ADDITION OF REAL NUMBERS

CHAPTER 1 SECTION 6

MTH 11203Algebra

Addition of Real Numbers

The four basic operations of arithmetic are:1. Addition2. Subtraction3. Multiplication4. Division

Negative numbers: overdrawn bank account, temperatures below zero, coal miner under ground, football lost yards in a play, profit/loss, surplus/deficit.

Adding Real Numbers Using a Number Line

Using Number line to add numbers. Represent the first number to be added by an arrow

starting at 0 Move the arrow left for a negative number and to the right

for a positive number. Any number without a sign in front of it is positive.

The second number is counted from the tip of the first number.

The sum is found at the tip of the second arrow.

Example #26 pg 48: -8 + 2 = -68 7 6 5 4 3 2 1 0 1 2 3 4 5

Adding Real Numbers Using a Number Line

Example #30 pg 48: -3 + (-5) = -8

Example #36 pg 48: 6 + (-5) = 1

8 7 6 5 4 3 2 1 0 1 2 3 4 5

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

Adding Real Numbers Using a Number Line

Example #31 pg 48: 6 + (-6) = 0

Example:6 + (-2) = 4

6 5 4 3 2 1 0 1 2 3 4 5 6 7

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

Adding Real Numbers Using a Number Line

Example: -7 + (3) = -4

Example:-2 + (-5) = -7

8 7 6 5 4 3 2 1 0 1 2 3 4 5

10 9 8 7 6 5 4 3 2 1 0 1 2

Adding Real Numbers Using a Number Line

Example: 10 + (-10) = 0

Example: A miner descends 120 feet into a mine shaft. Later, he descends another 145 feet. Find the depth of the miner -120 + (-145) = -265 ft

2 1 0 1 2 3 4 5 6 7 8 9 10 11

Adding Fractions

Adding fraction, where one or more or the fractions are negative 1. Find a common denominator

2. Add the numerators

3. Keep the common denominator

Example # 78 pg 48:

Use the sign of the larger number

4 5 4 3 12 LCD = 27

9 27 9 3 27

12 5 12 5 7

27 27 27 27

Adding Fractions

Example:

Use the sign of the larger number.

5 6 5 7 35 6 8 48 LCD = 56 and

8 7 8 7 56 7 8 56

35 48 35 ( 48) 13

56 56 56 56

Adding Fractions

Example # 89 pg 48:

When adding two negatives

we get a negative answer

5 3 5 5 25 3 6 18 LCD = 60 and

12 10 12 5 60 10 6 60

25 18 25 ( 18) 43

60 60 60 60

Adding Fractions

Example # 89 pg 48:

When adding two negatives

we get a negative answer

1 8 1 11 11 8 8 64 LCD = 88 and

8 11 8 11 88 11 8 88

11 64 11 ( 64) 75

88 88 88 88

Identify Opposites

Opposites or Additive Inverses are any two numbers whose sum is zero.

If a is any real number then –a is its opposite, because a + (-a) = 0

Negative signs are thought of as “opposites of”

-(-3) = 3

Example #13 pg 48:

Write the opposite of 9

The opposite of 9 is -9 because 9 + (-9) = 0

Identify Opposites

Example #14 pg 48:

Write the opposite of -7

The opposite of -7 is 7 because (-7) + 7 = 0

Example #20 pg 48:

Write the opposite of -¼

The opposite of -¼ is ¼ because (- ¼ ) + ¼ = 0

Identify Opposites

Example:

Write the opposite of 6

The opposite of 6 is -6 because 6 + (-6) = 0

Example:

Write the opposite of -3/5

The opposite of -3/5 is 3/5 because (- 3/5 ) + 3/5 = 0

Add Using Absolute Value

Rule # 1: Adding Real Numbers with the same sign

To add real numbers with the same sign, both positive or both negative, add their absolute values. The sum has the same sign as the numbers being added

Example # 49 pg 48: Example # 51 pg 48:

7 + 9 = 16 -8 + (-4) = -12

|7| + |9| |-8| + |-4|

7 + 9 8 + 4

16 12

Use the sign of the numbers being added

The sum of two positives will always be positive

The sum of two negatives will always be negative

Add Using Absolute Value

Example: Example # 51 pg 48:

12 + 7 = 19 -5 + (-10) = -15

|12| + |7| = 19 |-5| + |-10|

12 + 7 5 + 10

19 15

Use the sign of the numbers being added

The sum of two positives will always be positive

The sum of two negatives will always be negative

Add Using Absolute Value

Rule # 2: Adding Real Numbers with different sign, one positive and one negative. Subtract the smaller absolute value from the larger absolute value. The sum has the sign of the larger absolute value.

Example # 28 pg 48: Example # 44 pg 48:

9 + (-12) = -3 -9 + 13 = 4

|-12| - |9| |13| - |-9|

12 – 9 = 3 13 – 9 = 4

|-12| is larger, therefore -3 |13| is larger, therefore 4

Use the sign of larger absolute value

Add Using Absolute Value

Example: Example:

13 + (-5) = -8 14 + (-21) = -7

|13| - |5| |21| - |14|

13 – 5 = 8 21 – 14 = 7

|13| is larger, therefore 8 |21| is larger, therefore -7

Use the sign of larger absolute value

Add Using Absolute Value

Example: Example:

-16 + (9) = -7

|16| - |9|

16 – 9 = 7

|16| is larger, therefore -7

Use the sign of larger absolute value

3 2 19

4 9 36

36

3 9 27

4 9 36

2 4 8

9 4 36

27 8

36 36

27 8 19

36 36

LCD

Add Using Absolute Value

Example:

-17.56 + (-19.23) = -36.79

|17.56| + |19.23|

17.56 + 19.23

36.79

|19.23| is larger, therefore -36.79

Use the sign of larger absolute value

Appendix A may help with operation with decimals.

Add Using Absolute Value

Example: The Taggerty Bakery has a profit of $450,567 for the first five months of the year, and a loss of $52,987 for the reminder of the year. Find the net profit or loss for the year.

450,567 + (-52,987) = 397,580 profit

|450,567| - |52,987|

450,567 – 52,987

397,580

|450,567| is larger, therefore 397,580

Use the sign of larger absolute value

HOMEWORK 1.6

Page 48 - 49

15, 17, 23, 25, 29, 33, 53, 93, 107, 109