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

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

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

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

Types of Fractions Proper Improper 3, 4, 12, 11 19, 9, 13, 42 Numerator 3, 4, 12, 11 15 8 26 35 19, 9, 13, 42 19 4 10 29 Mixed Numbers Denominator 5, 3, 2, 1 8 17 9 8 2 9 15 4

Converting Improper Fractions to Whole or Mixed Numbers 24 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 21 1 4 4 5 R 1 4 21 20 1 = 5

Reducing Fractions to Lowest Terms by Inspection 24 24 / 6 4 30 30 / 6 5 Find the lowest whole number that will divide evenly into the numerator and denominator = =

Finding the Greatest Common Divisor 2 12 30 24 6 Step 1. Divide the numerator into the denominator - 12 30 Step 2. Divide the remainder in Step 1 into the divisor of Step 1 2 6 12 12 Step 3. Divide the remainder of Step 2 into the divisor of Step 2. Continue until the remainder is 0 12 / 6 2 30 / 6 5 =

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 12 6 14 7 36 12 69 23 140 1(40) 160 1(60) 15 3 20 4 12 2 18 3 90 9 100 10 3 + 6 = 9 / 3 = 3 6 + 9 = 15 / 3 = 5 35 7 40 8 =

Least Common Denominator (LCD) The smallest nonzero whole number into which all denominators will divide evenly. 5 16 20 10 + 40 60 20 What is the least common denominator?

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 2 3 5 9 9 9 + = 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 Find the LCD Raise the fraction to its equivalent Subtract the numerators 5 2 8 64 - 1 1 1 1 3 8 9 12 + + + 40 64 - 2 38 = 19 64 32 24 + 9 + 8 + 6 = 47 72 72 72 72 72

Multiplying Proper Fractions 2 Steps Multiply the numerator and the denominators Reduce the answer to lowest terms 5 2 4 40 20 2 5 7 70 35 = x

Multiplying Mixed Numbers Convert the mixed numbers to improper fractions Multiply the numerator and denominators 1 1 1 7 3 7 1 3 2 3 2 2 2 2 X 1 = X = = 3 1

Dividing Proper Fractions Invert (turn upside down) the divisor (the second fraction) Multiply the fractions . 1 2 1 3 3 8 3 8 2 16 . = X =