# Subtraction of two fractions. I'm learning math by reading books only and the book I'm currently s

Subtraction of two fractions.
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. $-7/8-\left(-1/3\right)=?$
$-7/8X3/3=21/24$ and $-1/3X8/8=8/24$ $-21/24+8/24=13/24$
My answer is $13/24$ but, according to the book the answer is $-1/2$
2. $12/13-\left(-3/7\right)=?$
$84/91-\left(-39/91\right)$ $84/91+39/91=123/91$
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.
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amanhantmk
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.