Kinh tế học - Chapter 2: Fractions

Chapter 2FractionsMcGraw-Hill/Irwin©2011 The McGraw-Hill Companies, All Rights ReservedRecognize the three types of fractionsConvert improper fractions to whole or mixed numbers and mixed numbers to improper fractionsConvert fractions to lowest and highest termsFractions#2Learning Unit ObjectivesTypes of Fractions and Conversion ProceduresLU2.12-2Add like and unlike fractionsFind the least common denominator (LCD) by inspection and prime numbersSubtract like and unlike fractionsAdd and subtract mixed numbers with the same or different denominatorsFractions#2Learning Unit ObjectivesAdding and Subtraction of FractionsLU2.22-3Multiply and divide proper fractions and mixed numbersUse the cancellation method in the multiplication and division of fractionsFractions#2Learning Unit ObjectivesMultiplying and Dividing FractionsLU2.32-4Types of Fractions1, 1, 1, 4, 184 2 12 7 55ProperNumeratorDenominatorProper fractions have a value less than 1; its numerator is smaller than its denominator.Types of Fractions14, 7, 15, 2214 6 14 19ImproperDenominatorImproper Fractions have a value equal to or greater than 1; its numerator is equal or greater than its denominator.NumeratorTypes of Fractions1, 9, 7, 5, 96 10 8 6 11558 33Mixed NumbersMixed numbers are the sum of a whole number greater than zero and a proper fraction139Converting Mixed Numbers to Improper Fractions Mixed Numbers3 Steps1. Multiply the denominator of the fraction by the whole number.2. Add the product from Step 1 to the numerator of the old fraction.3 Place the total from Step 2 over the denominator of the old fraction to get the improper fraction.(8 x 6) = 48(8 x 6) = 4848 + 1 = 4949 8 1 86Reducing Fractions to Lowest Terms by InspectionFind the lowest whole number that will divide evenly into the numerator and denominator24 24 / 6 430 30 / 6 5==Finding the Greatest Common DivisorStep 1. Divide the numerator into the denominator 124 30 24 6 46 24 24 0Step 2. Divide the remainder in Step 1 into the divisor of Step 124 / 6 430 / 6 5=Step 3. Divide the remainder of Step 2 into the divisor of Step 2. Continue until the remainder is 02430Adding Like FractionsAdd the numerators and place the total over the denominatorIf 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 number1 4 57 7 7+=-b5 6 11 29 9 9 9 +==1Least Common Denominator (LCD)The smallest nonzero whole number into which ALL denominators will divide evenly. 3 5 7 2174221+What is the least common denominator?Adding Unlike Fractions4 Steps1. Find the LCD 2. Change each fraction to a like fraction with the LCD.3. Add the numerators and place the total over the LCD.4. If necessary, reduce the answer to lowest terms.1 1 1 13 8 9 12+++24 + 9 + 8 + 6 = 4772 72 72 72 72Subtracting Like FractionsStep 1 - Subtract the numerators and place the total over the denominatorStep 2 - If necessary, reduce the answer to lowest terms 9 1 8 / 2 410 10 10 / 2 5 =-=Subtracting Unlike Fractions 5 2 8 64- 5 40 8 64 2 - 2 64 64 38 = 19 64 32Step 1. Find the LCD Step 2. Raise the fraction to its equivalent value.Step 3. Subtract the numerators and place the answer over the LCD.Step 4. If necessary, reduce the answer to lowest terms.-Subtracting Mixed Numbers 1 4 2 8 - 3 - 3 8 8 1 8Step 1. Subtract fractions, making sure to find the LCD. Step 2. Subtract whole numbers.Step 3. Reduce the fractions to lowest terms.When Borrowing is Not Necessary666Subtracting Mixed Numbers 1 2 6 2 4 4 3 3 3 4 4 4 3 4Step 1. Make sure the fractions have the LCD.Step 2. Borrow from the whole number.Step 3. Subtract whole numbers and fractions.Step 4. Reduce the fractions to lowest terms.When Borrowing is Necessary33 1 -1 -1 -12Multiplying Proper FractionsStep 1. Multiply the numerator and the denominatorsStep 2. Reduce the answer to lowest terms5 1 4 20 101 6 7 42 21==xxMultiplying Mixed NumbersConvert the mixed numbers to improper fractions Multiply the numerator and denominators1 1 7 3 7 13 2 3 2 2 223=X1X==11Reduce the answer to lowest termsDividing Proper Fractions1 2 1 3 38 3 8 2 16 ==XInvert (turn upside down) the divisor (the second fraction)Multiply the fractions..Reduce the answer to lowest termsDividing Mixed NumbersConvert all mixed numbers to improper fractions Invert the divisor and multiply3 5 35 6 105 34 6 4 17 34 348=X2X==Reduce the answer to lowest terms3