Question 145544: I'm trying to understand how to multiply mixed fractions for example 389 3/7* 245 1/3
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Well, there's several ways that you can do it but the way that I like best is as follows:
First, we need to realize that 389 3/7 can be written as 389+3/7 and 245 1/3 can be written as 245+1/3.
Next, we multiply 389 by 7 and at the same time divide 389 by 7 and this will transform 389 into 7th's. When we do this, we get:
7*389/7 or 2723/7 and now we have 2723/7+3/7=2726/7----an improper fraction
Now we transform 245 1/3 into 1/3rd's and we get
3*245/3+1/3=735/3+1/3=736/3. Now, we can multiply the two improper fractions:
(2726/7)*(736/3)=(2726*736/21)=2006336/21 Next, we divide this out to get the final answer as a mixed fraction and we get:
95539 17/21-------------------ans
Another way: We know that using FOIL (First Outer Inner Last):
(a+b)(c+d)=ac+ad+bc+bd. Now if we write our problem as:
(389+3/7)(245+1/3)=(245*389+389*1/3+245*3/7+3/7*1/3) simplifying, we get:
(95305+129 2/3 + 105 +3/21) further simplifying, we have:
(95410 +129 14/21 + 3/21) and this equals:
95539 17/21----------------------------ans
Hope this helps----ptaylor
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