Page 156 - Basic College Mathematics with Early Integers

2.4 SUBTRACTING INTEGERS Objectives

Subtract Integers.

In Section 2.2, we discussed the opposite of an integer. Add and Subtract Integers.
The opposite of 3 is -3. Evaluate an Algebraic Expression
The opposite of -6 is 6. by Subtracting.
In this section, we use opposites to subtract integers. Solve Problems by Subtracting
Integers.
Objective Subtracting Integers

To subtract integers, we will write the subtraction problem as an addition problem.
To see how to do this, study the examples below.
10 - 4 = 6
10 + 1-42 = 6
Since both expressions simplify to 6, this means that
10 - 4 = 10 + 1-42 = 6

Also,
3 - 2 = 3 + 1-22 = 1
15 - 1 = 15 + 1-12 = 14

Thus, to subtract two numbers, we add the first number to the opposite of the second
number. (The opposite of a number is also known as its additive inverse.)

Subtracting Two Numbers

If a and b are numbers, then a - b = a + 1-b2.

Examples Subtract. PRACTICE 1–4
Subtract.
first opposite of the
Subtraction = + 1. 12 - 7 2. -6 - 4
number second number
3. 11 - 1-142 4. -9 - 1-12
∂ ∂ ∂ ∂
1. 8 - 5 = 8 + 1-52 = 3
2. -4 - 10 = -4 + 1-102 =-14
3. 6 - 1-52 = 6 + 5 = 11
4. -11 - 1-72 = -11 + 7 = -4
Work Practice 1–4

Examples Subtract. PRACTICE 5–7
Subtract.
Î
Î
5. -10 - 5 =-10 + 1-52 =-15 5. 5 - 9 6. -12 - 4
7. -2 - 1-72
Î
Î
6. 8 - 15 = 8 + 1-152 =-7
Î
Î Answers
7. -4 - 1-52 =-4 + 5 = 1
1. 5 2. -10 3. 25 4. -8
Work Practice 5–7 5. -4 6. -16 7. 5
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