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I'm learning math by reading books only and the book I'm currently studying is Smart Math by Marcia Learner in which I practice basic operation on fractions. I can't solve the two following problems. Let me show you how I did it but my answers don't match the answers the book presents.

1. $-7/8-(-1/3) = ?$

$-7/8 X 3/3 = 21/24$ and $-1/3 X 8/8 = 8/24$ $-21/24 + 8/24 = 13/24$

My answer is $13/24$ but, according to the book the answer is $-1/2$

2. $12/13-(-3/7)=?$

$84/91 - (-39/91)$ $84/91+39/91 = 123/91$

Book's answer is $105/14$

Please tell me where I've done the mistakes. I correctly did the other problems of similar kind but couldn't understand where I've done wrong.

Community
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Bishnu
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    As far as the first problem is concerned, neither one of you is correct. Your answer should be negative, and the book is flat wrong. – imranfat Aug 11 '16 at 17:56
  • Thank you but the first answer is in negative. It is -1/2. I've written it in the post(in line no. 8) – Bishnu Aug 11 '16 at 18:00
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    You lost signs in the first one, but otherwise you’re on the mark. Second one is right. There’s a moral here: answers in the book are not guaranteed to be correct. – Lubin Aug 11 '16 at 18:03
  • your second answer is correct, in the first you missed a sign, it should be $-13/24$. the book is wrong both times – user190080 Aug 11 '16 at 18:04
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    Hard to believe that a book(!) is wrong twice with such calculations! – Peter Aug 11 '16 at 18:09
  • @user190080 Thank you, thank you very much. I'm relieved but at the same time I'm just feeling hopeless, thinking about how I could proceed. It's very frustrating. Thanks again. – Bishnu Aug 11 '16 at 18:13
  • @Lubin Thank you, thank you very much. I'm relieved but at the same time I'm just feeling hopeless, thinking about how I could proceed. It's very frustrating. Thanks again. – Bishnu Aug 11 '16 at 18:14
  • One other comment: when the denominators are relatively prime (have no factors in common other than $1$), then it must follow as the night the day that the denominator of the sum or difference of these two fractions must be exactly the product of the two separate denominators. So one can see at a glance that the book’s answers are wrong, wrong, wrong. – Lubin Aug 11 '16 at 18:22
  • @Peter It happed you see. Let me give you the book detail. Title: Math Smart (2nd Ed.) Author: Mercia Lerner, Published by The Princeton Review Inc. 2011 ISBN 978--0375-76216-1 The problems are at page No. 82 and the solutions are at page no. 123. (Quiz #6) – Bishnu Aug 11 '16 at 18:24
  • Okay, this is dumb. But are you sure you are looking up the right set of answers? – fleablood Aug 11 '16 at 22:14
  • @fleablood This is not dumb. I acted like a dumb. The book is right. I followed the wrong set of answers. I beg your (from all of you) apology for my stupidity. Please forgive me. – Bishnu Aug 12 '16 at 18:36
  • You weren't stupid! It was a valid question. It's reasonable for an inexperienced reader to assume he just doesn't know what he's doing wrong. In this case, we experienced users could see the answers were dead wrong. I just figured the most likely reasons were: i the author is a moron ii)a typsetter got something wrong and no-one noticed or iii)those were the wrong answer key. None of those are impossible but i) is rare ii) is kinda common but not to that extent iii) all to easy. (We've all done it!) – fleablood Aug 12 '16 at 18:56

1 Answers1

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When adding or subtracting fractions, the denominators of the terms need to be the same.

First let's simplify the number of signs:

$$-\frac{7}{8}-\left(-\frac{1}{3}\right) = -\frac{7}{8}+\frac{1}{3} = \frac{1}{3}-\frac{7}{8}.$$

Then we'll make the denominators the same by multiplying top and bottom by the same number on each term separately:

$$\frac{1}{3}-\frac{7}{8} = \frac{1 \cdot 8}{3 \cdot 8}-\frac{7 \cdot 3}{8 \cdot 3} = \frac{8}{24}-\frac{21}{24}.$$

Now we can subtract the numerators straight away:

$$\frac{8}{24}-\frac{21}{24} = \frac{8 - 21}{24} = -\frac{13}{24}.$$

So you almost got it except for the sign.

Do the same thing with the second problem.

John
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