Answer: [tex]\frac{29}{35}[/tex]
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[tex]\frac{7}{21}[/tex]+[tex]\frac{9}{21}[/tex] / 2[tex]\frac{7}{21}[/tex] * 1[tex]\frac{9}{21}[/tex]
2. Now, I would go and solve each side of the equation because we divide them, we can add 2[tex]\frac{7}{21}[/tex] and [tex]\frac{9}{21}[/tex] together to get 2[tex]\frac{16}{21}[/tex], because 7 + 9 = 16
2[tex]\frac{16}{21}[/tex] / 2[tex]\frac{7}{21}[/tex] * 1[tex]\frac{9}{21}[/tex]
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[tex]\frac{7}{21}[/tex] becomes [tex]\frac{49}{21}[/tex] and 1[tex]\frac{9}{21}[/tex] becomes [tex]\frac{30}{21}[/tex]
[tex]\frac{49}{21}[/tex] * [tex]\frac{30}{21}[/tex]
Now we can reduce them, and for our first fraction divide the top and bottom by 7, giving us [tex]\frac{7}{3}[/tex] and the second one by 3, which gives us [tex]\frac{10}{7}[/tex]
[tex]\frac{7}{3}[/tex] * [tex]\frac{10}{7}[/tex] now we cross divide, where we replace the 7's with ones because they're right across from each other to get [tex]\frac{1}{3}[/tex] and [tex]\frac{10}{1}[/tex], or just 10.
[tex]\frac{1}{3}[/tex] * 10 = [tex]\frac{10}{3}[/tex]
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.
[tex]\frac{58}{21}[/tex] / [tex]\frac{10}{3}[/tex]
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 [tex]\frac{58}{21}[/tex] * [tex]\frac{3}{10}[/tex] which if we multiply both sides, you get [tex]\frac{174}{210}[/tex]
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
[tex]\frac{29}{35}[/tex]
