MTH 11203 Algebra
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Transcript of MTH 11203 Algebra
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