Question

How do you order the following fractions from smallest to largest
\[\left\{ \dfrac{7}{9},\dfrac{5}{6},\dfrac{13}{20},\dfrac{11}{16} \right\}\]?

Answer 1

Hint: In this problem, we have to order the given fractions from smallest to largest. We are given fractions, so we have to convert them to decimal to find the smallest and the largest numbers. We can then arrange them from smallest to largest. We can find the decimal numbers from the fraction by dividing the given fractions.

Complete step by step solution:
We know that the given order of fractions,
\[\left\{ \dfrac{7}{9},\dfrac{5}{6},\dfrac{13}{20},\dfrac{11}{16} \right\}\]
We can now find the fraction for the above four terms one by one.
We can now find the fraction of the first term by dividing it, we get
\[\Rightarrow \dfrac{7}{9}=0.7777....\]
We can now find the fraction of the second term by dividing it, we get
\[\Rightarrow \dfrac{5}{6}=0.8333.....\]
We can now find the fraction of the third term by dividing it, we get
\[\Rightarrow \dfrac{13}{20}=0.65\]
We can now find the fraction of the fourth term by dividing it, we get
\[\Rightarrow \dfrac{11}{16}=0.68\]
We can now see that the smallest number is the third term and the next is the fourth term, first term and the second term.
Therefore, the order from the smallest to the largest is \[\left\{ \dfrac{13}{20},\dfrac{11}{16},\dfrac{7}{9},\dfrac{5}{6} \right\}\]

Note: Students make mistakes while converting the number from fraction to its decimal. We should also concentrate while arranging the terms in either ascending or descending order, where we should check for the exact largest or smallest number from the decimal numbers.