Solving Equations with Fractions in ThemDate: 12/06/2004 at 15:12:14 From: Amanda Subject: How do you solve equations with multiplication I'm stuck on -5/7 n = 35. I don't understand how you change a fraction like this to a whole number. Date: 12/06/2004 at 22:00:29 From: Doctor Boyd Subject: Re: How do you solve equations with multiplication Hi Amanda, Thanks for writing to Dr. Math. Let's look at a similar but slightly easier problem: 1 --- n = 35 7 We know that one seventh of "n" is 35, so now we need to collect together enough pieces of "n" to make a whole "n". Let's pretend that "n" is this long: +----------------------------------+ Now, I can break it into 7 pieces: +----+----+----+----+----+----+----+ And I know that each of these pieces is 35 35 35 35 35 35 35 35 +----+----+----+----+----+----+----+ So the total of "n" is 35 + 35 + 35 + 35 + 35 + 35 + 35 = 245 Now, notice that there are 7 of these, so it could be a multiplication: 7 * 35 = 245 So, if we look back at our original equation, we see that all we had to do was take 7 "1/7 n"s and 7 "35"s to find out how much one "n" was worth. In other words, we just multiply both sides by "7": 1 --- n = 35 7 1 7 * --- n = 7 * 35 -->(Multiply both sides by 7) 7 7 --- n = 7 * 35 -->( 7 * 1/7 = 7/7) 7 1 * n = 245 -->(7/7 = 1) n = 245 Does that give you a clue of how to solve your question? Please write back if you'd like some more help with this, or if you have any other questions. All the best, - Doctor Boyd, The Math Forum http://mathforum.org/dr.math/ |
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