# Descending order

Objects that are grouped in descending order are grouped from largest to smallest (from left to right). Objects such as shapes can be arranged in descending order by size, while numbers listed in descending order would start with the largest number and end with the smallest number.

## What is descending order

Ordering means arranging objects based on certain rules. Descending order refers to a method of ordering objects from largest to smallest. The bar graph below shows a descending order example:

In this case, the objects being listed in descending order are numbers, but many different objects can be listed in descending order.

## Descending order symbol

The symbol used to indicate objects in descending order is the greater than symbol: >. Referencing the example above, the numbers are written in descending order as: 8 > 6 > 4 > 3 > 2.

## Numbers in descending order

To arrange numbers in descending order, write the numbers from largest to smallest. To achieve this, think of the numbers in terms of their position on a number line. Number lines are arranged such that numbers on the left are smaller and numbers on the right are larger. To list numbers in descending order, read the number line from right to left, and order numbers in the same manner.

## Integers in descending order

To list a given set of integers in descending order, identify the smallest and the largest integers first and write them on the ends. The largest integer goes on the left and the smallest goes on the right. Leave enough space between the left-most and right-most integers. From there, compare the remaining numbers to each other and fit them in their appropriate position between the largest and smallest integers.

Example

List the following set of integers in descending order: 5, 12, 7, 19, 44, 62, 2

In the given set of integers, 2 is the smallest integer and 62 is the largest, so they go on the ends. Then, comparing the size of the remaining integers, the set of numbers listed above in descending order is:

62, 44, 19, 12, 7, 5, 2

## Decimal numbers in descending order

To write decimal numbers in descending order, compare the digits in each place value of the decimal numbers. Place values that are farther left of the decimal places are larger. For example, 2.534 is larger than 2.435, so we would write 2.534 > 2.435.

## Fractions in descending order

To list fractions in descending order, there are a few important things to remember.

- If the fractions being compared have the same denominators, the larger the numerator, the larger the value of the fraction.
- If the fractions being compared have the same numerators, the larger the denominator, the smaller the fraction.
- If fractions have different denominators and numerators, it is necessary to find a common denominator before comparing the sizes of their numerators.

Examples

List the following fractions in descending order.

1. :

2. :

3. :

The least common denominator of this set of fractions is 30. Convert the fractions to equivalent fractions of 30:

List the fractions in descending order:

Convert the fractions to their original forms:

## Date in descending order

To write a set of dates in descending order, write the most recent dates first, then write the older dates. For example: 9/15/2023 > 9/15/1989 > 8/12/1989.

## Letters in descending order

To write letters in descending order, consider A the smallest letter and Z the largest letter. Write the letters closest to Z first to list letters in descending order. For example, given the letters H, C and Z, they are written in descending order as: Z > H > C.

## Descending vs ascending

Objects arranged in descending order are arranged in the opposite way as objects in ascending order (smallest to largest). There are many reasons to arrange objects in descending, ascending, or other orders. For example, it is necessary to arrange numbers to be able to find statistical values like the median, and mode.

To list any of the examples above in ascending order, we would simply reverse the order in which the objects are listed. In the first example, the set of numbers was listed in descending order as 8 > 6 > 4 > 3 > 2. To list these in ascending order, we would instead write: 2 < 3 < 4 < 6 < 8, using the less than symbol as the ascending order symbol.