Answer:
Option C - ![2\frac{1}{6}-5\frac{2}{3}=-3\frac{1}{2}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B6%7D-5%5Cfrac%7B2%7D%7B3%7D%3D-3%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
Given : Expression ![2\frac{1}{6}-5\frac{2}{3}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B6%7D-5%5Cfrac%7B2%7D%7B3%7D)
To find : Perform the indicated operation in the expression ?
Solution :
Expression ![2\frac{1}{6}-5\frac{2}{3}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B6%7D-5%5Cfrac%7B2%7D%7B3%7D)
Write mixed fraction into fraction,
![2\frac{1}{6}-5\frac{2}{3}=\frac{13}{6}-\frac{17}{3}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B6%7D-5%5Cfrac%7B2%7D%7B3%7D%3D%5Cfrac%7B13%7D%7B6%7D-%5Cfrac%7B17%7D%7B3%7D)
Taking Least common denominator,
![2\frac{1}{6}-5\frac{2}{3}=\frac{13-34}{6}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B6%7D-5%5Cfrac%7B2%7D%7B3%7D%3D%5Cfrac%7B13-34%7D%7B6%7D)
![2\frac{1}{6}-5\frac{2}{3}=-\frac{21}{6}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B6%7D-5%5Cfrac%7B2%7D%7B3%7D%3D-%5Cfrac%7B21%7D%7B6%7D)
![2\frac{1}{6}-5\frac{2}{3}=-\frac{7}{2}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B6%7D-5%5Cfrac%7B2%7D%7B3%7D%3D-%5Cfrac%7B7%7D%7B2%7D)
Write improper fraction into mixed fraction,
![2\frac{1}{6}-5\frac{2}{3}=-3\frac{1}{2}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B6%7D-5%5Cfrac%7B2%7D%7B3%7D%3D-3%5Cfrac%7B1%7D%7B2%7D)
Therefore, Option C is correct.