Fractions Copyright 2014 by The McGrawHill Companies Inc All rights reserved McGrawHillIrwin Learning unit objectives 2 2 LU 21 Types of Fractions and Conversion Procedures Recognize the three types of fractions ID: 314089
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Slide1
Chapter Two
Fractions
Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/IrwinSlide2
Learning unit objectives
2-
2LU 2-1: 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.
LU 2-3: Basic Math Functions with Fractions
Add and subtract fractions.Multiply fractions.Divide fractions.
LU 2-2: Fraction and Decimal Conversions
Convert decimal fractions to decimals, proper fractions to decimals, mixed numbers to decimals, and pure and mixed decimals to decimal fractions.
Slide3
Types of Fractions
2-
31
,
1
,
1, 4, 184 2 12 7 55
Proper fractions have a value less than 1; its numerator is smaller than its denominator.Proper Fractions
Numerator
DenominatorSlide4
Types of Fractions
2-
4Improper Fractions
Improper fractions have a value equal to or greater than 1; its numerator is equal to or greater than its denominator.
14
,
7
, 15, 2214 6 14 19
Denominator
NumeratorSlide5
Types of Fractions
2-
5
1
,
9
, 7
, 5, 96 10 8 6 1155
8
33
Mixed Numbers
Mixed numbers are the sum of a whole number greater than zero and a proper fraction
139Slide6
Converting Improper Fractions to
Whole or Mixed Numbers
2-6
2 Steps
1. Divide the numerator of the improper fraction by the denominator
15
15
= 1
2. a. If you have no remainder, the quotient is a whole number
16
1
5 5
3 R 1
5 16
15
1
= 3
2 b. If you have a remainder, the quotient is a mixed number. The remainder is placed over the old denominator as the proper fraction of the mixed number.Slide7
Converting Mixed Numbers to Improper Fractions
2-
7
3 Steps
1. Multiply the denominator of the fraction by the whole number.
(8 x 6) = 48
1
8
6
(8 x 6) = 48
48 + 1 = 49
2. Add the product from Step 1 to the numerator of the old fraction.
49
8
3. Place the total from Step 2 over the denominator of the old fraction to get the improper fraction.Slide8
Converting (Reducing) Fractions
to Lowest Terms
Find the largest whole number that will divide into both the numerator and denominator without leaving a remainder.
24
24 / 6
430 30 / 6 5
==2-
8Slide9
Finding the Greatest Common Divisor
Step 1. Divide the numerator into the denominator.
1
24 30
24
6
4
6 24
24
0
Step 2. Divide the remainder in Step 1 into the divisor of Step 1.
24 / 6
4
30 / 6 5
=
Step 3. Divide the remainder of Step 2 into the divisor of Step 2. Continue until the remainder is 0.
2-
9
24
30Slide10
Converting (raising) Fractions to higher Terms
Multiply the numerator and the denominator by the same whole number.
1
2
24 2 8
x=2-10
The fractions are equivalent in value. By converting, you divided it into more parts.Slide11
4
7 28
28 0
Raising Fractions to Higher Terms
When Denominator is Known
2 Steps
Divide the new denominator by the old denominator to get the common number that raises the fraction to higher terms.
4
=
?
7 28
2-
11
4 x 4 = 16
16
28
2. Multiply the common number from Step 1 by the old numerator and place it as the new numerator over the new denominator.Slide12
Converting Proper Fractions to decimals
Divide the numerator of the fraction by its denominator.
Round as necessary.
=
=
2-
12
3
4
.75
3
8
.375
1
3
=
.333Slide13
Converting mixed numbers to decimals
Convert the fractional part of the mixed number to a decimal.
Add the converted fractional part to the whole number.
=
2-
13
2 5
8.40
8.00
+.40
8
.40
2
5
(Step 1)
(Step 2)Slide14
Converting pure and mixed numbers to Fractions
1. Place the digits to the right of the decimal point in the numerator of the fraction. Omit the decimal point.
2. Put a 1 in the denominator of the fraction.
2-
14
3
.3
3
1
(Step 1)
(Step 2)
3 Steps
3. Count the number of digits to the right of the decimal point. Add the same number of zeros to the denominator of the fraction.
1
3
10
Places
(Step 3)Slide15
Adding and subtracting Like Fractions
Add or subtract the numerators and place the total over the denominator.
If the total of your numerators is the same as your original denominator, convert your answer to a whole number. If the total is larger than your original denominator, convert your answer to a mixed number.
1
4
57 7 7+
=
4
1
3
7 7 7
-
=
2-
15Slide16
Adding or subtracting Unlike Fractions
4 Steps
1. Find the LCD.
1
1
1 13 8 9 12+
+
+
2-
16
24
9
8
6
47
72 72 72 72 72
+
+
+
=
2. Change each fraction to a like fraction with the LCD.
3. Add or subtract the numerators and place the total over the LCD.
4. If necessary, reduce the answer to lowest terms.Slide17
7
42
21
Least Common Denominator (LCD)
2-
17
What is the least common denominator?
The smallest nonzero whole number into which ALL denominators will divide evenly.
3
5
7 21
+Slide18
Prime Numbers
A prime number is a whole number greater than 1 that is only divisible by itself and 1. The number 1 is not a prime number.
Examples
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43
2-
18Slide19
Adding Mixed Numbers
3 Steps
1. Add the fractions.
2. Add the whole numbers.
3. Combine steps 1 & 2. Be sure you do not have an improper fraction in your final answer. If necessary, reduce the answer to
lowest terms.
7
720 203 125 20
1
5
4
20
24
4
20 20
4
20
4
4
6
6
18
= 1
+ 7
+7
Step 1
Step 3
Step 2
+
17
18
1
5
2-
19Slide20
1 4
2 8
-
3
3 8 8
1 8Subtracting Mixed Numbers
Step 1. Subtract fractions, making sure to find the LCD.
When Borrowing Is Not Necessary:
2-
20
6
6
6
Step 2.
Subtract
whole numbers.
Step 3.
Reduce
the fractions to lowest
terms
.
3 StepsSlide21
1
2
34
2
6 4 4
3 3 4 4 3 4
Subtracting Mixed Numbers
Step 1.
Make
sure the
fractions have
the LCD.
When Borrowing Is Necessary:
3
1
-1
-1
2
2-
21
3
-1
Step 2.
Borrow
from the whole number.
Step 3.
Subtract
whole numbers and
fractions
.
Step 4.
Reduce the fractions to lowest
terms
.
4 StepsSlide22
Multiplying Proper Fractions
5 56
Step 1. Multiply the numerator and the denominator.
1
5
7 8 =x
2-
22
Step 2. Reduce the answer to lowest terms.
2 StepsSlide23
Multiplying Mixed Numbers
1. Convert
the mixed numbers to improper fractions.
2. Multiply the numerator and denominators.
1
1
7 3 7 13 2 3 2 2 2
2
3
=
X
1
X
=
=
1
1
2-
23
3. Reduce the answer to lowest terms.Slide24
Dividing Proper Fractions
1. Invert (turn upside down) the divisor (the second fraction).
2. Multiply the fractions.
1
2
1 3 38 3 8 2 16
=
=
X
.
.
2-
24
3. Reduce the answer to lowest terms.Slide25
Dividing Mixed Numbers
1. Convert all mixed numbers to improper fractions.
2. Invert the divisor and multiply.
3
5
35
6 105 34 6 4 17 34 343. Reduce the answer to lowest terms.
8
=
2
X
=
=
3
2-
25
÷