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Equations with Fractions YUCK! x x2 7 2 6 What to do? What to do? Let’s get rid of the dang fractions! Remember the miracle of multiplying fractions: CANCELLATION! Cancellation 1 If you multiply by 2, you get 2 1 1 2 1 2 2 1 2 2 1 2 1 Cancellation If you multiply 5 6 by 6, you get 5 5 6 5 6 6 5 6 6 1 6 1 Getting rid of 2 denominators We have to get rid of both a 2 and a 6. What number can we multiply by that will cancel both of them? The Least Common Denominator! LCD Unless someone flat out asks you what the least common denominator is, you can really use any common denominator in most fraction problems. They just like to use the smallest one to keep the numbers in the problem small. LCD and Least Common Multiple If thinking of the LCD makes your eyes cross, go for the least common multiple instead! Multiples of 2: 2, 4, 6, 8, 10, 12 Multiples of 6: 6, 12, 18, 24, 30 Least Common Multiple Smallest number on both lists: Multiples of 2: 2, 4, 6, 8, 10, 12 Multiples of 6: 6, 12, 18, 24, 30 Common Multiples Notice that there are other numbers on both lists: Multiples of 2: 2, 4, 6, 8, 10, 12,…,18 Multiples of 6: 6, 12, 18, 24, 30 You could use any of these to get rid of the fractions in your equation. Let’s Multiply by 6! x x2 7 2 6 You have 2 terms on the left and 1 term on the right. x x2 7 2 6 So you'll need three 6's. Let’s Multiply by 6! x x2 7 2 6 6 x 6 x2 6 7 Don't forget the 7! 1 2 1 6 36 x 6 x 2 67 1 2 1 6 3x x 2 42 Now, isn't that easier? Wrap-up 3x + x + 2 = 42 4x + 2 = 42 4x = 42 – 2 4x = 40 X = 10 Check 10 10 2 7 2 6 12 5 7 6 5 2 7 77 check! Minus Signs Between Fractions 4( x 3) x 2 1 5 15 3 15 4( x 3) 15 x 2 15 1 Cancel the fractions! ( ) ( ) ( ) 1 5 1 15 1 3 (3)(4)( x 3) ( x 2) 5 12( x 3) ( x 2) 5 12 x 36 x 2 5 Distribute the -1 13x 34 5 13x 39 x 3 Dreaded Fractions Any time you have an equal sign and fractions: Determine a common denominator Multiply each term by it. If all your fractions don’t cancel, you picked the wrong number!.