copyright © 2011 pearson education, inc. publishing as prentice hall. 2.1 introduction to fractions...
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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
2.1
Introduction to Fractions and Mixed Numbers
Martin-Gay, Basic Mathematics, 4e 22
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Identifying Numerators and Denominators
In a fraction, the top number is called the numerator and the bottom number is called the denominator. The bar between the numbers is called the fraction bar.
Names Fraction Meaning
Numerator number of parts being considered
Denominator number of equal parts in the whole6
5
Martin-Gay, Basic Mathematics, 4e 33
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.P 109-110
17
10 .2
2
9 1.
Numerator isDenominator is
Numerator is Denominator is
92
1017
Practice Problems
Simplify
8
8 .4
2
0 3.
1
20 .6
0
4 5. 0
1
undefined
20
Identifying Numerators and Denominators and Reviewing Division Properties for 0 and 1
Martin-Gay, Basic Mathematics, 4e 44
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Write the fraction to represent the shaded part of the figure.
In this figure, 4 out of the 7 equal parts are shaded. Thus the fraction is .4
7
Martin-Gay, Basic Mathematics, 4e 55
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example 109
Write the fraction to represent the shaded part of the diagram.
In this diagram, 3 out of the 10 equal parts are shaded. Thus the fraction is .3
10
Martin-Gay, Basic Mathematics, 4e 66
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Draw a figure and then shade a part of it to represent the fraction .
Since the denominator is 6, we divide the rectangle into 6 equal parts. Then we shade 5 of the equal parts.
5
6
Martin-Gay, Basic Mathematics, 4e 77
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC COLLEGE MATHEMATICS, 3e – Slide #6
Practice Problems
Write a fraction to represent the shaded part of the following.
8
3Answer
P 113
7.
8.6
1Answer
Writing Fractions to Represent Shaded Areas of Figures 110
Martin-Gay, Basic Mathematics, 4e 88
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC COLLEGE MATHEMATICS, 3e – Slide #6
Practice Problems
Write a fraction to represent the shaded part of the following.
10
7Answer
P 111
9.
10. 16
9Answer
Writing Fractions to Represent Shaded Areas of Figures
Martin-Gay, Basic Mathematics, 4e 99
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC COLLEGE MATHEMATICS, 3e – Slide #6
Practice Problems
Draw and shade a part of a figure to represent each fraction.
figure a of 3
2
P 111
11.
12. figure a of 11
7
Create Shaded Areas of Figures To Represent each Fractions
Martin-Gay, Basic Mathematics, 4e 1010
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Identifying Proper Fractions, Improper Fractions and Mixed Numbers 112
Definition Example
Proper Fraction: A fraction whose numerator is less than its denominator.
Numerator Denominator
Improper Fraction: A fraction whose numerator is greater than or equal to its denominator.
8
3
4
10
4
22
Martin-Gay, Basic Mathematics, 4e 1111
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Examples 112
Identify each number as a proper fraction, improper fraction, or mixed number.
a.
b.
c.
9
11
41
5
14
13
a proper fraction
a mixed number
an improper fraction
Martin-Gay, Basic Mathematics, 4e 1212
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC COLLEGE MATHEMATICS, 3e – Slide #5
P 112
7
7 .b
8
5 a.
Practice Problem 14Identify each number as a proper fraction, improper fraction, or mixed number.
14
13 .d
13
14 c.
49
100 f.
4
1 5 e.
fractionproper
fractionimproper
fractionimproper
fractionproper
fractionimproper
number mixed
Identifying Proper Fractions, Improper Fractions, and Mixed Numbers
Martin-Gay, Basic Mathematics, 4e 1313
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Mixed Numbers and Improper Fractions
Martin-Gay, Basic Mathematics, 4e 1414
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Mixed Numbers and Improper Fractions
Martin-Gay, Basic Mathematics, 4e 1515
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Examples
Write each as a mixed number or a whole number.
a.
b.
c.
24
7
27
5
72
9
33
7
25
5
8
Martin-Gay, Basic Mathematics, 4e 1616
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC COLLEGE MATHEMATICS, 3e – Slide #6
Practice Problems
Write a fraction to represent the shaded part of the following.
3
8Answer
P 113
15.
16.4
5Answer
3
22
4
11
Identifying Proper Fractions, Improper Fractions, and Mixed Numbers
Martin-Gay, Basic Mathematics, 4e 1717
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC COLLEGE MATHEMATICS, 3e – Slide #5
P 113
3
15 .b
7
52 a.
Practice Problem 17Write each as an improper fraction
5
11 .d
10
39 c.
7
19 makes 51472
3
16 makes 11535
10
93 makes 390109
5
6 makes 1551
Identifying Proper Fractions, Improper Fractions, and Mixed Numbers
Martin-Gay, Basic Mathematics, 4e 1818
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC COLLEGE MATHEMATICS, 3e – Slide #5
P 114
6
17 .b
5
8 a.
Practice Problem 18Write each as an mixed number or a whole number
13
75 .d
4
48 c.
20
21 f.
7
51 e.
5
31
rdenominato original
remainderquotient
6
52
12
13
105
20
11
7
27
Identifying Proper Fractions, Improper Fractions, and Mixed Numbers
Martin-Gay, Basic Mathematics, 4e 1919
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
DONE