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Multiplying Fractions with Whole Numbers Example: 3/8 of 40 “of” = multiply Method #1: Picture Method #2: Put the whole number over 1 and then simplify and multiply

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Picture Method 4/8 of 64 The picture is worth the whole number Divide the picture up into the amount of pieces Label each piece Shade in the amount of pieces Total the amount of pieces

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Math Method 1) Put the whole number over 1 (make it a fraction) 2) Cross simplify/reduce: divide out a common factor from the numbers across 3) Re-write the problem 4) Multiply the numerators 5) Multiply the denominators 6) Reduce

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In multiplication, “of” = multiply So, 2/3 of 4/6 means 2/3 x 4/6 Simplifying before Multiplying Fractions: –Cross Simplify: Divide out a common factor from the numbers across

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Multiplying Fractions Notes Ex: 2 / 3 x 1 / 4 1.Cross reduce/simplify 1/3 x 1/2 2.Multiply the numerators, and then multiply the denominators. 1 x 1 = 3 x 2 = 3.Simplify if possible. 1 6 http://www.xpmath.com/forums/arcade.php?do=play&gameid=29

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Multiplication of Fractions with a Picture Draw a model representing 2 / 3 of 1 / 4.

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1. 2 / 3 x 1 / 4 = 2. 5 / 6 of 2 / 5 = 3. 1 / 3 · 9 / 10 = 4. 1 / 4 x 12 = Practice Problems:

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Simplest Form: when the only common factor of the numerator and denominator is 1. Ex: 2 / 3 is in simplest form since 2 and 3 have only 1 as a common factor. Write 20 / 25 in simplest form. 20: 1, 2, 4, 5, 10, 20 25: 1, 5, 25 20 / 25 = 4 / 5 List the factors for the numerator and denominator and find the GCF Divide the numerator and denominator by the GCF The fraction 20 / 25 written in simplest form is 4 / 5. Reducing Fractions to Simplest Form

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Changing a Mixed Number to an Improper Fraction Write 6 ¼ as an improper fraction. 1.Multiply the whole number by the denominator. 6 x 4 = 24. 2.Add the numerator to this total. 24 + 1 = 25 3.Write as an improper fraction. 25 / 4 http://www.xpmath.com/forums/arcade.php?do=play&gameid=37

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Multiplying Mixed Numbers Notes Ex: 2 1 / 7 x 2 2 / 5 1.Change to improper fractions. 15 / 7 x 12 / 5 2.Simplify diagonally (cross simplify) / 7 x 12 / 3.Multiply. 3 / 7 x 12 / 1 = 4.Simplify again. 36 / 7 =

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1.1 2 / 5 x 4 1 / 3 = 2.2 6 / 7 · 1 2 / 5 = 3.1 2 / 3 x 7 1 / 2 = Practice:

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Dividing Fractions Notes Ex: 8 4 / 5 1.Find the reciprocal of the second number. The reciprocal of 4 / 5 is 5 / 4. Just FLIP the second number. 2.Change to multiplication and simplify diagonally if you can. 8 / 1 x 5 / 4 3.Multiply. 2 / 1 x 5 / 1 = 4.Simplify. 10 / 1 = http://www.xpmath.com/forums/arcade.php?do=play&gameid=28

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Dividing Mixed Number Notes Ex: 5 1 / 3 2 2 / 5 1.Write each mixed number as an improper fraction. 16 / 3 12 / 5 2.Find the reciprocal of the second number. The reciprocal of 12 / 5 is 5 / 12. 3.Change to multiplication and simplify diagonally if you can. 16 / 3 x 5 / 12 4.Multiply. 4 / 3 x 5 / 3 = 5.Simplify. 20 / 9 =

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What is the reciprocal of each number? 9 / 7 5 2 / 3 8 1 6 / 7 1 / 23

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1. 3 / 8 3 = 2. 7 / 8 2 / 7 = 3.2 1 / 2 1 2 / 5 = Practice

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4. 1 2 / 3 1 / 2 = 5. 1 1 / 10 1 5 / 6 6. 9 / 10 3 Practice

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Find each quotient. 6 2 / 5 2 / 5 3 / 4 9 / 10 3 6 1 / 4 2 1 / 2 1 1 / 10 1 5 / 6

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