ࡱ> 463D} !bjbj55 4B__GGGGG[[[[d$[W52&DZ$444444479z4G~~~4GG5~"GG4~434 VR2[z44'50W54/:4j/:444/:G4$~~~~~~~44~~~W5~~~~/:~~~~~~~~~ : Teacher - Mrs. Volynskaya Fraction Operation Rules We need to be proficient with fractions. Here's a brief refresher:  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/ReducingFractionPicture.gif" \* MERGEFORMATINET  Simplifying/Reducing Fractions All fractions must be simplified/reduced to simplest form/lowest terms. Fractions are in lowest terms if the only whole number you can divide both the numerator and denominator by is 1 (one). Divide the numerator and denominator by any common factors until you have it reduced to lowest terms. The best and quickest way is to divide the numerator and denominator by their greatest common divisor (GCD).  EMBED Equation.3   INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/MixedPicture.gif" \* MERGEFORMATINET  Converting Mixed Numbers to Improper Fractions Multiply the whole number by the denominator. Add this product to the numerator. Write the new fraction using the original denominator and new numerator.  EMBED Equation.3   INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/ImproperPicture.gif" \* MERGEFORMATINET  Converting Improper Fractions to Mixed Numbers Divide the numerator by the denominator. The remainder becomes the fraction part of your mixed number.  EMBED Equation.3  42 5 = 8 with a remainder of 2 Sometimes when adding fractions, you might get a mixed number/improper fraction combo. You must change the improper fraction to a mixed number and combine the whole number amounts:  EMBED Equation.3   INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/AddingFractionsPicture.gif" \* MERGEFORMATINET  ADDITION Get a common denominator: Find the least common multiple (LCM) of the denominators in the problem. Add the numerators: DO NOT add the denominators (this is a common mistake students make). Add the whole numbers: If you are working with mixed numbers, add the whole number amounts next. Simplify/Reduce: Simplify/reduce your answer, converting back to a mixed number if necessary. Remember to check that your final answer is a fraction or mixed number in simplest form.  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/AddFractions.gif" \* MERGEFORMATINET  No answer may be left as a mixed number with an improper fraction -- these MUST be converted to proper mixed numbers.  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/SubtractPicture.gif" \* MERGEFORMATINET  SUBTRACTION Get a common denominator: Find the least common multiple (LCM) of the denominators in the problem. Subtract the numerators: DO NOT subtract the denominators (this is a common mistake students make). Subtract the whole numbers: If you are working with mixed numbers, subtract the whole number amounts next. Simplify/Reduce: Simplify/reduce your answer, converting back to a mixed number  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/SubtractFractions.gif" \* MERGEFORMATINET  Borrowing: If the second fraction is larger than the first, you must regroup the mixed number by- (a) borrowing/subtracting one (1) from the whole number, (b) converting the 1 to a fraction with a numerator and denominator the same as the denominator of the fraction in the mixed number, and (c) adding it to the fraction.  EMBED Equation.3  Note that  EMBED Equation.3   INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/MultiplicatoinPicture.gif" \* MERGEFORMATINET  MULTIPLICATION  HYPERLINK "http://www.ricelake.k12.wi.us/staff/roskama/Notes/Algebra1/Chapter01-02/Fraction.htm" \l "Mixed-Improper#Mixed-Improper" Change all mixed numbers to improper fractions. Simplify the problem by cross cancellation and/or reducing vertically. Multiply across numerators, then across denominators. Simplify/Reduce: Simplify/reduce your answer. Remember to check that your final answer is a fraction or mixed number in simplest form.  EMBED Equation.3   INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/ReciprocalPicture.gif" \* MERGEFORMATINET  Finding Reciprocals A number multiplied by its reciprocal always gives an answer of 1 (one). Finding the reciprocal of a fraction means "flipping" it upside down. If the number is a mixed number, you must first  HYPERLINK "http://www.ricelake.k12.wi.us/staff/roskama/Notes/Algebra1/Chapter01-02/Fraction.htm" \l "Mixed-Improper#Mixed-Improper" convert it to an improper fraction. The reciprocal of  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/Reciprocal01.gif" \* MERGEFORMATINET is  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/Reciprocal02.gif" \* MERGEFORMATINET because  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/Reciprocal03.gif" \* MERGEFORMATINET  The reciprocal of  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/Reciprocal04.gif" \* MERGEFORMATINET is  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/Reciprocal07.gif" \* MERGEFORMATINET because  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/Reciprocal06.gif" \* MERGEFORMATINET  (First convert  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/Reciprocal04.gif" \* MERGEFORMATINET to an improper fraction  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/Reciprocal05.gif" \* MERGEFORMATINET , and then flip to make its reciprocal  EMBED Equation.3 )  INCLUDEPICTURE "http://www.ricelake.k12.wi.us/staff/roskama/Pictures/DivisionPicture.gif" \* MERGEFORMATINET  DIVISION  HYPERLINK "http://www.ricelake.k12.wi.us/staff/roskama/Notes/Algebra1/Chapter01-02/Fraction.htm" \l "Mixed-Improper#Mixed-Improper" Change all mixed numbers to improper fractions. 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