Fundamentals of Mathematics
1.4 (Continue) & 1.5 Order of Operations
Ricky Ng
Lecture 8
September 13, 2013
Ricky Ng
Fundamentals of Mathematics
Announcements
Registration for Test 1.
Fingerprint in CASA.
Online Quiz 2 & 3 due 9/13 Friday.
Homework 2 is due on 9/14.
Homework 3 is up and due on 9/18.
Ricky Ng
Fundamentals of Mathematics
Last Time...
m
x
m−n
n = x
x n
n
x
= xyn
y
−n
n
n
x
= xy = xy n
y
√
x means positive square root.
√
View x as x1/2 and vice-versa.
Simplest radical form & perfect square.
Ricky Ng
Fundamentals of Mathematics
Fractions and Radicals
Usually when we deal with radicals and fractions, we do not
want radical in the denominator. When we encounter
situation like
a
√ ,
b
we do something similar to fraction addition. That is, we
transform, or rationalize, the fraction:
Rule
√
√
a
a
b
a× b
√ =√ ×√ =
.
b
b
b
b
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1.4 Exponents and Radicals
Examples
Write the following in the simplest radical form.
√3
5
q
4
7
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1.4 Exponents and Radicals
9 1/2
7
4 −1/2
11
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1.4 Exponents and Radicals
Popper 3: Question 1
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1.4 Exponents and Radicals
Popper 3: Question 2
Ricky Ng
1.4 Exponents and Radicals
Order
The order of operations matters! Consider
9 + 6 ÷ 2.
If we add first, then divide... we get 15
2 .
If we divide first, then add... we get 12.
Therefore, we need to set an order to perform operations.
Ricky Ng
1.5 Order of Operations
Here is the priority list:
1
Parentheses, from innermost to outward.
2
Exponential and roots.
3
Multiplication and division, left to right.
4
Addition and subtraction, left to right.
Ricky Ng
1.5 Order of Operations
Examples
Evaluate the following:
3+4×2
23 ÷ 4
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1.5 Order of Operations
(7 − 1)2 ÷ 3
3 · (2 + 3)
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1.5 Order of Operations
Popper 3: Question 3
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1.5 Order of Operations
More Examples
Evaluate the following:
3−
2
3
1
3
+ 12 .
÷ 32 .
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1.5 Order of Operations
Popper 3: Question 4
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1.5 Order of Operations
Popper 3: Question 5
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1.5 Order of Operations
More Examples
Evaluate the following:
24(−2) ÷ 4 ÷ 2(−2)
3 − (9 − (3 − 5)3 )
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1.5 Order of Operations
− 34 ÷
5
8
·
10
3
√ 3
16−2
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1.5 Order of Operations
Popper 3: Question 6
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1.5 Order of Operations
Absolute Value
Recall absolute value |x| just makes x positive. When it comes
to order of operation, absolute value is just like parentheses.
For example,
| − 2 − 5| × 3
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1.5 Order of Operations
Examples
Evaluate the following:
|23 (−3)|−10
4+6÷2
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1.5 Order of Operations
3+|4−52 |
1+6÷3
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1.5 Order of Operations
Popper 3: Question 7
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1.5 Order of Operations
Summary of the week
1
Exponent Rules
2
Fractions with exponents
3
Radicals and square root
4
Simplest radical form
5
Order of operations matters!
Ricky Ng
1.5 Order of Operations