Answer: ![\frac{29}{35}](https://tex.z-dn.net/?f=%5Cfrac%7B29%7D%7B35%7D)
Step-by-step explanation:
1. Make sure all your denominators are the same, you can do this by multiplying them all by 3 or 7, 2 and 1/3 would become 2 7/21, 3/7 would become 9/21, 2 and 1/3, would become 2 and 7/21, and so on and so forth, leaving us with
2
+
/ 2
* 1![\frac{9}{21}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B21%7D)
2. Now, I would go and solve each side of the equation because we divide them, we can add 2
and
together to get 2
, because 7 + 9 = 16
2
/ 2
* 1![\frac{9}{21}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B21%7D)
3. We can do the same thing to the other side, by multiplying the two of them. I'm going to convert both of them to just fractions, 2
becomes
and 1
becomes ![\frac{30}{21}](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7B21%7D)
* ![\frac{30}{21}](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7B21%7D)
Now we can reduce them, and for our first fraction divide the top and bottom by 7, giving us
and the second one by 3, which gives us ![\frac{10}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B7%7D)
*
now we cross divide, where we replace the 7's with ones because they're right across from each other to get
and
, or just 10.
* 10 = ![\frac{10}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B3%7D)
4. So now we can do a similar thing with the first half of our equation and convert it into a fraction and not a mixed number.
/ ![\frac{10}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B3%7D)
Now we multiply divide them, and the easiest way I learned how to do this was by keep the first fraction in its place, and flipping the denominator and numerator of the second, and multiplying them.
so
*
which if we multiply both sides, you get ![\frac{174}{210}](https://tex.z-dn.net/?f=%5Cfrac%7B174%7D%7B210%7D)
I'll save you some times and simplify it for you, the greatest common factor is 6 so we divide the top and bottom by 6 to get
![\frac{29}{35}](https://tex.z-dn.net/?f=%5Cfrac%7B29%7D%7B35%7D)