2. Chapter 2 Fractions McGraw-Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.

3. Learning Unit Objectives#2
Fractions
Learning Unit Objectives
LU2.1
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

4. Learning Unit Objectives#2
Fractions
Learning Unit Objectives
LU2.2
Adding and Subtraction 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

5. Learning Unit Objectives#2
Fractions
Learning Unit Objectives
LU2.3
Multiplying and Dividing Fractions
Multiply and divide proper fractions and mixed numbers
Use the cancellation method in the multiplication and division of fractions

6. Types of Fractions Proper Improper 3, 4, 12, 11 19, 9, 13, 42
Numerator
3, 4, 12, 11
19, 9, 13, 42
Mixed Numbers
Denominator
5, , , 1 2 9 15 4

7. Converting Improper Fractions to Whole or Mixed Numbers24
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
5 R 1 20 1
= 5

8. Reducing Fractions to Lowest Terms by Inspection/ /
Find the lowest whole number that will divide evenly into the numerator and denominator = =

9. Finding the Greatest Common Divisor2
12 30 24 6
Step 1. Divide the numerator into the denominator
Step 2. Divide the remainder in Step 1 into the divisor of Step 1 2 12
Step 3. Divide the remainder of Step 2 into the divisor of Step 2. Continue until the remainder is 0
12 /
30 / =

10. Divisibility Tests = Last digit is 0,2,4,6,8
Sum of the digits is divisible by 3
Last two digits can be divided by 4
Last digit is 0 or 5
The number is even and 3 will divide into the sum of the digits
The last digit is o
(40)
(60)
3 + 6 = 9 / 3 = 3
6 + 9 = 15 / 3 = 5 =

11. Least Common Denominator (LCD)
The smallest nonzero whole number into which all denominators will divide evenly. + 40 60 20
What is the least common denominator?

12. Adding and Subtracting Fractions with the Same Denominator
Add the numerators and place the total over the denominator
Subtract the numerators and place the total over the denominator + = / / - = =

13. Adding and Subtracting Proper Fractions with Different Denominators
Find the LCD
Change each fraction to a like fraction
Add the numerators
Find the LCD
Raise the fraction to its equivalent
Subtract the numerators - + + + 40 64
- 2
38 = 19
= 47

14. Multiplying Proper Fractions
2 Steps
Multiply the numerator and the denominators
Reduce the answer to lowest terms = x

15. Multiplying Mixed Numbers
Convert the mixed numbers to improper fractions
Multiply the numerator and denominators 1 2 X 1 = X = = 3 1

16. Dividing Proper Fractions
Invert (turn upside down) the divisor (the second fraction)
Multiply the
fractions . . = X =