Question

Find the ratio of the first number to the second one in its simplest form: - 112, 133?

Answer 1

Hint: Assume the expression for the ratio of 112 and 133 as E. Consider 112 in the numerator and 133 in the denominator. Now, use the method of prime factorization to write the numbers present in the numerator and denominator as the product of their prime factors. Check if there are any common factors or not, if there are common factors then cancel them and take the product of remaining factors to get the answer. If there are no common factors then we will say that the given fraction is already in simplified form.

Complete step by step answer:
Here we have been asked to write the ratio of 112 and 133 in its simplest form. That means we have to take 112 in the numerator and 133 in the denominator and cancel the common factors of both the numerator and denominator if present. To find whether they have common factors or not we use the prime factorization method to write the numbers as a product of their primes.
Let us assume this ratio as E, so we have,
\[\Rightarrow E=\dfrac{112}{133}\]
Here the numerator 112 can be written as \[112=2\times 2\times 2\times 2\times 7\] as the product of its prime factors. Also, the denominator 133 can be written as \[133=7\times 19\] as the product of its primes. So we get,
\[\Rightarrow E=\dfrac{2\times 2\times 2\times 2\times 7}{7\times 19}\]
Clearly we can see that 7 is common in numerator and the denominator so cancelling them we get,
\[\begin{align}
  & \Rightarrow E=\dfrac{2\times 2\times 2\times 2}{19} \\
 & \therefore E=\dfrac{16}{19} \\
\end{align}\]

Hence, $\dfrac{16}{19}$ is the required ratio in its simplest form.

Note: Do not get confused in considering the numerator and the denominator of the ratio as it is clearly stated that the first number is 112 and the second number is 133. Sometimes you may not be told directly to consider which number is the first and which is the second but you may be directly told to find the ratio of x and y. In that case always consider the number written first as the numerator and the second as the denominator.