Question

How do you order the numbers from least to greatest: $2\dfrac{2}{5},\dfrac{{11}}{5},2\dfrac{3}{{10}},\dfrac{{31}}{{10}}$?

Answer 1

Hint: According to given question, we have to order the numbers from least to greatest:$2\dfrac{2}{5},\dfrac{{11}}{5},2\dfrac{3}{{10}},\dfrac{{31}}{{10}}$
So, first of all we have to convert the fixed fraction into the normal fraction as mentioned below,
$a\dfrac{b}{c} = \dfrac{{ac + b}}{c}................................(A)$
Now, we have to convert all fractions into the like fraction. So first of all we have to understand about the like fraction as mentioned below.
Now, we have to compare the numerator of the obtained all like fractions and arrange that like fractions and similar to that given fraction from least to greatest order.

Complete step-by-step solution:
Step 1: First of all we have to convert the all given fixed fraction into the normal fraction by using the formula (A) as mentioned in the solution hint.
$ \Rightarrow 2\dfrac{2}{5} = \dfrac{{2 \times 5 + 2}}{5} = \dfrac{{12}}{5}$
$ \Rightarrow 2\dfrac{3}{{10}} = \dfrac{{2 \times 10 + 3}}{{10}} = \dfrac{{23}}{{10}}$
Step 2: So, first of all we have to take the L.C.M of the denominator of all the fractions as LC.M. equals to 10. Now, we have to convert all fractions into the like fraction as mentioned in the solution hint.
$ \Rightarrow \dfrac{{12 \times 2}}{{5 \times 2}},\dfrac{{11 \times 2}}{{5 \times 2}},\dfrac{{23}}{{10}},\dfrac{{31}}{{10}}$
$ \Rightarrow \dfrac{{24}}{{10}},\dfrac{{22}}{{10}},\dfrac{{23}}{{10}},\dfrac{{31}}{{10}}$
Step 3: Now, we have to compare the numerator of the obtained all like fractions and arrange that like fractions from least to greatest order.
$ \Rightarrow \dfrac{{22}}{{10}} < \dfrac{{23}}{{10}} < \dfrac{{24}}{{10}} < \dfrac{{31}}{{10}}$
Now, similar we have to arrange all the given fractions from least to greatest order,
$ \Rightarrow \dfrac{{11}}{5} < 2\dfrac{3}{{10}} < 2\dfrac{2}{5} < \dfrac{{31}}{{10}}$

Hence, the numbers from least to greatest: $2\dfrac{2}{5},\dfrac{{11}}{5},2\dfrac{3}{{10}},\dfrac{{31}}{{10}}$ are $\dfrac{{11}}{5} < 2\dfrac{3}{{10}} < 2\dfrac{2}{5} < \dfrac{{31}}{{10}}$

Note: Like fraction: The group of two or more fractions that have exactly the same denominator are called like fractions or we can say that the fractions which have the same numbers in the denominators are called like fractions. For example, $\dfrac{1}{7},\dfrac{2}{7},\dfrac{5}{7},\dfrac{7}{7}$ are all like fractions, whose denominator equal to 7.
It is necessary to convert all fixed fractions into the normal fractions
It is necessary to convert all fractions into the like fraction by converting all denominator equals.