Question

Which of the following is correct?
A. $ \dfrac{2}{3} < \dfrac{3}{5} < \dfrac{{11}}{{15}} $
B. $ \dfrac{3}{5} < \dfrac{2}{3} < \dfrac{{11}}{{15}} $
C. $ \dfrac{{11}}{{15}} < \dfrac{3}{5} < \dfrac{2}{3} $
D. $ \dfrac{3}{5} < \dfrac{{11}}{{15}} < \dfrac{2}{3} $

Answer 1

Hint: The fractions in general give us an idea about how much part of something is given. For example, say you ate $ 1 $ out of two breads, then the fraction of the breads you ate will be given by $ \dfrac{1}{2} $ . where $ 2 $ is the denominator and is indicator of how many total objects were there. The numerator is the quantity we measure like how much we ate so it is $ 1 $ . This can also be represented by percentage in that case we will say you ate $ 50\% $ of the bread.
In the question we have to compare fractions whose denominators are not equal. So we will make the denominators equal. The way to make these denominators equal to each other will be to multiply the denominator and numerator of each fraction by a number so that the denominator becomes equal.

Complete step-by-step answer:
Since all the four options have only three fractions compared to each other, we will first find the least common multiple (LCM) of denominator of all three fraction, the fractions are,
 $ \dfrac{2}{3},\dfrac{3}{5},\dfrac{{11}}{{15}} $
The denominators are $ 3,5,15 $ their lcm will be
 $ 15 $ .
So we will multiply first fraction’s both numerator and denominator to make its denominator equal to the LCM,
The number $ 5 $ will make the denominator of the first fraction to $ 15 $ , so we write,
 $ \dfrac{{2 \times 5}}{{3 \times 5}} = \dfrac{{10}}{{15}} $ ,
Similarly for second fraction we multiply by $ 3 $ we get
 $ \dfrac{{3 \times 3}}{{5 \times 3}} = \dfrac{9}{{15}} $
The third fraction already has a denominator equal to $ 15 $ . Now we will compare the numerator more the numerator of the fractions the more will be the denominator, thus we write,
 $ \dfrac{{11}}{{15}} > \dfrac{{10}}{{15}} > \dfrac{9}{{15}} $
Writing the fractions in their original form we get,
$ \dfrac{3}{5} < \dfrac{2}{3} < \dfrac{{11}}{{15}} $
So option B is correct.
So, the correct answer is “Option B”.

Note: This time we equated the denominator, in case the fractions in question have the same numerator given in them, the more the denominator of the fraction is the lesser the fraction will be, the opposite is the case in which denominator is same as we have seen above that since denominators were equalmore the numerator the higher will be the fraction.