WELCOME TO THE MM204

UNIT 1 SEMINAR

Seminar Policies Summary

Read the syllabus and other material in DocSharing. AIM name: tamitacker. Office Hours: Thursdays 6:30 – 7:30 pm

ET Email: ttacker@kaplan.edu Read the material in the book before the seminar. Don’t take notes; view the archive after class. Answer a question and make a “good” comment to get full credit.

Good comment: ask a question, make a comment that helps in the discussion, or answer a second question directed at the entire class.

Complete Seminar Quiz if you miss a seminar. Do your own work.

Question #1

1. If you’re having trouble with an algebra problem, which is the best course of action?

a. Throw your book across the room and scream about how hard algebra is.

b. Post a nasty note on the Discussion Board about algebra, Kaplan, MML, me, and the price of gasoline.

c. Take a break from algebra for a few days and decide to work on it again Tuesday night.

d. Take a short break, study a little more, and email me to ask for help.

Question #2

2. Which is the best order in which to complete your assignments?

a. Practice Problems, Discussion Board, MML Graded Practice, KU project, MML Quiz.

b. KU Project, MML stuff, Discussion Board. Forget the Practice Problems since they’re not graded.

c. It doesn’t matter. Don’t think about it until Tuesday night.

Question #3

3. True or False: Don’t bother mrs. t (that’s me) during office hours since that’s time reserved for grading.

4. True or False: After you’ve completed an assignment, there’s no need to look back at it.

5. True or False: Math is easier to read in paragraph form.

MML Viewing Pane

The Trifecta of Success

Fraction Review

Factoring a Number into Primes

Section 1.1: Simplifying Fractions

Reducing fractions to lowest terms Write numerator and denominator in prime factor form. Cancel any common factors.

Example: Reduce to lowest terms.

Factor each into primes.

Cancel common factors.

5040

5*5*25*2*2*2

52*2

54

=

=

=

Section 1.1: Simplifying Fractions

Example: Reduce

= Factor into Primes.

=

5624

7*2*2*23*2*2*2

73

Section 1.1 Continued

• Writing an Improper Fraction as a Mixed Number

- Divide the numerator by the denominator. - The result of that division becomes the whole number portion of the mixed number. - Write the remainder of the division over the original denominator.

Example: Write as a mixed number.

1. Seven goes into 33 four times. 2. Four will be our whole number. 3. The remainder is 5.

The answer is:

733

75

4

Section 1.1 Continued

Writing an Mixed Number as an Improper Fraction Multiply the whole number by the denominator of the fraction. Add that product to the original numerator. Write that sum over the original denominator.

Example: Write as an improper fraction.

1. Multiply: 4 * 2 = 8

2. Add in numerator: 8 + 3 = 11

3. Write 11 over the original denominator of 4.

The answer is:

43

2

411

Section 1.1 Continued

• Writing Equivalent Fractions– Compare denominator and desired number. – Find multiplier that makes desired number.– Multiply top and bottom by multiplier.

Example: Write with a denominator of 10.

1. Compare 2 and 10.

2. We multiply 2 * 5 to get 10. Five is our multiplier.

3. Multiply:

21

105

55

*21

Section 1.2 Adding & Subtracting Fractions

Adding or Subtracting Fractions with the Same Denominator Add or subtract the numerators. Write that sum or difference over the common denominator. Reduce to lowest terms.

Example: Add the fractions

= Add the numerators.

= Write the sum.

= Reduce.

92

94

924

96

32

Section 1.2 Continued

Finding the LCD of two or more Fractions List the multiples of each denominator. The LCD is the first number both lists have in common.

Example: Find the LCD of , , and

Write the multiples of each denominator:

2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …

3 = 3, 6, 9, 12, 15, 18, …

12 = 12, 24, 36, 48, …

The first number all three lists have in common is 12 and that is our LCD.

32

21

127

Section 1.2 Continued

Adding or Subtracting Fractions with Different Denominators First find the LCD. Write each fraction as an equivalent fraction with the LCD as the

denominator. Add or subtract the fractions. Reduce the resulting fraction to lowest terms.

