TOC Fraction_operations.ppt LW Sours 1 Fraction Operations

TOC Fraction_operations.ppt LW Sours 2 Signs of Fractions Mixed Number to an Improper fraction Improper Fraction to a Mixed Number Add Fractions –Using LCM –Cross Product –Mixed Numbers (without conversion) Subtract Fractions –Mixed Number (without conversion) Multiply Fractions Divide Fractions Table Of Contents (TOC)

TOC Fraction_operations.ppt LW Sours 3 Signs of Fractions … Numerator AND Denominator are negative THEN F r a c t i o n i s p o s i t i v e Denominato r is negative OR Fraction is negative Numerato r is Negative OR If the signs of numerator and denominator are the same, the fraction is positive (+). If the signs are different then fraction is negative.

TOC Fraction_operations.ppt LW Sours 4 Change a Mixed Number to Improper Fraction… 1)Multiply whole number times the fraction’s denominator. 2) Add this to the fraction’s numerator.  This sum is the improper fraction’s numerator.  The denominator’s number does not change.  The sign (positive or negative) of the improper fraction is the same as the mixed number.  The inproper fraction can then be reduced. (A mixed number implies addition: whole number + fraction) Visual The sign (positive or negative) remains the same

TOC Fraction_operations.ppt LW Sours 5 Change an Improper Fraction to Mixed Number … 3) Reduce the proper fraction, if needed. (A mixed number implies addition: whole number + fraction) 1) Divide the improper fraction’s numerator by its denominator. a) The whole number portion (left of decimal) of the answer (quotient) is the whole number portion of the mixed number. The sign (positive or negative) remains the same 2) The remainder is the numerator of the fractional part (always a proper fraction) of the mixed number. > The denominator is the same as the improper fraction’s denominator. Visual

TOC Fraction_operations.ppt LW Sours 6 Addend + Addend = Sum Add Fractions… 1) Convert the fractions to fractions with the same number in all denominators (common denominator). a) To change mixed numbers to improper fractions refer to “Mixed Numbers to Improper Fractions” section 2) Add the numerators. The answer’s denominator is the same as the fractions. 3) Reduce the fractional answer to lowest terms using the Greatest Common Factor (GCF). a) It may be a mixed number if the numerator’s value is greater than (>) the denominator’s value. Visual

TOC Fraction_operations.ppt LW Sours 7 Use LCM (Least Common Multiple) to get the Lowest Common Denominator (LCD)…they are the same! Add Fractions… Method 1 LCM Example: (Find LCD using LCM): Prime factors of 6 are 2 x 3 Prime factors of 4 are 2 x 2 = 2 2 LCD = LCM = 2 2 x 3 = 12 Visual

TOC Fraction_operations.ppt LW Sours 8 Add Fractions…Method 2 Cross-Product Can only have 2 fractions in Cross-Product, but is the same as… You can always multiply all of the non-lie denominators…the product is the Common Denominator 1) Multiply the denominators. The answer (product) is the is the sum’s denominator. 2) Multiply the numerator of the first fraction with the denominator of the second fraction. a) The product is the first fraction’s numerator. 3) Multiply the denominator of the first fraction with the numerator of the second fraction. a) The product is the second fraction’s numerator. Reduce fraction Num. x Denom. = new Num. Denom.. x Num.. = new Num. Add numerators Visual

TOC Fraction_operations.ppt LW Sours 9 Alternative Method for Mixed Numbers Add Fractions… 1. Add the whole number portions of the mixed number(s). a. If there is only one then assume the whole number portion is “0”. 2. Add the fraction portions (refer to “ADD FRACTIONS…” section). a. Convert this sum to a mixed number if it is an improper fraction. 3. Add the whole number portions, if any. a. The proper fraction is the fraction portion of the mixed number. b. Reduce the fractional portion to lowest terms using the GCF. 3) Add whole numbers and reduced fraction: 2) Add fractions and reduce: 1) Add whole numbers: Example: 1 2 / / 2

TOC Fraction_operations.ppt LW Sours 10 Subtract Fractions… Minuend – Subtrahend = Difference Calculate subtraction the same as addition of fractions except subtract numerators. REMEMBER that subtraction is adding negative numbers! -3 – 5 = (-3) + (-5) = -8 Refer to adding fractions. 3 - (-5) = = 8 6 – (-3) = = 6 -6 – (-3) = = 3 – 6 = -3 Visual

TOC Fraction_operations.ppt LW Sours 11 Subtract Fractions… Alternative Method for Mixed Numbers This procedure assumes that the minuend is larger than the subtrahend, if not arrange the expression this way. The sign of the answer is the larger number’s sign. If you cannot determine which is larger convert to improper fractions then subtract as fractions. 1. Change the fraction portion of each mixed number to fractions with the same denominators (refer to “ADD FRACTIONS…” section). 2. If the subtrahend’s numerator is greater than the minuend’s numerator, borrow “1” from the whole number portion of the minuend, convert to a fraction, and add its numerator to the minuend’s fraction‘s numerator. 4. When borrowing, is the sum of the denominator and numerator the numerator of the fraction portion of the mixed number? 3. The borrowed number’s whole number is subtracted by “1”. The numerator of the fraction portion is the same as the denominator, which equals “1” (amount borrowed). Example of Borrowing :

