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PLEASE HELP US OUT WITH THIS:
When you go to the open lab next door in 203, please make sure
you sign in on the log sheet and enter your instructor’s name and
your section number. We need to collect this information to
document lab usage and ensure future funding for tutors.
This is Math 010 section number 00 ???
My instructor’s last name is ???
(Your instructor will write this information on the
whiteboard; please copy it into your notebook.)
Monday through Thursday
8:00 a.m. – 6:30 p.m.
NOW
CLOSE
YOUR LAPTOPS
(You may reopen them when I finish the
lecture, at which time I will take roll for
today’s attendance points.)
NOTE:
There is ONE online homework assignments
due at the start of the next class period:
HW 1.3A – This one is completely online. You should still
show work for these problems in your class notebook, but
you don’t need to turn any work in, just enter the answers
online.
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Lecture Slides:
• Power Point lecture slides are always posted in the
“Daily Class Lecture Slides” section for each day, so
you can copy, view, or print them at any time.
• The slides might not always be projected during the
lecture, but they will give you a good overview/
preview and will also help you review for tests and
quizzes.
• If you have trouble keeping up with the pace of the
lecture, you can print the slides as a handout (3 or 4
to a page) before you come to class and then take
notes on them during the lecture.
How to get to the online version of the textbook
• Click on either:
– Interactive Online Textbook
– Screen Reader Accessible Textbook
For “Interactive Online Textbook”
• Click on textbook chapter of choice
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For “Screen Reader Accessible
Textbook”
• Click on “eBook”
• Click on “alternate version of your eBook”
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• Select the option that applies to your screen
reading program
Gateway Quiz Information:
•
•
•
•
The Gateway Quiz covers material from sections 1.3-1.7 on
fractions and the order of operations.
The first Gateway Quiz will be given on the day before Quiz 1
(in the fifth week of the semester).
You will have the chance to take several practice Gateway
Quizzes before then, and there will also be Gateway-type
problems covered in each day’s class lecture and on each day’s
homework assignment.
One-on-one or small group review/help/study sessions for the
Gateway Quiz are available with the specially trained tutors
and teaching staff in the Math TLC open lab in 203 JHSW from
8:00 a.m. until 6:30 p.m. every Monday, Tuesday, Wednesday
and Thursday. No appointments are necessary.
Gateway Quiz Overview:
• 8 questions on working with fractions and order of operations.
• No calculators are allowed for this quiz, so don’t use one
when you take the practice versions.
• Gateway Quiz must be passed with 100% score before you can
pass Math 010.
• You may take the quiz multiple times until you receive 100%,
with different versions of the quiz given each time.
• A worksheet for a preview Gateway homework assignment will
be handed out on the first day of class (due on the third day of
class.
• Practice versions of the Gateway Quiz, both online versions and
printed versions, can be found in the “Gateway Quiz Info”
menu area of the Math 010 CourseCompass web site.
HELPFUL HINT:
Make sure you always take written notes
during lecture (and as you do your homework
assignments). Notes will be a big help as you
study for quizzes and tests.
(And they might even earn you extra credit
points some days as the TA and I walk around
the class after lecture...)
Section 1.3A
Factoring a number means writing it as a product of
prime numbers.
A prime number is a natural number (other than 1)
whose only factors are 1 and itself.
The first few prime numbers are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
(It will help you on the Gateway Quiz
if you learn these by heart!)
Question: Why isn’t 6 a prime number?
Answer: Because it can be written as 2x3 (or 2·3)
Why isn’t 8 a prime number? 9? 10? 12?
Question:
What’s the next prime number after 29?
Check 30: Can you divide 30 by anything other than 1
and 30?
Yes, so it’s NOT prime.
(Numbers that are not prime are called composite numbers.)
Check 31: Try dividing it by all of the prime numbers
up to half of 31. If none of them work, then 31 is
prime.
Can you divide 31 by 2? NO By 3? NO By 5? NO
By 7? By 11? By 13? By 17?
( 17 is more than half of 31, and none of the primes up
through 17 divide into 31, so we conclude that 31 is
a prime number.)
Back to factoring numbers:
Factor the number 44 into a product of primes.
Solution:
First, think of some number that divides into 44.
How about 2?
Then write 44 as 2·22. (Because 44÷2 = 22)
2 is prime, but 22 can be divided further, into 2·11
So 2·22 = 2·2·11 (NOTE: We could also write this as 22·11)
These are now all prime numbers, so we’re done.
(Always arrange the numbers in order from smallest to
largest in your final answer).
Another example:
Factor the number 150 into a product of primes.
Solution:
First, think of some number that divides into 150.
How about 10?
Then write 150 as 10·15. (Because 150÷10 = 15)
Both of these can be divided further:
10·15 = 2·5·3·5
These are now all prime numbers, so we’re done,
except for arranging the numbers in order from
smallest to largest.
Final answer: 2·3·5·5 (or 2·3·52)
Sample problem from today’s homework:
ANSWER: 2•2•5
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Recall that a fraction is a quotient of two numbers.
(“quotient” means you’re dividing the top number by the bottom
number)
• The numerator is the top number.
• The denominator is the bottom number.
Simplifying fractions (reducing to lowest terms)
involves factoring numerator and denominator
into prime numbers and then canceling any
primes that appear on both top and bottom
Fundamental Principle of Fractions
• Can cancel common factors in numerator
and denominator.
• If a, b, c are real numbers such that b and
c  0.
a c a

bc b
Why this works:
c
 1 as long as c  0.
c
Example
Simplify the following fractions.
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2 35
5
5



