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Operations with Fractions

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Adding and Subtracting Fractions

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Rewrite the problem with equivalent fractions 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. Finally add and/or subtract from left to right as normal.

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WHAT DOES THAT MEAN? Let’s illustrate the steps with an example. 3 4 + 1 6

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3 4 + 1 6 Multiples of 4: 4, 8, 12, 16, 20 Multiples of 6: 6, 12, 18, 24, 30 + 12 x 3 9 x 2 2 12 11

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Example 2 9 10 2 5 10, 20, 30, 40, 50 5, 10, 15, 20, 25 10 x 1 9 x 2 4 = 10 5 = 1 2

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Example 3

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Example 4 improper fractions

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Practice ½ + 1/3 1/5 + ¼ 5/6 – 1/5 4/7 – 1/3

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Homework Time!

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Multiplying With Fractions

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Just Follow These Easy Steps! Multiply the numerators and write down the answer as your new numerator. Multiply the denominators and write down the answer as your new denominator. Simplify.

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Example 1 5 8 x 3 4 = 15 32 There are no common factors for 15 and 32, so this fraction cannot be simplified.

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Example 2 3 4 x 2 9 = 6 36 This fraction can be reduced. Divide the numerator and denominator by the GCF, which is 6. = 1 6

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Multiplying by a Whole Number If you want to multiply a fraction by a whole number, turn your whole number into a fraction by placing a 1 as the denominator. If your answer is improper, divide the bottom into the top. 4 5 x 20 1 = 80 5 = 16

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Another Example 15 x 1 61 = 6 15 and 6 have a GCF of 3. = 5 2 Five halves is improper, so we divide the bottom into the top. 25 2 4 1 2 1 2

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Practice

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Multiplying Fractions 1 Must simplify

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Homework Time!

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Review Multiplying Fractions

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Dividing Fractions

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To Divide Fractions: Rewrite the first fraction. Change the division sign to a multiplication sign. Flip the second fraction upside down. Multiply.

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Reciprocal When you flip the second fraction, you are writing that fraction’s reciprocal. 3 5 5 3

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Example 1 1 3 ÷ 1 2 Rewrite: 1 3 x 2 1 = 2 3

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Example 2 4 5 ÷ 4 9 Rewrite: 4 5 x 9 4 = 36 20 = 1 4 5

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Example 3 12 ÷ 3 5 1 Rewrite: 12 1 x 5 3 = 60 3 = 20

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Example 4 1 6 ÷ 2 1 Rewrite: 1 6 x 1 2 = 1 12

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Homework Time

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