Chapter 02 Section 03

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Chapter 02 Section 03

• Adding and Subtracting Integers

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2-3 ADDING AND SUBTRACTING INTEGERS
OBJECTIVES
To find the absolute value of a number and add
and subtract integers.

• What is absolute value?
• absolute value - distance between zero and a
  number on a number line
• Since distance can never be less than zero,
  absolute values are ALWAYS positive numbers.
• The symbol for the absolute value of a number is
  two vertical bars around the number.
• -125 125 is read The absolute value of -125
  equals 125.
• 200 200 is read The absolute value of 200
  equals 200.
• -7 6 1 is read The absolute value of the
  quantity -7 6 equals 1.

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2-3 ADDING AND SUBTRACTING INTEGERS
EXAMPLE 1a Evaluate -x 6 if x -10.
Substitute -10 for x.
--10 6
Add inside the absolute value bars.
--4
Take the absolute value of -4.
-(4)
-4
Drop the parenthesis.
EXAMPLE 1ß Evaluate each expression if r -5
and p 3. a. r 2 b. -4 r c.
-7 p
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2-3 ADDING AND SUBTRACTING INTEGERS
To add integers with the same sign, add their
absolute values. Give the result the same sign
as the integers. If the signs are alike, add and
keep the sign. To add integers with different
signs, subtract the lesser absolute value from
the greater absolute value. Give the result the
same sign as the integer with the greater
absolute value. If the signs are different,
subtract and keep the sign of the stronger one.
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2-3 ADDING AND SUBTRACTING INTEGERS
EX2ß
EXAMPLE 2a Find each sum. a. -10
(-17) b. 39 (-22) c. -28 16
METHOD 1 -10 (-17) -(-10 -17)
-(10 17) -27
METHOD 1 39 (-22) (39 - -22)
(39 - 22) 17
METHOD 2 Both numbers being added are
negative. Add the weight of each number and keep
the negative sign. 10 17 27 -27 is the answer.
METHOD 2 The signs are different on the two
terms, so subtract the weights of each number and
take the sign of the stronger number. 39 - 22
17 17 is the answer.
METHOD 2 The signs are different on the two
terms, so subtract and take the sign of the
stronger number. 28 - 16 12 -12 is the answer.
METHOD 1 -28 16 -(-28 - 16)
-(28 - 16) -12
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2-3 ADDING AND SUBTRACTING INTEGERS
EXAMPLE 2ß Find each sum. a. -6 (-2)
b. -56 42 c. 38 (-36)
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2-3 ADDING AND SUBTRACTING INTEGERS

• More terms.
• opposites - numbers with the same absolute value
  but different signs
• additive inverses - two numbers that add to zero
• Think about it The two number must be opposites
  to add to zero!

5 has an opposite, -5. -5 has an opposite,
5. Adding 5 (-5) or -5 5 equals 0.
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2-3 ADDING AND SUBTRACTING INTEGERS
To subtract a number is to add its
opposite. Taking away 3 is the same as adding
-3. Subtracting numbers and adding negative
numbers are one in the same. You have to train
yourself in this VERY IMPORTANT skill!
Example 6 - 2 4 and 6
(-2) 4
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2-3 ADDING AND SUBTRACTING INTEGERS
EX3ß
EXAMPLE 3a Find each difference. a. 6 -
14 b. -12 - (-8) c. 43 - (-26)
To subtract 14, add -14. 6 - 14 6 (-14)
signs opposite so subtract and take sign of
stronger -8 To subtract -8, add its
inverse, 8. -12 - (-8) -12 8 signs
opposite so subtract and take sign of stronger
-4 43 - (-26) 43 26
69
Special note here To subtract a negative is to
do the opposite of subtraction adding. So,
minus-a-minus is a plus.
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2-3 ADDING AND SUBTRACTING INTEGERS
EXAMPLE 3ß Find each difference. a. -9
(-4) b. -3 7 c. 12 (-48)
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2-3 ADDING AND SUBTRACTING INTEGERS
EX4ß
The rule for subtracting integers and the
distributive property can be used to combine like
terms. EXAMPLE 4a Simplify 2x - 5x.
2x 5x Use the additive inverse. 2x
(-5)x Use the distributive property. 2
(-5)x Two plus negative five yields -3x
EXAMPLE 4ß Simplify 4a 9a.
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2-3 ADDING AND SUBTRACTING INTEGERS
Solving the problems in this section can be done
in many different ways. The methods presented
show the actual step-by-grueling-step
processes. When you feel comfortable doing so,
steps should be skipped and quicker means
employed. DO THESE PROBLEMS HOW YOU FEEL MOST
COMFORTABLE - AS LONG AS YOUR WAY GIVES YOU A
CORRECT ANSWER!
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2-3 ADDING AND SUBTRACTING INTEGERS
HOMEWORK
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