48 2  2  2  2  3 2  2  2 8
22
2 11

45 3  3  5
Since there are no common terms, the original
fraction is already simplified.
2 23
12
1


60 2  2  3  5 5
Sample problem from today’s homework:
ANSWER: 5
7
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Sample problem from today’s homework:
ANSWER: 2 (it’s already in simplest form)
9
22
.
.
Multiplying and Dividing Fractions
Without Using a Calculator
Using Factoring
NOTE: Gateway Quiz problems 3 & 5 on
multiplying and dividing fractions can both
be done using the similar steps that will be
covered in the following slides. There will be
some problems in the online homework for
sections 1.3A & B that also use these
techniques.
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Basic strategy for multiplying and
dividing fractions:
These kinds of problems DO NOT require
finding a common denominator. They can
be most easily done by factoring both the
numerator (top number) and denominator
of both fractions into a product of prime
numbers, and then canceling any common
factors (numbers that appear on both the top and
the bottom.)
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Sample Problem: Multiplying fractions
Step 1: Factor both the numerators and denominators into
prime factors, then write each fraction in factored form:
First fraction:
Second fraction:
39= 3∙13 and 50 = 2∙5∙5
15= 3∙5 and 26 = 2∙13
So you can write 39 • 15 as 3∙13 • 3∙5
50 26
2∙5∙5 2∙13
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Sample Problem: Multiplying fractions (continued)
Step 2: Now just cancel any common factors that appear in
both numerator and denominator. Once you multiply out
any remaining factors, the result is your simplified answer.
/ • 3∙5
/ = 3∙3 = 9
3∙13
/ 2∙13
/
2∙5∙5
2∙5∙2 20
.
NOTE: It is much easier to factor first and then cancel, rather
than multiplying out the numerators and denominators and then
trying to simplify the answer (especially if you aren’t using a
calculator!) If you multiplied first, you’d have gotten
585, which would be nasty to simplify by hand…
1300
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Sample problem from today’s homework:
ANSWER: 1
10
.
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Sample Problem: Dividing fractions
Step 1: Multiply the first fraction by the
reciprocal of the second fraction.
45 ÷ 21 = 45 • 26
13 26 14 21
(i.e. flip the second fraction upside down and change ÷ to • .)
Step 2: Factor both the numerators and denominators into
prime factors, then write each fraction in factored form:
First fraction:
45 = 3∙3∙5 and 13 = 13 (prime)
Second fraction:
26 = 2∙13 and 21 = 3∙7
So you can write 45 • 26 as 3∙3∙5 • 2∙13
13 21
13
3∙7
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Sample Problem: Dividing fractions (continued)
Step 3: Now just cancel any common factors that appear in
both numerator and denominator. Once you multiply out
any remaining factors, the result is your simplified answer.
/ • 2∙13
/ = 3∙5∙2 = 30
3∙3∙5
/
/3∙7
13
7
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NOTE: Once again, it is much easier to factor first and then
cancel, rather than multiplying out the numerators and
denominators and then trying to simplify the answer (especially if
you aren’t using a calculator!) If you multiplied first, you’d have
gotten 1170 , which would be pretty hard to simplify by hand.
273
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Sample problem from today’s homework:
ANSWER: 5
7
30
Now open your laptops
1. Open your browser. (http://pearsonmylabandmastering.com)
2. Sign in to MyLab and Mastering using the id and
password you created when you registered on day 1.
3. Click on the name of this course.
Here’s what you should now be seeing:
Now click the “Homework” button at the left side of
the screen.
• Then click on today’s lesson HW 1.3A
•
• Now click on Exercise 1
Here’s what you should now be seeing:
• After you enter the answer to a problem, click “Check Answer” to see if it’s
correct. For most problems, you’ll get three tries to get it right.
• Even if you get a problem wrong, you can do it over until you get it right
(the computer will generate a new version for you to try.)
• You DO NOT need to save or print your
homework or email me your results – as soon
as you click “check answer” on a problem,
your results are automatically saved and
recorded in the online gradebook (yours and
mine.)
• If you are having trouble with a problem,
check the on-line help available for each
problem:
• Help Me Solve This
• Textbook Pages
• Animation(for some problems)
IMPORTANT: Even if you get a problem wrong on each of your
three tries, you can still go back and do it again by clicking
“similar exercise” at the bottom of the exercise box. You can
do this nine times, for a total of 30 tries (3 tries at each of 10
different problems. You should always work to get 100% on
each assignment!
IMPORTANT:
You can go back in and work on an
assignment even after submitting it,
provided the deadline has not expired, so
again, you should always work to get 100%
on each assignment.
Another thing to remember:
Take notes as you do each homework problem.
Write down all steps (show your work!). Again,
this helps tremendously when you’re studying
for tests.
(Some days I might do a random “notebook check” after
lecture, and will give extra credit attendance points to those
who’ve taken legible notes.)
If there’s still time left in the class
session after lecture, you have to stay in
the classroom to work on your
homework till the end of the session.
When you finish your homework to
100% before the end of the class period,
you may work on Gateway problems
until the class ends.
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Reminder:
Today’s homework assignment on section 1.3A is
due at the start of our next class session.
Monday through Thursday
8:00 a.m. – 6:30 p.m.