# 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. The bar graph below shows a set of numbers in descending order.

Objects arranged in descending order are arranged in the oposite 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.

## How to arrange numbers in descending order

One way to arrange numbers is to think of them 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

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

### Fractions

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: