Basic Mathematics for College Students

 

156 Chapter 2 The Integers

 

WRITING

97. Is the sum of a positive and a negative number
    always positive? Explain why or why not.


98. How do you explain the fact that when asked to add
    and 8, we must actually subtractto obtain the
    result?


99. Explain why the sum of two negative numbers is a
    negative number.


100. Write an application problem that will require
     adding and.


101. If the sum of two integers is 0, what can be said
     about the integers? Give an example.


102. Explain why the expression is not written
     correctly. How should it be written?

 6  5

 50  60

 4

REVIEW

103. a. Find the perimeter of the rectangle shown
     below.
     b. Find the area of the rectangle shown below.


104. What property is illustrated by the statement
     ?


105. Prime factor 250. Use exponents to express the
     result.


106. Divide:

144

12

5  15  15  5

5 ft

3 ft

SECTION 2.3

Subtracting Integers

Objectives

1 Use the subtraction rule.

2 Evaluate expressions involving

subtraction and addition.

3 Solve application problems

by subtracting integers.

In this section, we will discuss a rule that is helpful when subtracting signed numbers.

1 Use the subtraction rule.

The subtraction problem can be thought of as taking away 4 from 6. We can use

a number line to illustrate this. Beginning at 0, we draw an arrow of length 6 units long

that points to the right. It represents positive 6. From the tip of that arrow, we draw a

second arrow, 4 units long, that points to the left. It represents taking away 4. Since we

end up at 2, it follows that 6  4  2.

6  4

Note that the illustration above also represents the addition .We

see that

Subtracting 4 from 6... is the same as... adding the opposite of 4 to 6.

The results are the same.

This observation suggests the following rule.

6  4  2 6 (4) 2

6 (4) 2

6  4  2

− 4 − 3 − 2 −101 234

4

5 6 7

End

Begin

6