Lets find the prime factorization of 22, 165, 35 and 210. Prime factorization of a number is breaking a number down into the set of prime numbers which multiply together to result in the original number.
The prime factorization of the number 22 is:
![22=2\times11](https://tex.z-dn.net/?f=22%3D2%5Ctimes11)
Similarly, for 165, 35 and 210 we have
![\begin{gathered} 165=3\times5\times11 \\ 35=5\times7 \\ 210=2\times3\times5\times7 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20165%3D3%5Ctimes5%5Ctimes11%20%5C%5C%2035%3D5%5Ctimes7%20%5C%5C%20210%3D2%5Ctimes3%5Ctimes5%5Ctimes7%20%5Cend%7Bgathered%7D)
Then, we can solve the given questions.
Question 1.
![\frac{22}{165}=\frac{2\times11}{3\times5\times11}](https://tex.z-dn.net/?f=%5Cfrac%7B22%7D%7B165%7D%3D%5Cfrac%7B2%5Ctimes11%7D%7B3%5Ctimes5%5Ctimes11%7D)
so we can cancel out the number 11 and get
![\frac{22}{165}=\frac{2}{3\times5}=\frac{2}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B22%7D%7B165%7D%3D%5Cfrac%7B2%7D%7B3%5Ctimes5%7D%3D%5Cfrac%7B2%7D%7B15%7D)
Then, the answer is
![\frac{2}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B15%7D)
Question 2.
![\frac{35}{210}=\frac{5\times7}{2\times3\times5\times7}](https://tex.z-dn.net/?f=%5Cfrac%7B35%7D%7B210%7D%3D%5Cfrac%7B5%5Ctimes7%7D%7B2%5Ctimes3%5Ctimes5%5Ctimes7%7D)
and we can cancel out the number 5 and 7, then we obtain
![\frac{35}{210}=\frac{1}{2\times3}](https://tex.z-dn.net/?f=%5Cfrac%7B35%7D%7B210%7D%3D%5Cfrac%7B1%7D%7B2%5Ctimes3%7D)
then, the answer is