 2 1/8 points. How many points did the stock drop in this time period?

You can also evaluate expressions involving the addition and subtraction of rational numbers.

Exercise 4:

a. Evaluate p - 3.5 if p = 2.8

b. Evaluate 11/4 - x if x = 27/8

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: 15 - 45 odd, 47 - 54

Alternative Homework: Enriched: 14 - 42 even, 43 - 54

Extra Practice: Students book page 760 Lesson 2-5

Extra Practice Worksheet: Click Here.

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