Question

Use prime factorization to reduce each fraction 1. 22/165 2. 35/210

Answer 1

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*11`

Similarly, for 165, 35 and 210 we have

`\begin{gathered} 165=3*5*11 \\ 35=5*7 \\ 210=2*3*5*7 \end{gathered}`

Then, we can solve the given questions.

Question 1.

`(22)/(165)=(2*11)/(3*5*11)`

so we can cancel out the number 11 and get

`(22)/(165)=(2)/(3*5)=(2)/(15)`

Then, the answer is

`(2)/(15)`

Question 2.

`(35)/(210)=(5*7)/(2*3*5*7)`

and we can cancel out the number 5 and 7, then we obtain

`(35)/(210)=(1)/(2*3)`

then, the answer is

`(1)/(6)`