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ADDING AND SUBTRACTING FRACTIONS What Is Adding and Subtracting Fractions with Unlike Denominators? • Fractions can only be added or subtracted if the denominators are the same. For instance, 7/9 + 1/9 = 8/9 or 11/13 – 6/13 = 5/13 • In order to add or subtract two fractions with unlike denominators, one or more must be changed to an equivalent fraction. To solve 2/3 + 1/9, first change 2/3 to n/9 by multiplying times 3/3 (which is 1). Then solve, 6/9 + 1/9. The sum is 7/9. How to add and subtract fractions with unlike denominators: • Before adding or subtracting, both fractions must have the same denominators. • Any number multiplied by one is the same number: 6 x 1 = 6 45 x 1 = 45 ¼ x 1 = ¼ • Begin by choosing a denominator for which both denominators are a factor. This is called the least common denominator (LCD). 15 would be the LCD for 3 and 5 --- 21 would be the LCD for 3 and 7 --- 24 would be the LCD for 8 and 3 • Multiply each fraction by a fraction equal to one. For example, 5/5 or 3/3 is equal to one, so the denominators are the same. The LCD for 2/3 and 1/4 is 12 a. Multiply 2/3 x 4/4 → 8/12 b. Multiply ¼ x 3/3 → 3/12 c. Add 8/12 + 3/12 = 11/12 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

• Just as you cannot add 6 oranges and 4 bananas and have 10 oranges/bananas, you cannot add 7/9 + 2/10 and have 9/19. Note: Only fractions with like denominators can be added or subtracted. • Here are two examples: o 4/7 + 2/5 → 20/35 + 14/35 = 34/35 Change both denominators to 35. o 7/8 – ½ → 7/8 – 4/8 = 3/8 Change ½ to 4/8 because 2 is a factor of 8. Try This! 2/3 – 4/18 = ______________________________________________________ 3/5 + 2/6 = _______________________________________________________ 11/12 – 4/9 = _______________________________________________________ 4/7 + 1/4 = _______________________________________________________ 7/8 – 2/7 = _______________________________________________________ © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.