ku122: introduction to math skills and strategies kirsten muller, m. a., m. ed. unit 2 seminar

KU122: Introduction to Math Skills and Strategies

Kirsten Muller, M. A., M. Ed.Unit 2 Seminar

Fraction Notation2.1 Fraction Notation and Simplifying2.2 Multiplication and Division2.3 Addition and Subtraction; Order2.4 Mixed Numerals2.5 Applications and Problem Solving2.6 Order of Operations; Estimation

Slide 2/35

22CHAPTER

Fraction Notation and Simplifying

Identify the numerator and the denominator of a fraction and write fraction notation for part of an object.

Simplify fraction notation like n/n to 1, 0/n to 0, and n/1 to n.

Multiply a fraction by a fraction.

Use multiplying by 1 to find different fraction notation for a number.

Simplify fraction notation.

2.2.aa

bb

cc

dd

ee

Objective AA

Identify the numerator and the denominator of a fraction and write fraction notation for part of an object.

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•The following are some examples of fractions:

•This way of writing number names is called fraction notation. The top number is called the numerator and the bottom number is called the denominator.

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3 13 7 3, , , , 4 21 6 4

a ab b

Example

• What part of the circle is shaded?

• Solution• The object is divided into 8 equal parts.• 3 of the parts are shaded

• of the circle is shaded.

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38

Example C•What part is shaded?

•Solution•Each cylinder is divided into 2 equal parts.•The unit is ½. •The denominator is 2. •We have 5 of the units shaded.ells us the numerator is 5. is shaded

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52

Example D• Simplify.

• Solution

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77

1212

1515

7 17

12 112

15 115

The Number 0 in Fraction Notation

• • for any whole number n that is not 0.

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0 0,n

Example • Simplify.

• Solution

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012

022

06

0 012

0 022

0 06

A Denominator of 0• • is not defined for any whole number n.

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0n

Any Whole Number In Fraction Notation

• •Any whole number divided by 1 is the whole number. That is, for any whole number n.

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,1n n

Example F

• Simplify.

• Solution

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81

521

41

8 81

52 521

4 41

To multiply a fraction by a fraction,

• a) Multiply the numerators to get a new numerator, and

• b) Multiply the denominators to • get the new denominator.

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9 3 9 3 277 4 7 4 28

Example • Multiply.

•

• Solution:

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2 13 7

2 13 7

2 13 7

221

259

5 21 9

259

109

Objective

• Multiply a fraction by a fraction.

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cc

To multiply a fraction by a fraction,

• a) Multiply the numerators to get a new numerator, and

•

• b) Multiply the denominators to • get the new denominator.

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9 3 9 3 277 4 7 4 28

Example

Solution:

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2 13 7

2 13 7

2 13 7

221

259

5 21 9

259

109

Example•Find a name for with a denominatorof 36.

•Solution•Since 9 × 4 = 36, we multiply by :

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34

99

34

934 9

3 94 9

27 .36

Example

•Find a name for with a denominator of 48.

•Solution•Since 12 × 4 = 48, we multiply by :

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1112

44

41112 4

44 .48

1112

Example •Simplify.

•1. 2. 3.

•1.

•2.

•3. Slide 2- 21

2835

324

832

2835

4 75 7

745 7

45

324

1 38 3

318 3

18

The number 1 allows for pairing of factors in the numerator and the denominator.

832

1 84 8

814 8

14

Example •Simplify:

•Solution

•The fraction is not simplified since common factors remain in the numerator and denominator.

210 .245

210245

42 549 5

542

49 5

4249

To find the 42, we divided 210 by 5.

To find the 49, we divided 245 by 5.

210 42245 49

6 77 7

767 7

To find the 6, we divided 42 by 7.

To find the 7, we divided 49 by 7.

67

Multiplication and Division

Multiply and simplify using fraction notation.

Find the reciprocal of a number.Divide and simplify using fraction

notation. Solve equations of the type a · x = b

and x · a = b, where a and b may be fractions.

2.2.aa

bb

cc

dd

Objective D

• Multiplying by 1.

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ReciprocalsIf the product of two numbers is 1, we say that they are reciprocals of each other. To find the reciprocal of a fraction, interchange the numerator and denominator. Number Reciprocal3

443

Example C• Find the reciprocal.

• 1. 2. 3. 4.

• Solution 1. The reciprocal of is

2. The reciprocal of is

3. The reciprocal of is

4. The reciprocal of is Slide 2- 26

67

59

14

89

67591489

76

.

95

.

4.

98

.

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0 Has No ReciprocalThe number 0, or has no reciprocal.

(Recall that is not defined.)

0n

0n

Objective C

• Divide and simplify using fraction notation.

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Slide 2- 29

To divide fractions, multiply the dividend by the reciprocal of the divisor.

3 44 3

2 2 2 4 85 5 5 3 15

Multiply by the reciprocal of the divisor.

Example D

•Divide and simplify.

•Solution•

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3 54 16

3 54 16

63

415

3 4 44 5

4 3 44 5

125

Example E• Divide and simplify.

• Solution

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9 1310 15

3 3 3 52 5 13

5 3 3 35 2 13

2726

9 1310 15

39

10151

MML Quizzes

You have to take your quizzes using MML.

You only have 12 hours to take them (but they will NOT take 12 hours to complete). Just don’t start taking it until you are ready.

Do the tutorials, read the chapter, and do the practice problems before you start the quiz.

My Math Lab (MML)

You need to log into the MML to get registered before you can start taking any quizzes or viewing the tutorials.

Please do so as soon as possible.

For more information on using the MML, look at the MML Resources area under Course Home on the class website.

Unit 2 Assignments

The following assignments are due by 11:59pm ET on Tuesday:

1.) Live seminar2.) Discussion Board3.) Practice Problems4.) MML Ungraded Tutorials5.) MML Quiz