# simplify fraction with parentheses

$$(3/2 - 7/10)$$ / $$2/3 + 1/10$$

In this case $$( )$$ should be done first right

so $$4/5$$ / $$2/3 + 1/10$$

now because of order of operations it should be $$4/5 * 3/2$$ and then $$+ 1/10$$ right ?

At the end I get $$13/10$$ and because 13 is a prime number you cant simplify it anymore

but according to symbolab it should be $$24/23$$

copy this \frac{\left(\frac{3}{2}-\frac{7}{10}\right)}{\frac{2}{3}+\frac{1}{10}}

Is this not the same ? or does it change because $$/$$ is for only $$(3/2 - 7/10)$$ / $$2/3$$ If it is like that then I am dumb as**** for confusing it

• Parentheses matter: $8/1+3=11$, but $8/(1+3)=2$. Commented Sep 10, 2020 at 19:33
• yeah but what if it is like the image shows does $2/3$ need to be with $1/10$ inside an parentheses for it to work like the link ? Commented Sep 10, 2020 at 23:06
• The code you've given, \frac{\left(\frac{3}{2}-\frac{7}{10}\right)}{\frac{2}{3}+\frac{1}{10}}, groups the $2/3$ with the $1/10$. In this case, strictly speaking, there are no parentheses in the denominator (and in fact the parentheses in the numerator are not necessary), but the terms are grouped together because they are both under the line: $$\frac{\left(\frac{3}{2}-\frac{7}{10}\right)}{\frac{2}{3}+\frac{1}{10}}$$ So I could have said: parentheses matter, especially if you're writing fractions all on the same line. To write $\frac{a+b}{x+y}$ on one line: $(a+b)/(x+y)$, not $a+b/x+y$. Commented Sep 10, 2020 at 23:40
• just to be clear, the image is showing $a+b/x+y.$ right so $13/10$ should be the right answer and not $24/23$ Commented Sep 11, 2020 at 0:35
• That's correct. You could write it like so: \frac{\frac{3}{2}-\frac{7}{10}}{\frac{2}{3}}+\frac{1}{10}, i.e., $$\frac{\frac{3}{2}-\frac{7}{10}}{\frac{2}{3}}+\frac{1}{10}$$ Commented Sep 11, 2020 at 2:54

$$\frac{\left(\frac{3}{2}-\frac{7}{10}\right)}{\frac{2}{3}+\frac{1}{10}}$$

You were evaluating: $$\frac{\left(\frac{3}{2}-\frac{7}{10}\right)}{\frac{2}{3}}+\frac{1}{10}$$

with the code: \frac{\left(\frac{3}{2}-\frac{7}{10}\right)}{\frac{2}{3}}+\frac{1}{10}

• added an image to the question just to make sure Commented Sep 10, 2020 at 19:26
• I have a question just to clarify I posted an image of the question and it is 13/10 right because there is no (2/3+1/10) Commented Sep 10, 2020 at 23:02

The problem its easy to solve. First of all, your code its not the same what you want, the correct code is \dfrac{\frac{3}{2}-\frac{7}{10}}{\frac{2}{3}}+\frac{1}{10}. After that,

$$\dfrac{\frac{3}{2}-\frac{7}{10}}{\frac{2}{3}}+\frac{1}{10}=\dfrac{\frac{4}{5}}{\frac{2}{3}}+\frac{1}{10}=$$ $$\frac{12}{10}+\frac{1}{10}=\frac{13}{10}$$

• yeah turns out I was confused today is just a bad day for me :( Commented Sep 10, 2020 at 19:29
• I have a question just to clarify I posted an image of the question and it is $13/10$ right because there is no $( 2/3 + 1/10)$ Commented Sep 10, 2020 at 23:01