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Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The
McGraw-Hill Companies. All rights reserved.
1
Chapter 2
Fractions
Prepared by Dr. Elena Skliarenko
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The
McGraw-Hill Companies. All rights reserved.
2
#2
Fractions
LU2.1
Learning Unit Objectives
Types of Fractions and
Conversion Procedures
•
Recognize the three types of fractions
•
Convert improper fractions to whole or mixed
numbers and mixed numbers to improper
fractions
•
Convert fractions to lowest and highest terms
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The
McGraw-Hill Companies. All rights reserved.
3
#2
LU2.2
Fractions
Learning Unit Objectives
Adding and Subtracting of
Fractions
•
Add like and unlike fractions
•
Find the least common denominator (LCD) by
inspection and prime numbers
•
Subtract like and unlike fractions
•
Add and subtract mixed numbers with the same or
different denominators
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The
McGraw-Hill Companies. All rights reserved.
4
#2
LU2.3
Fractions
Learning Unit Objectives
Multiplication and Division of
Fractions
•
Multiply and divide proper fractions and mixed
numbers
•
Use the cancellation method in the multiplication
and division of fractions
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The
McGraw-Hill Companies. All rights reserved.
5
#2
LU2.4
Fractions
Learning Unit Objectives
Using a Calculator
•
Use a calculator in operations with fractions and
mixed numbers
•
Convert improper fractions into mixed numbers
•
Add and subtract like and unlike fractions and
mixed numbers
•
Multiply and divide fractions and mixed numbers
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The
McGraw-Hill Companies. All rights reserved.
6
Types of Fractions
Numerator
Improper
Proper
3, 4, 12, 11
15 8 26 35
19, 9, 13, 42
19 4 10 29
Denominator
Mixed Numbers
2
1,
5,
8,
6
7
6
5
3 28 9 9
10
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McGraw-Hill Companies. All rights reserved.
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Converting Improper Fractions to
Whole or Mixed Numbers
24
24
2 Steps
• 1 Divide the numerator by
the denominator
• 2a. If you have no
remainder, the quotient is a
whole number
21 = 5 1
4
4
4
• 2b. If you have a
remainder, the quotient is a
mixed number
=1
5R1
21
20
1
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McGraw-Hill Companies. All rights reserved.
8
Reducing Fractions to Lowest Terms
by Inspection
Find the lowest whole
number that will divide
evenly into the numerator
and denominator
24 = 24 ÷ 6 = 4
30
30 ÷ 6
5
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Finding the Greatest Common
Divisor
Step 1. Divide the numerator
into the denominator - 12
30
Step 2. Divide the remainder in
Step 1 into the divisor of Step 1
Step 3. Divide the remainder of Step
2 into the divisor of Step 2.
Continue until the remainder is 0
2
12 30
24
6
2
6 12
12
0
12 ÷ 6=
2
30 ÷ 6
5
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McGraw-Hill Companies. All rights reserved.
10
Divisibility Tests
2
Last digit is
0,2,4,6,8
12
6
14 = 7
3
4
Sum of the
digits is
divisible by 3
36
12
69 23
3 +=
6=9
Last two
digits can be
divided by 4
÷3=3
6 + 9 = 15
÷
5
140
160
35
3 = 5 40
1(40)
1(60)
Last digit is
0 or 5
15
20
3
=4
6
The number
is even and
3 will divide
into the sum
of the digits
12
18
=
2
3
=
10
The last digit
is 0
90
100
=109
=
= 87
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McGraw-Hill Companies. All rights reserved.
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Least Common Denominator
(LCD)
• The smallest nonzero
whole number into
which all
denominators will
divide evenly.
What is the least
common
denominator?
5 + 16
20
10
40
60
20
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McGraw-Hill Companies. All rights reserved.
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Adding and Subtracting Fractions with
the Same Denominator
• Add the numerators
and place the total over
the denominator
2 3 =5
+
9 9 9
• Subtract the
numerators and
place the total over
the denominator
7 - 1 = 6 ÷ 2= 3
- =
12 12 12 ÷ 2 6
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McGraw-Hill Companies. All rights reserved.
13
Adding and Subtracting Proper Fractions
with Different Denominators
Find the LCD
Find the LCD
Change each fraction to a like Raise the fraction to its
fraction
equivalent
Add the numerators
Subtract the numerators
1 1 1 1
+ + +
3 8 9 12
24 + 9 + 8 + 6 = 47
72 72 72 72
72
40
64
- 2
64
5 - 2
8 64
38 = 19
64
32
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McGraw-Hill Companies. All rights reserved.
14
Multiplying Proper Fractions
2 Steps
Multiply the numerator and
the denominators
5 2 4 40 20
x x = =
2 5 7 70 35
Reduce the answer to lowest
terms
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McGraw-Hill Companies. All rights reserved.
15
Multiplying Mixed Numbers
Convert the mixed
numbers to
improper
fractions
2 1
3
Multiply the
numerator and
denominators
X 11 = 7 X 3 = 7 = 3 1
2
3
2
2
2
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McGraw-Hill Companies. All rights reserved.
16
Dividing Proper Fractions
Invert (turn upside
down) the divisor (the
second fraction)
Multiply the
fractions
1 ÷ 2 = 1 X3 = 3
8
3
8
2
16
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McGraw-Hill Companies. All rights reserved.
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Using a Calculator
How to use the ab/c button?
You can use the “magic” ab/c button
for conversion of improper fractions
into a mixed number.
Example 1:
1 + 1 + 1 + 1
3 8
9
12
Enter given fractions and add them in sequence.
1 a b/c
3 + 1 a b/c
8 + a b/c + 1 a b/c 9 + 1 a b/c + 12 = 47 r 72
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McGraw-Hill Companies. All rights reserved.
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Proper use of the calculator
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McGraw-Hill Companies. All rights reserved.
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