Question

How do you simplify the ratio 35 to 55?

Answer 1

Hint: We start solving the problem by recalling the fact that the ratio of a to b is defined as $ \dfrac{a}{b} $. We use this fact to find a ratio of 35 to 55. We then find the factorization of both the numbers 35 and 55. We then substitute the result if factorization in the ratio and then make the necessary calculations to get the simplified form of the ration which is the required answer.

Complete step by step answer:
According to the problem, we are asked to find the ratio of 35 to 55.
We know that the ratio of a to b is defined as $ \dfrac{a}{b} $ .
Let us assume \[r=\dfrac{35}{55}\] ---(1).
Let us first factorize numbers 35 and 55.
So, we get $ 35=5\times 7 $ ---(2).
Also $ 55=5\times 11 $ ---(3).
Let us substitute equations (2) and (3) in equation (1).
 $ \Rightarrow r=\dfrac{5\times 7}{5\times 11} $ .
 $ \Rightarrow r=\dfrac{7}{11} $ .
So, we have found the simplified form of the ratio 35 to 55 as $ \dfrac{7}{11} $ .
 $ \therefore $ The simplifies form of the ratio 35 to 55 is $ \dfrac{7}{11} $ .

Note:
 We can also report the answer to the ratio in terms of decimals by performing the division. We can also check whether the obtained fraction is a recurring or non-recurring decimal. Whenever we get this type of problem, we try to divide the numerator and denominator of the ratio with the greatest common factor of both of them to simplify it. Similarly, we can expect to find the ratio of the numbers 20 to 55.