Question

Compare the following pair of ratio:
$\dfrac{5}{18},\dfrac{17}{121}$

Answer 1

Hint: To solve this question, first of all we need to convert the denominator of both fractions. Since, the denominators are different and do not have any common factor. So, we will multiply by the denominator of the second fraction into the numerator and denominator of the first fraction and multiply by first denominator to the numerator and denominator of the second fraction to make the same denominator in both fractions. After that we will compare the fraction by observing the numerator. The greater number of numerators will help to decide which fraction is greater than.

Complete step by step answer:
Since, the given fractions are $\dfrac{5}{18}$ and $\dfrac{17}{121}$.
Let’s start with first fraction that is $\dfrac{5}{18}$ as:
$= \dfrac{5}{18}$
Since, the denominator second fraction is $121$. We will multiply by this denominator $121$ in the numerator and denominator of fraction $\dfrac{5}{18}$ as:
$= \dfrac{5\times 121}{18\times 121}$
After doing multiplication, we will have the new fraction as:
$= \dfrac{605}{2178}$ … $\left( i \right)$
Now, we will convert the second fraction that is $\dfrac{17}{121}$ as:
$= \dfrac{17}{121}$
Since, the denominator of the first fraction is $18$. We will multiply by this denominator $18$ in the numerator and denominator of fraction $\dfrac{17}{121}$ as:
\[= \dfrac{17\times 18}{121\times 18}\]
After doing multiplication, we will have the new fraction as:
$= \dfrac{306}{2178}$ … $\left( ii \right)$
After comparing equation $\left( i \right)$ and $\left( ii \right)$, we can clearly see that the first fraction is greater than second fraction that has same denominator as:
$= \dfrac{605}{2178}>\dfrac{306}{2178}$
So, we can write the above fraction into its original form as:
$\Rightarrow \dfrac{5}{18}>\dfrac{17}{121}$
Hence, the final conclusion is that the first fraction is greater than the second fraction.

Note: Here is another method to solve the given question by converting the given fraction into decimal numbers and after that we can clearly observe which number is greater than.
Since, the given fractions are $\dfrac{5}{18}$ and $\dfrac{17}{121}$.
The first fraction is:
$= \dfrac{5}{18}$
Convert it into decimal number as:
$= 0.28$
And the second fraction is:
$= \dfrac{17}{121}$
We will convert it also into decimal number as:
$= 0.14$
After comparing the decimal value of first fraction to the decimal value of the second fraction, we have:
$\Rightarrow 0.28>0.14$
In the fraction, we can write the above step as:
$\Rightarrow \dfrac{5}{18}>\dfrac{17}{121}$
The obtained answer is the same as we obtained in the solution. Hence, the solution is correct.