Ascending order and Descending order – Examples

Ascending order and Descending order

Ascending order

When we arrange numbers such that we find larger values as we move forward, it is known as the ascending order of numbers.

Here the arrangement is from a smaller number to a larger number.

It is also known as increasing order. The first number is the lowest and the last number is the highest.

It is similar to climbing up the stairs. As we move forward, our height from the ground keeps on increasing.

Descending order

When we arrange numbers such that we find smaller values as we move forward, it is known as the descending order of numbers.

Here the arrangement is from a larger number to a smaller number.

It is also known as decreasing order. The first number is the largest and the last number is the lowest

It is similar to climbing down the stairs. As we move forward, our height from the ground keeps on decreasing.

How to represent numbers in ascending and descending order

Ascending order

The symbol “<” is used in-between numbers in ascending order.
The number on the right of the symbol “<” is always greater than the number on the left of this symbol.

Descending order

The symbol “>” is used in-between numbers in descending order.
The number on the right of the symbol “>” is always smaller than the number on the left of this symbol.

Ascending and descending order of negative numbers

The absolute value of a negative number is its value without the negative sign. For arranging negative numbers in ascending we have to refer to their absolute values.

The negative number having a greater absolute value is less than the negative number having a smaller absolute value. This implies greater the absolute value, the smaller is the negative number.

Examples:

1. (-2) < (-1)

The absolute value of (-1) is 1 and the absolute value of (-2) is 2.

2 is greater than 1.

The greater is the absolute value, the smaller is the negative number.

Hence (-1) is greater than (-2).

2. (-1) > (-3) > (-7)

Ascending and descending order of fractions

Case-1:

When the denominator of the fractions is the same.

In a group of fractions having the same denominators, the fraction having the greater numerator is the greater one and vice-versa.

Example:

The given fractions have the same denominators.
Since 9 > 6 > 1 , we can say that  \frac{9}{7}>\frac{6}{7}>\frac{1}{7}.

Case-2: 

When the denominator of the fractions is different.

In a group of fractions having different denominators, we have to convert them into like fractions first and then arrange them in the increasing order of their numerators. 

Example:

\frac{1}{2}, \frac{2}{3}, \frac{1}{6}

The given fractions have different denominators. Hence we have to convert them into like fractions.

LCM of 2, 3 and 6 = 6 

\frac{1}{2}=\frac{1 \times 3}{2 \times 3}=\frac{3}{6}

\frac{1}{6}=\frac{1 \times 1}{6 \times 1}=\frac{1}{6}

Since 1 < 3 < 4, we can say that \frac{1}{6}<\frac{3}{6}<\frac{4}{6}.

Hence \frac{1}{6}<\frac{1}{2}<\frac{2}{3}.

Solved Examples

1. Arrange 1,5,3,9,2 and 10 in ascending order first and then in descending order also.

Ascending order

1 < 2 < 3 < 5 < 9 < 10

Descending order

10 > 9 > 5 > 3 > 2 > 1

2. Vickey, Mohit, Ashok and Rahul secured 80%, 98%, 95% and 85% respectively in the final exams. Arrange their marks in ascending order. Who scored the highest among all four boys? 

Marks of Vickey = 80%

Marks of Mohit = 98%

Marks of Ashok = 95%

Marks of Rahul = 85%

Arranging the marks in ascending order
80% < 85% < 95% < 98%

Hence Mohit secured the highest marks and Vickey secured the lowest marks.

3. Priya, Sonia, Preeti and Neha have Rs 400, Rs 100, Rs 200 and Rs 300 respectively.

Arrange them in decreasing order of the money they have.

Money with Priya = Rs 400

Money with Sonia = Rs 100

Money with Preeti = Rs 200

Money with Neha = Rs 300

Arranging the money in decreasing order

Rs 400 > Rs 300 > Rs 200 > Rs 100
Priya > Neha > Preeti > Sonia
Priya is richer than the other 3 girls.