Rational Numbers, Properties, Operations
Rational Numbers in Ascending Order
We will learn how to arrange the rational numbers in ascending order.
General method to arrange from smallest to largest rational numbers (increasing):
Step 1: Express the given rational numbers with positive denominator.
Step 2: Take the least common multiple (L.C.M.) of these positive denominator.
Step 3: Express each rational number (obtained in step 1) with this least common multiple (LCM) as the common denominator.
Step 4: The number having the smaller numerator is smaller.
Solved examples on rational numbers in ascending order:
1. Arrange the rational numbers \(
\frac{{ - 7}}
{{10}},\frac{5}
{{ - 8}}and\frac{2}
{{ - 3}}
\) in ascending order:
\(
\begin{gathered}
\frac{{ - 7}}
{{10}},\frac{5}
{{ - 8}},\frac{2}
{{ - 3}} \hfill \\
\Rightarrow \frac{{ - 7}}
{{10}},\frac{{ - 5}}
{8},\frac{{ - 2}}
{3} \hfill \\
\end{gathered}
\)
Now LCM of 10, 8, 3 is 120
\(
\begin{gathered}
\Rightarrow \frac{{ - 7 \times 12}}
{{10 \times 12}},\frac{{ - 5 \times 15}}
{{8 \times 15}},\frac{{ - 2 \times 40}}
{{3 \times 40}} \hfill \\
\Rightarrow \frac{{ - 84}}
{{120}},\frac{{ - 75}}
{{120}},\frac{{ - 80}}
{{120}} \hfill \\
\end{gathered}
\)
Among the above
\(
\frac{{ - 84}}
{{120}} < \frac{{ - 80}}
{{120}} < \frac{{ - 75}}
{{120}}
\)
Ascending order is \(
\frac{{ - 7}}
{{10}},\frac{2}
{{ - 3}},\frac{5}
{{ - 8}}
\)
In arranging the rational numbers in descending order. After expressing denominator as LCM as above case.
The number having the greater numerator is greater that should be written first and go from greater to smaller.
Descending order of \(
\frac{{ - 7}}
{{10}},\frac{5}
{{ - 8}}and\frac{2}
{{ - 3}}
\) is \(
\frac{5}
{{ - 8}},\frac{2}
{{ - 3}},\frac{{ - 7}}
{{10}}
\)