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Fractions XV Multiplication of Fractions with Mixed Numbers by Monica Yuskaitis Times You Would Multiply a Mixed Number Times a Fraction In a car race, the track is 2 ¼ miles long. If the car breaks down ½ way through the course, how far did you go? 1/2 of 2 1/4 or 1/2 x 2 1/4 Copyright © 2000 by Monica Yuskaitis Multiplying Fractions Conceptual Understanding When you multiply a positive mixed number by a fraction between 0 and 1 the product is less than the mixed number. 1¼ x ½ = 5/8 Look at the diagram on the next slide to understand why. Copyright © 2000 by Monica Yuskaitis Multiplying Fractions Conceptual Understanding 1¼ x ½ = 5/8 ¼ ¼ ¼ ¼ 1/8 1/8 1/8 1/8 ¼ ¼ ¼ ¼ 1/8 Copyright © 2000 by Monica Yuskaitis How to Find a Fraction of a Mixed Number The first thing to remember is “of” means multiply in mathematics. of = x Copyright © 2000 by Monica Yuskaitis How to Find a Fraction of a Mixed Number Step 1 - When you see a fraction problem you know when you read “of” in the problem you multiply. 1 of 4 x 3 2 9 Copyright © 2000 by Monica Yuskaitis How to Find a Fraction of a Mixed Number Step 2 – Change the mixed number to an improper fraction. 27 + 4 + x 1 x 3 4 31 2 27 9 9 Copyright © 2000 by Monica Yuskaitis How to Find a Fraction of a Mixed Number Step 3 – Multiply the numerators straight across. 1 x 31 = 31 2 9 Copyright © 2000 by Monica Yuskaitis How to Find a Fraction of a Mixed Number Step 4 – Multiply the denominators straight across. 1 x 31 = 31 2 9 18 Copyright © 2000 by Monica Yuskaitis How to Find a Fraction of a Mixed Number Step 5 – Simplify your answer. In this case change the improper fraction to a mixed number. 13 118 1 x 31 = 31 18)31 2 9 18 18 13 Copyright © 2000 by Monica Yuskaitis Multiply and Simplify 35 + 4 1 x 5 4 39 = 39 4 35 7 7 11 28 1 28 28) 39 + x Copyright © 2000 by Monica Yuskaitis Multiply and Simplify 27 + 1 4 x 3 1 28 = 112 7 27 9 9 63 ÷7 49 7 1 63 ÷7 = 9 63)112 + x Copyright © 2000 by Monica Yuskaitis Multiply and Simplify 24 + 3 4 x 6 3 27 = 108 5 24 4 4 ÷ 20 8 4= 2 5 20 ÷ 4 5 20)108 + x Copyright © 2000 by Monica Yuskaitis Multiply and Simplify You’re 24 + 1 shining! 2 x 6 1 25 = 50 5 24 4 4 20 ÷10 10 1 2 20 ÷10 = 2 20)50 + x Copyright © 2000 by Monica Yuskaitis Credits Clipart from “Microsoft Clip Gallery” located on the Internet at http://cgl.microsoft.com/ clipgallerylive/default.asp Copyright © 2000 by Monica Yuskaitis