lcd 19 2b

download report

Transcript lcd 19 2b

1-1
Chapter 2
Fractions
1-2
McGraw-Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.
#2
Fractions
Learning Unit Objectives
LU2.1 Types of Fractions and Conversion
Procedures
1-3
•
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
#2
Fractions
Learning Unit Objectives
LU2.2 Adding and Subtraction of Fractions
1-4
•
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
#2
Fractions
Learning Unit Objectives
LU2.3 Multiplying and Dividing Fractions
1-5
•
Multiply and divide proper fractions and mixed
numbers
•
Use the cancellation method in the
multiplication and division of fractions
Types of Fractions
Improper
Proper
Numerator
3, 4, 12, 11
15 8 26 35
Denominator
19, 9, 13, 42
19 4 10 29
Mixed Numbers
2 5, 9 3, 152, 4 1
8
17
9
8
1-6
Converting Improper Fractions to Whole
or Mixed Numbers
2 Steps
• 1 Divide the numerator by the
denominator
• 2a. If you have no remainder,
the quotient is a whole
number
• 2b. If you have a remainder,
the quotient is a mixed
number
1-7
24
24 = 1
21
1
=5
4
4
4
5R1
21
20
1
Reducing Fractions to Lowest Terms by
Inspection
Find the lowest whole
number that will divide
evenly into the numerator
and denominator
1-8
24 = 24 / 6 = 4
30
30 / 6
5
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
1-9
2
12 30
24
6
2
6 12
12
0
12 / 6 = 2
30 / 6 5
Divisibility Tests
2
3
Last digit
is 0,2,4,6,8
12
14
=6
7
Sum of the
digits is
divisible by 3
Last two
digits can be
divided by 4
36
12
140
=
69 23
160
3+6=9/3=3
6 + 9 = 15 / 3 = 5
1-10
4
1(40)
= 1(60)
35
40
15
20
=7
8
5
6
Last digit is
0 or 5
The number
is even and
3 will divide
into the sum
of the digits
3
=4
12 2
=
18 3
10
The last digit
is o
90
9
=
100 10
Least Common Denominator (LCD)
• The smallest nonzero
whole number into which
all denominators will
divide evenly.
5 + 16
20
10
40
What is the least
common
denominator?
1-11
60
20
Adding and Subtracting Fractions with
the Same Denominator
• Add the numerators
and place the total over
the denominator
2 + 3 =5
9 9 9
1-12
• Subtract the
numerators and
place the total over
the denominator
7 - 1 6 / 2 3
=
=
12 12 12 / 2 6
Adding and Subtracting Proper Fractions with
Different Denominators
Find the LCD
Change each fraction to a like
fraction
Add the numerators
1 1 1 1
+ + +
3 8 9 12
24 + 9 + 8 + 6 = 47
72 72 72 72
72
1-13
Find the LCD
Raise the fraction to its
equivalent
Subtract the numerators
5 - 2
8 64
40
64
- 2
64
38 = 19
64
32
Multiplying Proper Fractions
2 Steps
Multiply the numerator and
the denominators
Reduce the answer to lowest
terms
1-14
5 x 2 x 4 = 40 = 20
2 5 7 70 35
Multiplying Mixed Numbers
Convert the mixed
numbers to improper
fractions
Multiply the
numerator and
denominators
1
1
1
7
3
7 31
=
=
2 X 1 = X
3
2
3
2
2
2
1-15
1
Dividing Proper Fractions
Invert (turn
upside down)
the divisor (the
second fraction)
1
8
1-16
.
.
Multiply the
fractions
2 = 1 X3 = 3
3
8 2 16