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Fraction Multiplication And Cancelation Fraction Multiplication • • Here are some fraction multiplication problems Can you tell how to multiply fraction from these examples? 2 5 10 3 7 21 1 1 1 3 3 9 4 1 4 5 7 35 2 5 10 3 1 3 3 5 15 4 12 48 6 4 24 5 10 50 Recall that multiplication by a whole number can be represented as repeated addition. For example, 4 • 5 = 5 + 5 + 5 + 5. You can multiply a whole number by a fraction using the same method. 1 1 __ __ 3• = 4 4 + + 1 __ 4 + + 1 __ 4 = = 3 __ 4 There is another way to multiply with fractions. Remember that a whole number can be written as an improper fraction with 1 in the denominator. 3. So 3 = __ 1 __ 3 3•1 3 __ 1 = ______ __ • = 1 1•4 4 4 Multiply numerators Multiply denominators Notice that when you multiply a proper fraction and a number greater than 1, the product is between the factors. 1 1 One way to find __ of __ is to make a model. 4 3 1 1 Find __ of __ . 4 3 1 1 1 __ __ __ = • 4 3 12 Multiplying Fractions 1 1 2 3 1 1 1 of 2 3 6 Multiplication • • Multiply numerator by numerator And denominator by denominator 2 5 10 3 1 3 N1 N 2 N1 N 2 D1 D2 D1 D2 Try some. • Multiply the following: 1 5 3 8 2 4 3 5 5 5 8 8 4 2 9 3 Answers • Multiply the following: 1 5 5 3 8 24 2 4 8 3 5 15 5 5 25 8 8 64 4 2 8 9 3 27 Mixed Numbers • • • Because of the order of operations, Mixed numbers cannot be multiplied as is Change mixed numbers to improper fractions, then multiply. 2 5 3 1 5 8 17 13 5 8 17 13 221 5 8 40 221 40 5 with a remainder of 21 21 5 40 Try some • • • Change any whole or mixed numbers to improper. Multiply straight across. Simplify answers 2 1 7 5 1 8 5 Answers • • • Change any whole or mixed numbers to improper. Multiply straight across. Simplify answers 2 7 7 49 4 1 7 9 5 5 1 5 5 1 1 8 8 3 8 1 5 5 1 5 5 Cancelling Reduce before you multiply Canceling • Reducing before multiplying is called canceling. 25 12 300 32 35 1120 • ICK! Instead think the following in your head. 25 12 25 12 5 5 4 3 32 35 32 35 8 4 7 5 5 5 4 3 5 3 15 8 4 7 5 8 7 56 Try one • • Say “--- goes into ____ this many times.” As you cross each number out and write what is left after canceling above the number. 5 1 3 10