Example on next slide…

Section 1.2 Continued

Subtracting with Different Denominators Example:

Step 1: 6 = 6, 12, 18, 24, … Find the LCD of the two fractions

9 = 9, 18, 27, 36, …

Step 2: Rewrite fractions with LCD.

Step 3: Subtract the Fractions.

=

This is already in lowest terms. We cannot reduce it.

Notice each step is on its own line!!!

92

65

1815

33

*65

184

22

*92

184

1815

1811

Section 1.2 Continued

Example of Subtracting Mixed Numbers:

= Write both as improper fractions.

= Find LCD.

= Subtract.

This is worked out in more detail in the Seminar Notes in DocSharing.

51

332

7

516

323

1548

15115

1567

Section 1.3 Multiplying & Dividing

Multiplying Fractions Rewrite as one fraction. Factor the top and bottom. Cancel out any common factors. Multiply together any numbers left.

Example: Multiply

= Multiply tops and bottoms.

= Factor each number.

= Cancel out common factors.

= Multiply remaining numbers.

245

*208

24*205*8

3*2*2*2*5*2*25*2*2*2

3*2*21

121

Section 1.3 Continued

Multiplying a Fraction by a Whole Number Write the whole number over 1. Write both numerators and denominators in prime-factored form. Cancel out any common factors across the fraction bar. Multiply together any numbers still left in either the numerator or the

denominator.

Example: Multiply 5 *

= Rewrite 5 as

= Multiply the fractions together.

=

212

212

*15

21*12*5

2110

15

Section 1.3 Continued Dividing a Fraction by a Fraction

Keep the first fraction the same. Flip the second fraction.. Change the division symbol to multiplication. Follow multiplication rules.

Example: Divide.

= KFC!

= Multiply fractions together.

= Factor each number.

= Rewrite.

114

72

411

*72

4*711*2

7*2*211*2

1411

Section 1.4 Using Decimals

Writing a Fraction in Decimal Form Divide the Numerator by the Denominator. Round to the required decimal place if necessary.

Example: Write as a decimal and round to the tenths place.

-22

80 The instructions asked us to round to the nearest tenths place.

-77 Our answer will be .3

30

-22

8

113

272.000.311

Section 1.4 Continued

Writing a Decimal in Fractional Form Write the decimal as a fraction with the denominator as the appropriate

multiple of 10. Write both numerators and denominators in prime-factored form. Cancel out any common factors across the fraction bar.

Example: Write 0.684 as a fraction.

= We had three decimal places (the thousandths place).

= Factor each number.

= Cancel out two 2’s.

=

1000684

5*5*5*2*2*219*3*3*2*2

5*5*5*219*3*3

250171

Section 1.4 Continued

Adding or Subtracting Decimals Write the problem vertically and line up all of the decimal points. Add or subtract accordingly.

Example: Subtract 2.5143 from 7.75

We will add zeros to the end of 7.75 to help us line up the numerals a bit better.

7.7500

- 2.5143

5.2357

Section 1.4 Continued

Multiplying Decimals Multiply the digits as you would whole numbers. Add zeros at the end of each number if necessary. Count the total number of decimal places in all of the factors. Move the decimal point to the left the number of places determined in

step 2 and add zeros to the left as necessary.

Example: Multiply 0.315 * 0.16

0.315 3 decimal places

x 0.16 2 decimal places

1890 The product of 6 and 0.315

3150 The product of 1 and 0.315

.05040 Place the decimal point 5 places from the right.

.0504 is acceptable, too, since a zero on the end has no bearing.

Section 1.4 Continued

Dividing Decimals Count the number of decimal places in the divisor. Move the decimal point to the right in both the divisor and the dividend the

exact number of places from step 1. Mark the place where the decimal place should be. Divide Place the decimal point in the quotient above the mark in the dividend.

Example: Divide 3.108 by 1.4

There is one decimal place in the divisor; we count over 1

28 more place in the dividend and move the decimal

30 straight up.

28

28

28

0

22.208.3114

Thanks for Participating!

AIM: tamitacker Read, read, read! Email me if you have questions.