Fractions XIV Multiplication of Fractions

Copyright © 2000 by Monica Yuskaitis We can think of multiplying fractions as finding a fraction of another fraction. How much is of ? Make another with 3/4 x 2/3 Copyright © 2000 by Monica Yuskaitis

Real Life Example of Multiplication of Fractions Andrea and Allison are partners in a relay race. Each girl will run half the total distance. On race day, Andrea stops for water after running of her half of the race. What portion of the race had Andrea run when she stopped for water? Copyright © 2000 by Monica Yuskaitis 3

Copyright © 2000 by Monica Yuskaitis 4

Copyright © 2000 by Monica Yuskaitis The Brownie Problem Nadine is baking brownies. In her family, some people like their brownies frosted without walnuts, others like them frosted with walnuts, and some just like them plain. So Nadine frosts 3/4 of her batch of brownies and puts walnuts on 2/3 of the frosted part. How much of her batch of brownies has both frosting and walnuts? Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Wedding Cake Your family eats 1/8 of 1/2 of a left over wedding cake. 1/8 of 1/2 or 1/8 x 1/2 Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Reading a Novel Jose had already read 1/2 of his novel. Today he read 1/12 of the 1/2 left. How much of the book has he read? 1/12 of 1/2 or 1/12 x 1/2 Copyright © 2000 by Monica Yuskaitis

Multiplying Fractions Conceptual Understanding When you multiply two fractions that are between 0 and 1 the product is smaller than both fractions. ½ x ¾ = 3/8 Look at the diagram on the next slide to understand why. Copyright © 2000 by Monica Yuskaitis

Multiplying Fractions Conceptual Understanding ½ x ¾ = 3/8 ¼ ¼ ¼ ¼ 1/8 1/8 1/8 Copyright © 2000 by Monica Yuskaitis

How to Find a Fraction of a Fraction 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 Fraction Step 1 - When you see a fraction problem you know when you read “of” in the problem you multiply. 1 4 x of 2 9 Copyright © 2000 by Monica Yuskaitis

How to Find a Fraction of a Fraction Step 2 – Multiply your numerators straight across. 1 x 4 4 = 2 9 Copyright © 2000 by Monica Yuskaitis

How to Find a Fraction of a Fraction Step 3 – Then multiply your denominators straight across. 1 x 4 4 = 2 9 18 Copyright © 2000 by Monica Yuskaitis

How to Find the Fraction of a Fraction Step 4 – Simplify your answer. In this case we simplify. 1 x 4 4 2 2 ÷ = = 2 9 18 2 9 ÷ Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Multiply and Simplify 1 9 9 3 3 of ÷ x = = 6 5 30 3 10 ÷ Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Multiply and Simplify 8 3 24 12 2 of x ÷ = = 9 4 36 12 3 ÷ Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Multiply and Simplify 4 7 4 28 of x = 6) 28 2 3 6 24 4 2 2 ÷ 4 4 = 4 6 2 3 ÷ Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Multiply and Simplify 3 3 9 27 3 8 of x = 8) 4 2 8 27 24 3 Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Multiply and Simplify 2 7 8 56 9 6 of x = 6) 3 2 6 56 54 2 2 1 ÷ 9 = 9 2 6 ÷ 2 3 Copyright © 2000 by Monica Yuskaitis

Copyright © 2000 by Monica Yuskaitis Multiply and Simplify Super job! 4 4 3 12 1 8 of x = 8) 2 4 8 12 8 4 4 1 ÷ = 1 1 4 8 4 2 ÷ Copyright © 2000 by Monica Yuskaitis

Multiplying Mixed Numbers In Real Life     Copyright © 2000 by Monica Yuskaitis

Multiplying Mixed Numbers Try a few on your own. Remember to change your mixed numbers into improper fractions first.             Copyright © 2000 by Monica Yuskaitis