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Fraction Addition & Subtraction (w/ different denominators) Copyright © 1999 Lynda Greene

3 2 4 5 + Find the Least Common Denominator (LCD) 1) Find the multiples of each denominator 2) Pick the smallest number both lists have in common LCD = 20 4, 8, 12, 16, 20, 24, ... 5, 10, 15, 20, 25, 30, ... Copyright © 1999 Lynda Greene

Now that we can find the LCD, we are able to add & subtract fractions with different denominators 15 3 2 4 5 + 20 = x5 1) Find the LCD (20) 2) Rewrite each fraction with the LCD on the bottom. Ask yourself: 4 x ? = 20 Multiply the top and bottom by this number 3) Now figure out (for each fraction) what number changes the old bottom number into the new LCD 8 x4 Ask yourself: 5 x ? = 20 Multiply the top and bottom by this number Copyright © 1999 Lynda Greene

15 8 + 20 20 15 + 8 20 23 = 20 Now that the two fractions have a Common Denominator we can: Add the tops Keep the bottom Reduce if possible + 20 20 15 + 8 20 23 = 20 This fraction can’t be reduced Copyright © 1999 Lynda Greene

+ 8 8 + LCD = 8 Another Example: 1) Find the LCD multiples of 4: 4, 8, 12, 16, 20, 24, multiples of 8: 8, 16, 24, 32, 8 8 + 2) Re-write the fractions with the LCD on the bottom Copyright © 1999 Lynda Greene

+ 3 10 8 8 + = x2 3) The first fraction: the bottom number didn’t change, so leave the top the same. 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 ADD THE TOPS KEEP THE BOTTOMS 6) Now that the denominators (bottoms) are the same, we can add the tops. ALWAYS REDUCE IF POSSIBLE = Copyright © 1999 Lynda Greene

More than two fractions: x1 x3 x2 + + LCD = 6 Rewrite all three fractions with a 6 on the bottom 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,... Multiply the tops by the correct numbers + 15 2 7 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 ADD/SUBTRACT THE TOPS KEEP THE BOTTOM 15 + 2 + 7 6 6  6 REDUCE 6 24 = = 3 1 Copyright © 1999 Lynda Greene

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 Create 2 fractions with This denominator

27 28 Now multiply each fraction (top and bottom) by the number that will make them into 12’s. 27 28 Now that they have the same denominators, we can subtract the tops(numerators). This can’t be reduced

Addition & Subtraction Practice: Press enter to see answers Copyright © 1999 Lynda Greene