Section 1.4 Addition and Subtraction of Real Numbers.

Section 1.4

Addition and Subtraction of Real Numbers

1.4 Lecture Guide: Addition and Subtraction of Real Numbers

Objective 1: Add positive and negative real numbers. There is a difference in the process for adding two numbers with like signs versus adding two numbers with unlike signs.

Verbally Numerical Examples

Graphical Examples

To add numbers with like signs, first add the absolute values of the terms. Then use the same sign as the terms.

4 2

4 2

-8 -6 -4 -2 0 2 4 6 8

-8 -6 -4 -2 0 2 4 6 8

Adding Real Numbers with Like Signs

Adding Real Numbers with Unlike Signs

Verbally Numerical Examples

Graphical Examples

To add numbers with unlike signs, first subtract the smaller absolute value from the larger absolute value. Then use the sign of the term with larger absolute value.

5 2

5 2 -8 -6 -4 -2 0 2 4 6 8

-8 -6 -4 -2 0 2 4 6 8

1. 2. 3.

Find each sum where each term has the same sign.

10 7 6 14 14 14

4. 5. 6.

Find each sum where each term has the same sign.

8 5 3 11 12 12

7. 8. 9.

Find each sum where each term has the same sign.

2.4 5.2 2 27 7

1 36 5

Find each sum where each term has the same sign.

10. 11. 12. 0.3 9.4 3 411 11

3 510 6

Find each sum where each term has the same sign.

13. 14. 15.7 12 9 2 6 6

Find each sum where each term has the same sign.

16. 17. 18. 10.8 4.3 2 53 6

1 15 2

Determine if the terms have like or unlike signs.

If the terms have _______________ signs, add the absolute values. The sum will have the _______________ sign as both terms.

If the terms have _______________ signs, subtract the absolute values. The sum will have the same sign as the term with the _______________ absolute value.

Summary of Addition of Real Numbers

19. 20.

Find each sum.

3 12 4 4 9 7 17

Algebraically Verbally Numerical Example

Commutative property of addition:

The sum of two ____________ in either order is the same.

Associative property of addition:

Terms can be ____________ without changing the sum.

Objective 2: Use the commutative and associative properties of addition.

Properties of Addition

a b b a 2 5

5 2

a b c a b c 1 2 3

1 2 3

21. Explain the distinction between the commutative property of addition and the associative property of addition.

22.There are two different ways to use the commutative property of addition to rewrite the following expression: .

Can you write both?

x y z

__________________ and __________________

23. 24. 25.

Perform the indicated operations.

5 82 18 1 2 35 5 5

0.4 5.1 7.6

Objective 3: Subtract positive and negative real numbers.

It is helpful when first performing a subtraction to actually rewrite the subtraction as addition. This is not generally done once you are comfortable with performing subtraction mentally.

Algebraically Verbally Numerical Example

For any real numbers x and y,

.

To subtract y from x, add the ________ of y to x.

x y x y

6 4 6 ______

______

Subtraction

26. 27. 28.

Perform the indicated operations.

8 1 13 9 17 17

Perform the indicated operations.

29. 30. 31.0.7 3.4 5 19 3 3 3

5 8

32. 33. 34. 15 15 11 8 9 3

The terms in each expression have opposite signs. First rewrite each difference as a sum and then give its value.

35. 36. 37.4 19 3

1 55 8

7.3 5.1

The terms in each expression have opposite signs. First rewrite each difference as a sum and then give its value.

38. Determine the value of each expression.

(a) (b)7 2 2 7

(c) (d) 7 2 2 7

39. We know that addition is commutative.

What about subtraction?

40. The number of riders on the Top Thrill Dragster at Cedar Point amusement park is shown in the chart below. Determine the change in the number of riders from 2003 to 2005.

Riders on the Top Thrill Dragster

953,945943,313

562,438

0

500,000

1,000,000

1,500,000

2003 2004 2005

Phrases Used To Indicate Addition:

Key Phrase Verbal Example Algebraic Example

Plus "12 plus 8"

Total "The total of $25 and $40"

Sum "The sum of x and y"

Increased by "An interest rate r is increased by 0.5%"

More than "7 more than x“

12 8

$25 $40

x y

0.005r

7x

Phrases Used To Indicate Subtraction:

Key Phrase Verbal Example Algebraic Example

Minus "x minus y"

Difference "The difference between 12 and 8“

Decreased by "An interest rate r is decreased by 0.5%“

Less than "7 less than x"

Change "The change from .

7x

0.005r

12 8

x y

9670 to 96 70

Translate each verbal statement into algebraic form.

41. The total of t and six is nine.

42. Five more than z is zero.

Translate each verbal statement into algebraic form.

43. The sum of a real number b and its additive inverse is zero.

44. t minus seven equals v.

Translate each verbal statement into algebraic form.

45. The difference from x to y is ten.

46. w is four less than x.

Translate each verbal statement into algebraic form.

48. The subtraction fact 25 – 9 = 16 can be written as the addition fact ______________.

47. The subtraction fact 11 – 7 = 4 can be written as the addition fact that 4 + 7 = _______________.