SUBTRACTION OF REAL NUMBERS

CHAPTER 1 SECTION 7

MTH 11203Algebra

Subtract Numbers

Any subtraction problem can be rewritten as an addition problem using the additive inverse.

If a and b represent any two real numbers thena – b = a + (-b)

In other words to subtract b from a, add the opposite or additive inverse of b to a.

Subtract Numbers

Example # 14 pg 58:

17 – (+8) = 17 + (-8) = 9

Example # 16 pg 58:

9 – 4 = 9 + (-4) = 5

Example # 18 pg 58:

-6 - 3 = -6 + (-3) = -9

Example:

8 – (+3) = 8 + (-3) = 5

Subtract Numbers

Example:

7 – 10 = 7 + (-10) = -3

Example # 16 pg 58:

6 – 2 = 6 + (-2) = 4

Example # 18 pg 58:

-11 - 13 = -11 + (-13) = -24

Example:

27.54 – 29.86 = 27.54 + (-29.86) = -2.32

Subtract Numbers

When we subtract a negative number, we can replace the two negative signs with a plus sign.

Example # 24 pg 58:

9 – (-9) = 9 + 9 = 18

Example # 31 pg 58:

6 – (-3) = 6 + 3 = 9

Example # 41 pg 58: The difference in 12 and 8 is 4

-8 – (-12) = -8 + 12 = 4 12 is larger so positive answer

Subtract Numbers

Example:

15 – (-19) = 15 + 19 = 34

Example:

6 – (-5) = 6 + 5 = 11

Example: The difference in 24 and 2 is 22

-24 – (-2) = -24 + 2 = -22 24 is larger so negative answer

Subtract Numbers

Example: Subtract 16 from 5

5 – 16 = 5 + (-16) = -11

Example: Subtract 33 from 33

33 – 33 = 33 + (-33) = 0

Example: Subtract -7.38 from 3.59

3.59 – (-7.38) = 3.59 + 7.38 = 10.97

Subtract Fractions

Example # 70 pg 58:

Example # 87 pg 58:

4 5 4 6 24 5 5 25 LCD = 30 and

5 6 5 6 30 6 5 30

24 25 24 ( 25) 1

30 30 30 30

3 5Subtract - from -

10 12

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

12 10 12 10 12 5 60 10 6 60

25 18 25 18 7

60 60 60 60

Subtract Fractions

Example:

40

13

40

)38(25

40

3825

40

38

40

2540

38

2

2

20

19

40

25

5

5

8

5 40 LCD

20

19

8

5

Subtract Fractions

Example:

65

14

65

3925

65

39

65

25

65

39

65

2565

39

13

13

5

3

65

25

5

5

13

5 65 :LCD

5

3

13

5

13

5- from

5

3-Subtract

Evaluate Expression Containing More Than Two Numbers

Work from left to right unless parentheses or other grouping symbols appear.

Remember the Order of Operations. Parentheses, Exponents, Multiply or Divide, Add or Subtract.

The expression “Please Excuse My Dear Aunt Sally” may help you remember

In General, any real numbers a and b a + (-b) = a – b and a – (-b) = a + b

Evaluate Expression Containing More Than Two Numbers

Example # 118 pg 58:

-7 + 6 – 3

-1 – 3 same as -1 + (-3)

-4

Example # 122 pg 58:

-2 – 7 – 13 same as -2 + (-7) + (-13)

-9 – 13 same as -9 + (-13)

-22

Evaluate Expression Containing More Than Two Numbers

Example:

-6 - 13 - 5 same as -6 + (-13)

-19 - 5 same as -19 + (-5)

-24

Example:

-7 – (-3) + (-13) + (-2) same as -7 + 3

-4 + (-13) + (-2) same as -4 + (-13)

-17 + (-2)

-19

Evaluate Expression Containing More Than Two Numbers

Example # 126 pg 58:

-9 – 3 – (-4) + 5

-9 – 3

-12 – (-4) same as -12 + 4

-8 + 5

-3

Example # 127 pg 58:

17 + (-3) – 9 – (-7) same as 17 – 3

14 – 9 same as 14 + (-9)

5 – (-7) same as 5 + 7

12

Evaluate Expression Containing More Than Two Numbers

You can also simplify first then evaluate

Example # 129 pg 58:

-9 + (-7) + (-5) – (-3)

-9 – 7 – 5 + 3

-16 – 5 + 3

-21 + 3

-18

HOMEWORK 1.7

Page 58 - 59

13, 15, 21, 23, 38, 46, 57, 61, 65, 69, 107, 120, 131