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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.a b c d e
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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.
Slide 4/35
•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.
Slide 5/35
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.
Slide 6/35
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
Slide 2- 7
52
Example D• Simplify.
• Solution
Slide 8/35
77
1212
1515
7 17
12 112
15 115
The Number 0 in Fraction Notation
• • for any whole number n that is not 0.
Slide 9/35
0 0,n
Example • Simplify.
• Solution
Slide 2- 10
012
022
06
0 012
0 022
0 06
A Denominator of 0• • is not defined for any whole number n.
Slide 11/35
0n
Any Whole Number In Fraction Notation
• •Any whole number divided by 1 is the whole number. That is, for any whole number n.
Slide 12/35
,1n n
Example F
• Simplify.
• Solution
Slide 13/35
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.
Slide 14/35
9 3 9 3 277 4 7 4 28
Example • Multiply.
•
• Solution:
Slide 2- 15
2 13 7
2 13 7
2 13 7
221
259
5 21 9
259
109
Objective
• Multiply a fraction by a fraction.
Slide 17/35
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.
Slide 2- 17
9 3 9 3 277 4 7 4 28
Example
Solution:
Slide 18/35
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 :
Slide 20/35
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 :
Slide 21/35
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.
Slide 25/35
Slide 26/35
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
.
Slide 28/35
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.
Slide 2- 28
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•
Slide 31/35
3 54 16
3 54 16
63
415
3 4 44 5
4 3 44 5
125
Example E• Divide and simplify.
• Solution
Slide 31/35
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