# Arrange rational number in descending order

In this chapter we will learn to arrange rational numbers in descending order with solved examples.

In descending order, the numbers arranged from largest to smallest.

To understand this chapter, you should have basic knowledge of rational numbers. Click the red link to lean about rational numbers in detail.

## Method to arrange rational number in descending order

Here we will try to compare the values of given rational number and arrange it from greatest to smallest.

To arrange the numbers follow the below steps;

(a) Write the rational number in fraction form

(b) Find LCM of denominators

(c) Multiply each rational number to make its denominator equal to LCM

(d) Now compare the numerator number and arrange number from greatest to smallest.

I hope you understood the process. Let us see some examples for further clarity.

Example 01
Arrange the below rational number in descending order.
\mathtt{\Longrightarrow \frac{11}{5} ,\ \frac{13}{6} \ \&\ \frac{8}{3}}

Solution

(a) Find LCM of denominators.

LCM (5, 6, 3) = 30

(b) Multiply each rational number to make denominator equal to 30.

(i) Rational number 11 / 5

Multiply numerator & denominator by 6

\mathtt{\Longrightarrow \frac{11}{5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{11\times 6}{5\times 6}}\\\ \\ \mathtt{\Longrightarrow \ \frac{66}{30}}

(ii) Rational number 13 / 6

Multiply numerator and denominator by 5.

\mathtt{\Longrightarrow \frac{13}{6}}\\\ \\ \mathtt{\Longrightarrow \ \frac{13\times 5}{6\times 5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{65}{30}}

(iii) Rational number 8 / 3

Multiply numerator & denominator by 10

\mathtt{\Longrightarrow \frac{8}{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{8\times 10}{3\times 10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{80}{30}}

We have numbers with same denominator. Now simply compare the numerators and arrange in ascending order.

(c) Comparing the numerators & arranging in descending order.

\mathtt{\Longrightarrow \frac{80}{30} >\ \frac{66}{30} >\frac{65}{30}}

Putting the original values we get;

\mathtt{\Longrightarrow \frac{8}{3} >\ \frac{11}{5} >\frac{13}{6}}

Example 02
Arrange the below rational number in descending order.

\mathtt{\Longrightarrow \frac{2}{7} ,\ \frac{-1}{5} \ \&\ \frac{3}{8}}

Solution
Note that one of the rational number is negative.

The negative number is the always less than the positive number. Hence the rational number -1 / 5 is the smallest.

Now we will compare the other two positive numbers 2 / 7 & 3 / 8.

(a)Find the LCM of denominator

LCM (7, 8) = 56

(b) Multiply each rational number to make denominator 56

(i) Rational number 2/7

Multiply numerator & denominator by 8.

\mathtt{\Longrightarrow \frac{2}{7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{2\times 8}{7\times 8}}\\\ \\ \mathtt{\Longrightarrow \ \frac{16}{56}}

(ii) Fraction 3 / 8

Multiply numerator and denominator by 7

\mathtt{\Longrightarrow \frac{3}{8}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3\times 7}{8\times 7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{21}{56}}

Now we have numbers with same denominator. We can easily compare rational numbers using numerator value.

(c) Comparing numerators and arranging in descending order.

\mathtt{\Longrightarrow \frac{21}{56} >\ \frac{16}{56} >\frac{-1}{5}}

Putting the original values.

\mathtt{\Longrightarrow \frac{3}{8} >\ \frac{2}{7} >\frac{-1}{5}}

Example 03
Arrange the below rational numbers in descending order.
\mathtt{\Longrightarrow \frac{10}{11} ,\ \frac{-5}{6} \ \&\ \frac{-6}{5}}

Solution
Here one number is positive and the other two numbers are negative.

We know that positive number is always greater than negative number, so the number 10/11 is the greatest.

Now let’s compare the other two negative numbers -5 / 6 & -6 / 5.

(a) Take LCM of denominator.

LCM (6, 5) = 30

(b) Multiply the rational number to make denominator equal to 30

(i) Rational number -5/6

Multiply numerator and denominator by 5.

\mathtt{\Longrightarrow \frac{-5}{6}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-5\times 5}{6\times 5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-25}{30}}

(ii) Rational number -6/5

Multiply numerator and denominator by 6

\mathtt{\Longrightarrow \frac{-6}{5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-6\times 6}{5\times 6}}\\\ \\ \mathtt{\Longrightarrow \ \frac{-36}{30}}

We have got the fractions with same denominator. Now we can compare the numerator to find greater value.

(c) Comparing numerators and writing in descending order.

\mathtt{\Longrightarrow \frac{10}{11} >\ \frac{-25}{30} >\frac{-36}{30}}

Putting the original values.

\mathtt{\Longrightarrow \frac{10}{11} >\ \frac{-5}{6} >\frac{-6}{5}}