TOC Fraction_operations.ppt LW Sours 12 Subtract Fractions… Alternative Method for Mixed Numbers Example: 2. Subtract the numerators; this difference will be the answer’s numerator. The denominator is the same. 3. Reduce the fractional portion to lowest terms using the Greatest Common Factor (GCF), if required. … minuend and subtrahend have the same denominator … minuend’s numerator is larger than the subtrahend’s numerator –– may have to borrow from the whole number ASSUMPTIONS are that the subtraction… … has a minuend larger than subtrahend 1. Subtract the whole numbers.

TOC Fraction_operations.ppt LW Sours Convert improper fractions to mixed numbers (refer to “Improper Fraction to Mixed Number” section). Multiply Fractions… Factor x Factor = Product How is multiplication indicated? 1.Convert mixed numbers to improper fractions, if any (refer to “Mixed Number to Improper Fraction” section). 2. Multiply all factors’ numerator to get the product’s numerator. 3. Multiply all factors’ denominator to get the product’s denominator. 5. Reduce the fractional answer (product). 4. Use the Greatest Common Factor (GCF) for a proper fraction. Visual

TOC Fraction_operations.ppt LW Sours 14 – cont– Multiply Fractions 1.Convert mixed numbers to improper fractions, if any. 2. Multiply all factors’ numerator to get the product’s numerator. 3. Multiply all factors’ denominator to get the product’s denominator. 4. Use the Greatest Common Factor (GCF) for a proper fraction. 6. Convert improper fractions to mixed numbers Example 1: 5. Reduce the fractional answer (product). “1”, “1” Visual Note: 7 / 14 should be reduced first but is left in this form to show the method 2, 7 3 2, 3, 7 Number GCF is 2 x 7 = Prime factors 42

TOC Fraction_operations.ppt LW Sours 15 1.Convert mixed numbers to improper fractions, if any (refer to “Mixed Number to Improper Fraction” section). Method 1 Divide Fractions… How is division indicated? 2. Multiply the first fraction (dividend) with the reciprocal of the second fraction (divisor). Example: 3. Reduce the quotient. Visual

TOC Fraction_operations.ppt LW Sours 16 Divide Num and Denom by “7” (GCF) Method 2 Divide Fractions… Cross–Product Num 1 x Denom 2 = new Num. Denom 1 x Num 2 = new Denom. 1.Convert mixed numbers to improper fractions, if any (refer to “Mixed Number to Improper Fraction” section). 2. Multiply the first fraction’s numerator (dividend) with the second fraction’s (divisor) denominator for the quotient’s numerator. 4. Reduce the fraction (quotient). 3. Multiply the first fraction’s denominator (dividend) with the second fraction’s (divisor) numerator for the quotient’s denominator. Example: Visual

TOC Fraction_operations.ppt LW Sours 17 1/61/6 … 1/61/6 …… 1/61/6 1/61/6 …… 1/61/6 … 1/61/6 1/61/6 ………… 1/61/6 1/61/6 … …… 1/61/ /61/6 1/61/6 1/61/6 1/61/6 1/61/6  Improper Fraction Mixed Number and Improper Fraction…  5/65/6 1 6/66/6 5/65/ = 23 Mixed Number to improper fraction slide Improper fraction to mixed number slide 5/65/ /66/6 6/66/6 6/66/6 6/66/6 6/66/6 5/65/6 1 1

TOC Fraction_operations.ppt LW Sours 18 Adding Fractions + = Fraction is already in lowest terms (mixed number or proper fraction) Change to both to 12 th ’s Back

TOC Fraction_operations.ppt LW Sours 19 Subtracting Fractions – = Fraction is already in lowest terms (mixed number or proper fraction) Change to both to 12 th ’s Back 9 – 2 = 7

TOC Fraction_operations.ppt LW Sours 20 Multiplying Fractions 1 / 42 ……………………………… ……………………………… ……………………………… ……………………………… ……………………………… ……………………………… Divide into thirds Reduce fraction Add two thirds Back Num x Num Denom x Denom

TOC Fraction_operations.ppt LW Sours 21 Dividing Fractions 1 / 42 ……………………………… ……………………………… ……………………………… How many 14/42 (1/3) are there? Back There are 1 ½ 14 / 42 ’s Using the shortcut there are seven 3 / 42 ’s ( 3 / 42 = 1 / 14 ) which equals 21 / 14, which equals 1 7 / 14, which equals 1 ½.

TOC Fraction_operations.ppt LW Sours 22