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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. – 7:30 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 are TWO online homework assignments

due at the start of the next class period:

1. Gateway Homework #1 – This one has a required paper worksheet on which you must show all the steps of your work for all 8 problems. (This worksheet was handed out on Day 1, but if you didn’t get a copy, just pick one up from a TA before you leave class today.) This worksheet must be turned in at the start of the next class period in order to get full credit for the assignment. (You still need to enter the answers online, AND show work on the worksheet.)

2. 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. 4

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”8

• 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 fourth 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 7:30 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 1.3AFactoring 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 = 2·5·3·5These 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:

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ANSWER: 2•2•5

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.

b

a

cb

ca

Why this works:

1c

cas long as c 0.

Example

Simplify the following fractions.

48

30

32222

532

222

5

8

5

45

22

533

112

Since there are no common terms, the original

fraction is already simplified.

60

12

5322

322

5

1

Sample problem from today’s homework:

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ANSWER: 5 7

Sample problem from today’s homework:

22

ANSWER: 2 (it’s already in simplest form)

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.

.

Multiplying and Dividing Fractions Without Using a Calculator

Using Factoring

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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.

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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Basic strategy for multiplying and dividing fractions:

Sample Problem: Multiplying fractions

Step 1: Factor both the numerators and denominators into prime factors, then write each fraction in factored form:

First fraction: 39= 3 13 ∙ and 50 = 2 5 5∙ ∙ Second fraction: 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 13∙ • 3 5∙ = 3 3∙ = 9 .

2 5 5 2 13 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:

27

ANSWER: 1 .

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Sample Problem: Dividing fractions

Step 1: Multiply the first fraction by the 45 ÷ 21 = 45 • 26reciprocal of the second fraction. 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∙ 28

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.

3 3 5∙ ∙ • 2 13∙ = 3 5 2∙ ∙ = 30 13 3 7 7 7∙

/ / / /

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 29

Sample Problem: Dividing fractions (continued)

Sample problem from today’s homework:

30

ANSWER: 5 7

REMINDER:There are TWO online homework assignments

due at the start of the next class period:

1. Gateway Homework #1 – This one has a required paper worksheet on which you must show all the steps of your work for all 8 problems. (This worksheet was handed out on Day 1, but if you didn’t get a copy, just pick one up from a TA before you leave class today.) This worksheet must be turned in at the start of the next class period in order to get full credit for the assignment. (You still need to enter the answers online, AND show work on the worksheet.)

2. HW 1.3A – This one is completely online. You should still show work for these 20 problems in your class notebook, but you don’t need to turn any work in, just enter the answers online. 31

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.

Now open your laptops

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

• 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.)

Here’s what you should now be seeing:

• 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.

If you have finished the homework already, or if you get it finished before the end of the class period, show your on-screen 100% score to the teacher or TA and you may then leave class early.

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Reminder:Today’s homework assignment on section 1.3A is

due at the start of our next class session, along with Gateway HW #1 (if you didn’t get a

worksheet for that on Day 1, get one before you leave class today).

Monday through Thursday 8:00 a.m. – 7:30 p.m.