What is 4/5 x 10?Date: 10 Feb 1995 15:19:52 -0500 From: Joy Sakoguchi Subject: Michael's queston Dr. Math, What is the answer to this fraction? Here the problem is 4/5 x10. Please explain. Date: 15 Feb 1995 20:05:35 GMT From: Dr. Math Subject: Re: Michael's queston Hello there! When I multiply fractions, I like to write _both_ of the numbers as fractions. So I would take your problem and notice that 10 = 10/1, so we have 4 4 10 - x 10 = - x -- 5 5 1 Then we have to remember how to multiply two fractions. When we multiply two fractions together, we multiply everything in the top together, and then everything in the bottom together. Then we take what we get and put it in a new fraction. So we get 4 10 4 x 10 - x -- = ------ 5 1 5 x 1 This, technically, is our answer, but we can make it simpler in a couple of ways. First, notice that 5 x 1 = 5. So we can write the fraction as 4 x 10 4 x 10 ------ = ------ 5 x 1 5 Now we do the tricky part. Notice that 10 = 2 x 5. So let's replace 10 in the top by 2 x 5, to get 4 x 10 4 x 2 x 5 ------ = --------- 5 5 Now when we have the same thing in the top as we do in the bottom, we can cancel them both out, but (this is very important) we can only do it when the top and bottom each have multiplication separating the parts, not addition or subtraction or anything else!! So if the top had been 4 + 2 + 5, we wouldn't have been able to cancel anything. In this case though, we're fine. So we get 4 x 2 x 5 4 x 2 --------- = ----- = 4 x 2 = 8. 5 1 So the answer to our problem is 8. This may seem like a lot of work, but if you do it enough, you'll get really good at it, and you'll start doing it in your head. To let you know what you have to look forward to when you get good at these, when I looked at this problem, I knew the answer in less than a second! I hope this helps you. -Ken "Dr." Math |
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