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## Adding and Subtracting Unlike Fractions

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**Adding and Subtracting Unlike Fractions**Lesson 5.2**Reading a Diagram**• If the diagram has two rows that are even, it is an addition problem. • The addition problem is found in the top row. • The answer is found in the bottom row.**Example**The top row is “one half plus one fourth” 1 2 1 4 The bottom row holds the answer: Count up the fourths. We have three fourths. 1 4 1 4 1 4**Subtracting With a Diagram**• If the top row and bottom row is uneven, then it is a subtraction problem. • Think of it as the top row minus the bottom row.**Example**1 12 1 12 1 12 1 12 1 12 1 4 This problem says: 5/12 - 1/4 Cancel out the one fourth, and the same amount on the top row. Count what is left: two twelfths. When you reduce 2/12, you get 1/6.**Most problems will be solved with pencil and paper.**• List the multiples of both denominators. • Find the least common multiple (LCM). • Write new fractions with the LCM as the new denominator. • Find the factor you multiply by to get from your original denominator to your new denominator. • Use that same factor, and multiply it by your original numerator to get a new numerator.**WHAT DOES THAT MEAN?**Let’s illustrate the steps with an example. 3 1 + 4 6**3**1 + 4 6 9 2 x 3 x 2 + 12 12 11 Multiples of 4: 4, 8, 12, 16, 20 12 Multiples of 6: 6, 12, 18, 24, 30**Example 2**9 2 10, 20, 30, 40, 50 5, 10, 15, 20, 25 5 10 5 x 1 x 2 9 4 = 10 10 10 1 = 2