Multiplying and Adding FractionsDate: 04/01/97 at 23:31:39 From: Eric Pelfrey Subject: Multiplying and Adding Fractions (1/3 + 2/5) * 3/4. I can't find the answer! Please help me. Date: 04/02/97 at 06:26:04 From: Doctor Mitteldorf Subject: Re: Multiplying and Adding Fractions Dear Eric, People spend a lot of time in school studying fractions before they take on a problem as tough as this one. Here's a way you might think about it. First, you might break up the multiplication: the 3/4 multiplies the sum of the other two fractions, but you could just as well make it multiply each one separately: 1/3 * 3/4 + 2/5 * 3/4 The first part is 1/3 of 3/4. Well, this is easy, since 1/3 of 3 anythings is 1 anything. If you have 3 fourths, you have 1/4, 1/4 and 1/4. So a third of that is just 1/4. The next part is harder. 2/5 of 3/4. I'd think of my 2/5 as 4/10 to start with, if I were you. Then it's just 3/4 of 4/10 that you want. Well, 1/4 of 4 tenths is just 1 tenth - same way we did the other one. If 1/4 of 4 tenths is 1 tenth, then 2/4 of it makes 2/10 and 3/4 of it makes 3 tenths. So the answer is 3/10. Here's what we've got so far: (1/3 + 2/5) * 3/4 1/3 * 3/4 + 2/5 * 3/4 1/4 + 3/10 Now what's left is to add 1/4 and 3/10. I don't know if you've studied this yet - there's a trick that they teach you in 6th grade, that goes like this: Think of the 1/4 as so many twentieths. It's the same as 5/20. Think of the 3/10 as so many twentieths. It's the same as 6/20. Now you can just add them up. 1/4 + 3/10 is the same as 5/20 + 6/20, which is 11/20. That's the answer. Whew - that had a lot of steps. Did you get them all? Anything we should go over again? The one thing I'd be asking if I were you: How did I know to change the 1/4 and 3/10 to twentieths? Where did I get the number 20? Are there any other numbers I could have used instead of 20? What do you think? -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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