In algebra, the ascending and ascending orders are frequently used to arrange the fractions, integers, percentages, & decimals. The arrangement can be from least to greatest or vice versa. It is generally known as the order of fractions to arrange the terms in ascending or descending order.

The order of fractions plays a vital role in the arrangement of numbers for solving various mathematical and statistical problems. In this post, we will learn the definition and working of the order of fractions along with solved examples.

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**What are the ascending and descending orders?**

In mathematics, the ascending and descending orders are used to arrange the fractions from least to greatest or greatest to least. It is also called the order of fractions. When the numbers, fractions, and integers are arranged from least to greatest, it is known as ascending order.

While the descending order is the arrangement of the integers, fractions, and terms from greatest to least. The proper, improper, and mixed fractions can be arranged easily either in ascending order or descending order.

The terms that can be written in the form of u/v where u & v are the integers are said to be the fractions. The decimals and the percentages are also written in the form of u/v. The decimal numbers have a point in the numbers like 1/4 = 0.25, 1/2 = 0.5, 1/3 = 0.333, etc.

While the percentage has a % symbol along with the natural numbers and be written in the form of fractions by placing 100 in the denominator or each term like 12% = 12/100, 15% = 15/100, 25% = 25/100, etc.

The term ascending order is like climbing from lower steps to a higher step of the stair. While descending order is the opposite of ascending order.

**Methods of the order of fractions**

There are two well-known methods to arrange the fractions either from smaller to bigger or bigger to smaller.

**Making the same denominator of the fraction i.e., like fractions.**

In this method, you have to find the least common multiple of the denominators of the fractions, then make all the fraction’s denominators equal to the LCM, and then arrange the given terms from least to greatest or greatest to least.

**Finding the quotient of the fractions i.e., converting the fractions into decimals.**

According to this method, you have to divide the fractions and take the result to arrange the fractions.

These methods of the order of fractions play a vital role in the arrangement of various kinds of numbers in ascending or descending order. While dealing with the mixed fraction, make them in the form of improper fractions and then apply one of the above methods.

**How to arrange the fractions?**

The natural numbers, integers, fractions, decimals, & percentages can be ordered easily by using the like fraction method or converting to decimals method. For the arrangement of fractions, you must be familiar with the methods of this arrangement.

**Example 1: By using the like fraction method**

Arrange the given terms in ascending and descending order by using the like fraction method.

13/4, 15/6, 9/8, 21/9, 16/5, 32/3

**Solution **

**Step 1:** Write the given fractions.

13/4, 15/6, 9/8, 21/9, 16/5, 32/3

**Step 2:** Take the denominators of the given fractions and calculate the least common multiple of the denominators.

Fraction’s denominators = 3, 4, 5, 6, 8, 9

Use the list of multiples method and find the times table of each term.

The times table of 3 = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, …}

The times table of 4 = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …}

The times table of 5 = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, …}

The times table of 6 = ({6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, …}

The times table of 8 = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, …}

The times table of 9 = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, …}

Least common multiple of 3, 4, 5, 6, 8, 9 = 360

**Step 4:** Now make the denominators of each fraction equal to 360 to get like fractions.

13/4 = 13 * 90 / 4 * 90 = 1170/360

15/6 = 15 * 60 / 6 * 60 = 900/360

9/8 = 9 * 45 / 8 * 45 = 405/360

21/9 = 21 * 40 / 9 * 40 = 840/360

16/5 = 16 * 72 / 5 * 72 = 1152/360

21/3 = 21 * 120 / 3 * 120 = 2520/360

**Step 5:** Write the like fraction from least to greatest and also write their corresponding fractions.

405/360, 840/360, 900/360, 1152/360, 1170/360, 2520/360

Their corresponding fractions are:

Ascending order = 9/8, 21/9, 15/6, 16/5, 13/4, 21/3

**Step 7:** Similarly, the descending order of the given fractions are:

Descending order = 21/3, 13/4, 16/5, 15/6, 21/9, 9/8

You can also use a least to greatest calculator to get the result in a fraction of seconds with steps. Follow the below steps to find the order of fractions using this tool.

**Step 1:** Input the comma-separated fractions.

**Step 2:** click the calculate button.

**Step 3:** The result will show below the calculate button.

**Step 4:** Press the show more button to view the solution with steps.

**Example 2: By dividing the fractions**

Arrange the given terms in ascending and descending order by using the dividing of quotient method.

125/25, 48/8, 12/6, 15%, 24%, 3 5/9

**Solution **

**Step 1:** Write the given percentages, proper, improper, & mixed fractions

125/25, 48/8, 12/6, 15%, 24%, 3 5/9

**Step 2:** Convert the proper and improper fractions into decimals.

125/25 = 25/5 = 5

48/8 = 24/4 = 12/2 = 6

12/6 = 2/1 = 2

**Step 3:** Convert the percentages into decimals by taking 100 as a denominator.

15% = 15/100 = 3/20 = 0.15

24% = 24/100 = 12/50 = 0.24

**Step 4:** Now convert the mixed fraction into an improper fraction and then convert it into a decimal.

3 5/9 = 32/9 = 3.56

**Step 5:** Write the decimal terms along with the corresponding terms.

125/25, 48/8, 12/6, 15%, 24%, 3 5/9

5, 6, 2, 0.15, 0.24, 3.56

**Step 6:** Write the decimals from least to greatest.

Ascending order =0.15, 0.24, 3.56, 2, 5, 6

Least to greatest = 15%, 24%, 3 5/9, 12/6, 125/25, 48/8

**Step 7:** Similarly, write the decimals from greatest to least.

Descending order = 6, 5, 2, 3.56, 0.24, 0.15

Greatest to least = 48/8, 125/25, 12.6, 3 5/9, 24%, 15%

**Summary **

Now you are witnessed that the arrangement of the fractions, whole numbers, integers, and percentages is not a difficult topic. You can grab all the basics of ascending and descending order from this post.

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