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:

$22=2\times11$

Similarly, for 165, 35 and 210 we have

$\begin{gathered} 165=3\times5\times11 \\ 35=5\times7 \\ 210=2\times3\times5\times7 \end{gathered}$

Then, we can solve the given questions.

Question 1.

$\frac{22}{165}=\frac{2\times11}{3\times5\times11}$

so we can cancel out the number 11 and get

$\frac{22}{165}=\frac{2}{3\times5}=\frac{2}{15}$

Then, the answer is

$\frac{2}{15}$

Question 2.

$\frac{35}{210}=\frac{5\times7}{2\times3\times5\times7}$

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

$\frac{35}{210}=\frac{1}{2\times3}$

then, the answer is

$\frac{1}{6}$