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August 1st, 2013, 03:59 AM   #1
njc
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Practical Algebra: Reciprocals

Hello. I'm working my way through the book Practical Algebra. I'm now learning about reciprocals and I'm well and truly stuck. Usually when I don't understand something I can look at the answer and work out how they came to that answer but not in this case.

The problem: 1 2/3k = 5, k =

To clarify, that is 1 & 2/3k, not sure how to type it out.

The answer they give is 3/5 * 5/3k = 3/5 * 5, k = 3

To solve this problem we are supposed to use the following rule:
Quote:
To solve an equation for an unknown having a fractional coefficient, multiply both numbers by the reciprocal of the fractional coefficient. For example, if 3/4x = 6, multply both sides by 4/3 (the reciprocal of 3/4). This gives 4/3 * 3/4 = 4/3 * 6, or x = 8.
Ok I don't really understand this at all, I did manage to get the 3 questions before this correct although I'm not really sure what is going on, but I just don't understand were the 3/5 comes from as it's not in the question at all. I thought it would use 3/2 as that is the reciprocal of 2/3.

If any of you could spare the time to help me understand this I would be very grateful.
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August 1st, 2013, 05:11 AM   #2
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The coefficient of k is 1 & 2/3, i.e., 1 + 2/3, which is 5/3 and has reciprocal 3/5.
Multiplying the equation by 3/5 gives (3/5)(5/3)k = (3/5)5, which simplifies to k = 3.
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August 1st, 2013, 05:17 AM   #3
njc
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Re:

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Originally Posted by skipjack
The coefficient of k is 1 & 2/3, i.e., 1 + 2/3, which is 5/3 and has reciprocal 3/5.
Multiplying the equation by 3/5 gives (3/5)(5/3)k = (3/5)5, which simplifies to k = 3.

Ok thanks. I'm not sure how 1 + 2/3 makes 5/3 so I think maybe I should put the algebra book on hold while I learn more about fractions. Thanks again.
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August 1st, 2013, 06:22 AM   #4
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Re: Re:

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I'm not sure how 1 + 2/3 makes 5/3 so I think maybe I should put the algebra book on hold while I learn more about fractions. Thanks again.
Well, how many thirds are there in 1? 1 = 3/3 (surely), so 1 + 2/3 = 3/3 + 2/3 = 5/3.

Alternatively, imagine two chocolate bars cut into thirds. You are given the whole of the first bar and 2/3 of the second bar, so how many thirds do you have?
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