Numbers Containing Whole Number, Decimal, and Fraction at OnceDate: 10/19/2004 at 15:32:57 From: nesha Subject: solving a problem that has both a decimal and a fraction When dealing with a problem with a whole number, decimal, and a fraction all in one number, what kind of formula would I use? Example: 3.366 2/3. The problem asks to rename the following decimals as proper fractions in lowest terms. I know how to find a fraction from a decimal, and I know how to find a decimal from a fraction. The formulas are different, so when the problem has both I don't know what kind of formula to use. Date: 10/19/2004 at 18:47:49 From: Doctor Ian Subject: Re: solving a problem that has both a decimal and a fraction Hi Nesha, First of all, I wouldn't worry too much about this, because you're never, ever going to come across something like 3.366 2/3 in real life. There is absolutely no point in writing a number this way. However, when in doubt, start from definitions. When we write a decimal number, like 3.366, it's really a sum: 3 6 6 3 + -- + --- + ---- 10 100 1000 So what would 3.366 2/3 mean? It would mean 3 6 6 2/3 3 + -- + --- + ------- 10 100 1000 which is to say, 3 6 20/3 3 + -- + --- + ---- 10 100 1000 or 3 6 20 3 + -- + --- + ---- 10 100 3000 Does that make sense? Now you need to convert everything to a common denominator, add, and simplify: 9000 900 180 20 10100 ---- + ---- + ---- + ---- = ----- 3000 3000 3000 3000 3000 / / / / 2 * 2 * 5 * 5 * 101 = --------------------------------- 2 * 2 * 2 * 3 * 5 * 5 * 5 / / / / 101 = --------- 2 * 3 * 5 101 = --- 30 To check, divide 101 by 30: 3.3 6 6 ____________ 30 ) 1 0 1.0 0 0 9 0 ---- 1 1 0 9 0 ----- 2 0 0 1 8 0 ----- 2 0 0 1 8 0 ----- 2 0 Now, we could keep going; or we could stop here, and think about what to do with the numerator. If you think back to when you were first learning division, you worked on problems like 5 ___ 3 ) 17 17 divided by 3 = 5 remainder 2 15 -- 2 Later on, you learned to interpret the remainder as a fraction, with the denominator equal to the divisor: 5 ___ 3 ) 17 17 divided by 3 = 5 2/3 15 -- 2 It's the same thing here: 3.3 6 6 ____________ 30 ) 1 0 1.0 0 0 101 divided by 30 = 3.366 20/30 9 0 ---- 1 1 0 9 0 ----- 2 0 0 1 8 0 ----- 2 0 0 1 8 0 ----- 2 0 where 20/30 is the same as 2/3, and it means 2/3 of the last PLACE VALUE for which you obtained part of the quotient. In the case of 17 divided by 3, the last place is the units place, so it's 5 + (2/3 of 1) In the case of 101 divided by 30, the last place is the thousands place, so it's 3.366 + (20/30 of 1/1000) which is what we would mean by 3.366 2/3 if we ever actually wrote it that way. Which we don't. :^D Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 10/20/2004 at 10:28:51 From: nesha Subject: Thank you (solving a problem that has both a decimal and a fraction ) Thank you so much for the answer to my question. My math book did not explain in as much detail as you did. Now I understand how they were coming up with their answers, whereas before I was completely lost. |
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