Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 September 24th, 2010, 09:26 PM #1 Newbie   Joined: Sep 2010 Posts: 1 Thanks: 0 please help adding fractions??? What are the steps? I've been on this for 7 days and don't know what to do. Like if there's 1/7+4/8= lcd is between 41 or 40 for this problem? Like I know you're supposed to find the lcd for the bottoms to get a common denominator, but when you find the lcd what's next ???
 September 24th, 2010, 09:54 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: please help adding fractions??? First, we should reduce both fractions if possible to simplify the process, so we work with the smallest numbers we can. 1/7 is fully reduced, but 4/8 may be written as 4/(2·4) = 1/2 So we have 1/7 + 1/2. The two denominators share no common factors (both are in fact prime) so the lcd will be 2·7 = 14. Begin with 1/7 and ask yourself what the denominator 7 must be multiplied by to get 14, and as we saw, that is 2. So we need to multiply 1/7 by 1 (so we don't change its value, only the way its represented) in the form of 2/2. (1/7)(2/2) = 2/14 Now, consider 1/2. What must the denominator 2 be multiplied by to get 14, which is 7. So as before we multiply by 7/7. (1/2)(7/7) = 7/14 Now, our two fractions have a common denominator, and we can directly add them together. 2/14 + 7/14 = 9/14 Notice how the numerator is the sum of the original denominators and the denominator is the product of the original denominators?
September 25th, 2010, 04:28 PM   #3
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Quote:
 Originally Posted by alternap18 . . . you're supposed to find the lcd for the bottoms to get a common denominator . . .
You need to use a common denominator, but it needn't be the LCM (least common multiple) of the original denominators. Any other common multiple of the denominators could be used instead.

For example, 5/6 - 7/10 = (5/6)(5/5) - (7/10)(3/3) = 25/30 - 21/30 = 4/30 = 2/15,
or . . . $\text{ }$ 5/6 - 7/10 = (5/6)(10/10) - (7/10)(6/6) = 50/60 - 42/60 = 8/60 = 2/15.

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