Properties of Real Numbers
Download
Report
Transcript Properties of Real Numbers
Properties of Real Numbers
Section R-1
Chapter R: Review
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
1
Translating Words
Action
Operation
Possible Context Clues
Combine
Add
Separate
Subtract
Difference, Subtract
Combine equal
groups
Multiply
Product, Multiply
Divide
Quotient, Divide
Separate into equal
groups
3/29/2016 11:47 AM
Sum, Add, Total
R-1: Properties of Real Numbers
2
Quick Examples
Write an algebraic expression to represent each situation.
A. the number of apples in a basket
of 12 after n more are added
12 + n
Add n to 12.
B. the number of days it will take to
walk 100 miles if you walk M miles
per day
Divide 100 by M.
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
3
Quick Examples
Write an algebraic expression to represent each situation.
C. the difference of a number less 2
equals 7.
n–2=7
D. Write out: 21 ÷ 7 = 3
The quotient of 21 and 7 is 3.
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
4
Order of Operations
To evaluate operations, one way to remember the order of
operations is by using the mnemonic PEMDAS.
Order of Operations
1.
2.
3.
4.
Parentheses and grouping symbols.
Exponents.
Multiply and Divide from left to right.
Add and Subtract from left to right.
REMEMBER: Multiplication and Addition doesn’t always go
first before Division and Subtraction
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
5
Example 1
exponents
complete
parenthesis
complete
addition
multiplication
––
apply
combine
and
the subtraction,
exponent
these
and division,
firstnow
leftleft
to to
right
right
6 54 3
PEMDAS
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
6
Example 2
exponents
––apply
the subtraction,
exponent
complete
parenthesis
complete
multiplication
addition
combine
and
and
these
division,
firstnow
left
lefttotoright
right
22252
63332422 4 44
84310
2
2 5 3 3 2 4
2 2
PEMDAS
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
7
Example 3
2 [4 2 (10 6)]
22 +
[4
2+ (10
·32]
16]
++236
6)]
2 [4
+2 [4
38
PEMDAS
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
8
Your Turn
2 [8 3(4 2)] 3
11
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
9
Example 4
2 5 4 6 3 4
12
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
10
Example 5
5 3
9 10
15 3 1
9 10 2
3
1
6
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
11
Your Turn
21 100
25 3
28
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
12
Warm_Up #2
1. Solve
4 2[3 (6 7)] 8
2. Write the equation of “The product of 5 and x is
the product of 2 and 10.”
3/29/2016 11:47 AM
1-2
R-1:: Properties of Real Numbers
13
Add/Subtract fractions
1. List the factors of the bottom number to find
the “Least Common Denominator”
2. Multiply the LCD to the top number
3. Evaluate by add or subtracting across BUT
keeping the bottom number
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
14
Example 6
4 1
3 2
What are the MULTIPLES of the denominator:
3 : 3, 6,9,12,15...
2 : 2, 4, 6,8,10...
What is the SMALLEST SAME MULTIPLE
84
3
1
63 26
11
6
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
15
Example 7
4 1
5 2
3
10
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
16
Your Turn
2 8
15 9
46
45
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
17
Assignment
Pg 16
27-65 odd, OMIT 43
3/29/2016 11:47 AM
R-1: Properties of Real Numbers
18