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Sagot :
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:
[tex]22=2\times11[/tex]Similarly, for 165, 35 and 210 we have
[tex]\begin{gathered} 165=3\times5\times11 \\ 35=5\times7 \\ 210=2\times3\times5\times7 \end{gathered}[/tex]Then, we can solve the given questions.
Question 1.
[tex]\frac{22}{165}=\frac{2\times11}{3\times5\times11}[/tex]so we can cancel out the number 11 and get
[tex]\frac{22}{165}=\frac{2}{3\times5}=\frac{2}{15}[/tex]Then, the answer is
[tex]\frac{2}{15}[/tex]Question 2.
[tex]\frac{35}{210}=\frac{5\times7}{2\times3\times5\times7}[/tex]and we can cancel out the number 5 and 7, then we obtain
[tex]\frac{35}{210}=\frac{1}{2\times3}[/tex]then, the answer is
[tex]\frac{1}{6}[/tex]
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