ziphumulegn

2022-07-04

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.

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.

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