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SLIDE SHOW INSTRUCTIONS This presentation is completely under your control. This lesson will show only one step at a time, to see the next step you must press a key. (Actual names written on a key are in green) •TO STOP THE SLIDE SHOW: press ‘escape’ (Esc, top left of keyboard) •TO MOVE FORWARD: press the “spacebar” or Enter (PageDn, , , also work) •TO MOVE BACKWARD: press the key (PageUp, or also work) Fraction Addition & Subtraction (w/ different denominators) Copyright © 1999 Lynda Greene Find the Least Common Denominator (LCD) 3 4 2 + 5 1) Find the multiples of each denominator 4, 8, 12, 16, 20, 24, ... 5, 10, 15, 20, 25, 30, ... 2) Pick the smallest number both lists have in common LCD = 20 Copyright © 1999 Lynda Greene Now that we can find the LCD, we are able to add & subtract fractions with different denominators 1) Find the LCD (20) 2) Rewrite each fraction with the LCD on the bottom. 3) Now figure out (for each fraction) what number changes the old bottom number into the new LCD 3 x5 4 x5 = 15 20 Ask yourself: 4 x ? = 20 Multiply the top and bottom by this number x4 2 = + 5 x4 8 20 Ask yourself: 5 x ? = 20 Multiply the top and bottom by this number Copyright © 1999 Lynda Greene 15 8 + 20 20 Now that the two fractions have a Common Denominator we can: 1) Add the tops 2) Keep the bottom 3) Reduce if possible 15 + 8 = 23 20 20 This fraction can’t be reduced Copyright © 1999 Lynda Greene Another Example: 1) Find the LCD multiples of 4: 4, 8, 12, 16, 20, 24, multiples of 8: 8, 16, 24, 32, 2) Re-write the fractions with the LCD on the bottom 3 5 + 8 4 8 + LCD = 8 8 Copyright © 1999 Lynda Greene 3) The first fraction: the bottom number didn’t change, so leave the top the same. 3 5 + 8 4 x2 4) The second fraction: We changed a 4 into an 8, so 4 x ? = 8 (2) x2 5) Multiply the top and bottom of the second fraction by 2 3 10 + 8 8 6) Now that the denominators (bottoms) are the same, we can add the tops. 3 10 8 ADD THE TOPS 13 = 8 ALWAYS REDUCE IF POSSIBLE KEEP THE BOTTOMS Copyright © 1999 Lynda Greene More than two fractions: 5 x3 1 x2 7 + + 6 2 x3 3 x2 x1 x1 LCD = 6 multiples of 2: 2, 4, 6, 8, 10, 12,... multiples of 3: 3, 6, 9, 12, 15,... multiples of 6: 6, 12, 18, 24, 30,... Rewrite all three fractions with a 6 on the bottom Multiply the tops by the correct numbers 15 + 2 + 7 6 6 6 Fraction 1: 2 x ? = 6 (3) Fraction 2: 3 x ? = 6 (2) Fraction 3: 6 x ? = 6 (1) Copyright © 1999 Lynda Greene Now that the three fractions have a Common Denominator we can: * Add (or subtract) the tops * Keep the bottom * Reduce if possible 15 + 2 + 7 6 6 6 ADD/SUBTRACT THE TOPS REDUCE 15 + 2 + 7 = 24 6 6 6 6 =3 3 1 KEEP THE BOTTOM Copyright © 1999 Lynda Greene 9 7 4 3 We need a common denominator Find the LCM’s: 4,8, 12, 20,… 3, 6, 9, 12, 15, … 4 and 3 have “12” in common 12 Create 2 fractions with This denominator 12 9 3 7 4 4 3 3 4 27 12 28 12 Now multiply each fraction (top and bottom) by the number that will make them into 12’s. Now that they have the same denominators, we can subtract the tops(numerators). 27 28 1 12 12 This can’t be reduced Addition & Subtraction Practice: Press enter to see answers 7 3 10 5 1) 8 8 8 4 3 9 2) 10 5 5 2 3) 6 9 21 10 11 18 3 7 3 37 4) 4 2 8 8 1 2 3 5) 35 5 7 11 5 38 19 6) 6 3 2 6 1 3 104 7) 2 4 3 5 15 7 2 5 8) 3 3 3 Copyright © 1999 Lynda Greene