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**

Follow the below steps;**(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.

Follow the below steps;

(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.

Follow the below steps;

(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}}