Question

# Arrange the following fractions in ascending or descending order: $\dfrac{4}{11},\dfrac{10}{15},\dfrac{6}{18},\dfrac{12}{22},\dfrac{15}{33}$.

Hint: Take LCM of the denominators of each of the given fractions. Suppose the LCM of the denominators is $x$. Divide $x$ by the denominator of each fraction and multiply the numerator and denominator of the fraction by the value you get on dividing $x$ by the denominator of the fraction. As the denominators of all the fractions are the same now, compare the numerators of the fractions and arrange them in ascending or descending order. Once you arrange the fractions in ascending or descending order, divide the numerator and denominator by the value you got on dividing $x$ by the denominator.

We have the fractions $\dfrac{4}{11},\dfrac{10}{15},\dfrac{6}{18},\dfrac{12}{22},\dfrac{15}{33}$. We have to arrange them in ascending or descending order. We will do so by evaluating the LCM of the denominators of each of the fractions.
Thus, we have the numbers $11,15,18,22,33$.
The LCM of numbers $11,15,18,22,33$ is $11\times 2\times 9\times 5=990$.
We can rewrite the fraction $\dfrac{4}{11}$ as $\dfrac{4}{11}=\dfrac{4\times 90}{11\times 90}=\dfrac{360}{990}$.
Similarly, we can rewrite the fraction $\dfrac{10}{15}$ as $\dfrac{10}{15}=\dfrac{10\times 66}{15\times 66}=\dfrac{660}{990}$.
We can rewrite the fraction $\dfrac{6}{18}$ as $\dfrac{6}{18}=\dfrac{6\times 55}{18\times 55}=\dfrac{330}{990}$.
We can rewrite the fraction $\dfrac{12}{22}$ as $\dfrac{12}{22}=\dfrac{12\times 45}{22\times 45}=\dfrac{540}{990}$.
We can rewrite the fraction $\dfrac{15}{33}$ as $\dfrac{15}{33}=\dfrac{15\times 30}{33\times 30}=\dfrac{450}{990}$.
Thus, we have the fractions $\dfrac{4}{11},\dfrac{10}{15},\dfrac{6}{18},\dfrac{12}{22},\dfrac{15}{33}$ rewritten as $\dfrac{360}{990},\dfrac{660}{990},\dfrac{330}{990},\dfrac{540}{990},\dfrac{450}{990}$.
Arranging these fractions in ascending order, we have $\dfrac{330}{990}<\dfrac{360}{990}<\dfrac{450}{990}<\dfrac{540}{990}<\dfrac{660}{990}$.
Hence, the fractions arranged in ascending order are $\dfrac{6}{18}<\dfrac{4}{11}<\dfrac{15}{33}<\dfrac{12}{22}<\dfrac{10}{15}$.
We can also arrange these fractions in descending order as $\dfrac{10}{15}>\dfrac{12}{22}>\dfrac{15}{33}>\dfrac{4}{11}>\dfrac{6}{18}$.

Note: A fraction represents a part of a whole. Arranging the fractions in ascending order means arranging them in the increasing order of their value. While, arranging the fractions in descending order means arranging them in decreasing order of their values. Be careful while evaluating the LCM of the denominators as the LCM of any two numbers might not be the same as LCM of five numbers