What is the order of fractions and how to arrange fractions, whole numbers, and percentages?
In mathematics, the ordering fractions is used to arrange the fractions, whole numbers, and percentages from least to greatest or greatest to least. In simple words, the order of fractions is a general rule that arranges the fractions either in ascending or descending order.
In this post, we will learn about the order of fractions and how to arrange the fractions, whole numbers, and percentages with a lot of examples.
What is the order of fractions?
To arrange the fractions, whole numbers, and percentages, you must have some knowledge about these terms.
- Fractions are the numbers that are written as numerators and denominators using the “/” sign. The fraction can be proper, improper, or mixed.
- Whole numbers are those numbers that have a decimal point like 0.35, 4.5, etc.
- While percentages are the number that makes a fraction having 100 as a denominator. The percentage is usually denoted by the “%” sign.
The order of fractions means to arrange the fractions either in ascending or descending order. Least to greatest and greatest to least are two methods to arrange the fractions.
- The least to greatest means to arrange the fraction, whole number, or percentage according to ascending order.
- While greatest to least is used to arrange these terms according to descending order.
There are two ways to arrange the fraction either in ascending order or descending order:
- By making like fractions
- By converting the fractions into decimals.
If the mixed fractions are given make them improper fractions and then implement any principle either by converting them to fractions or decimals.
To arrange the percentage numbers, convert the given percentage data into a fraction and apply the above rules.
You can also use the ordering fractions calculator to get the result from least to greatest or Vice Versa with steps in no time.
How do arrange fractions, whole numbers, and percentages from least to greatest and Vice Versa?
To arrange the fractions, percentages, and whole numbers, let’s take some examples.
Example 1: For proper and improper fractions
Arrange 2/3, 9/4, 12/13, 13/16, 2/14, and 22/3 from least to greatest and greatest to least.
Solution
Step 1: Write the given proper and improper fractions.
2/3, 9/4, 12/13, 13/16, 2/14
Step 2: Now take the denominators of the fractions to find the LCM.
Denominators = 3, 4, 13, 16, 14
Step 3: Now take the LCM of the above numbers.
multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 …
multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …
multiples of 13 = 13, 26, 39, 52, 65, 78, 91, 104, 117. 130, …
multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, …
multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, …
LCM of 3, 4, 13, 16, 14 = 4368
Step 4: Now make the denominators 4368 for making like fractions.
2/3 = 2 x 1456 / 3 x 1456 = 2912/4368
9/4 = 9 x 1092 / 4 x 1092 = 9828/4368
12/13 = 12 x 336 / 13 x 336 = 4032/4368
13/16 = 13 x 273 / 16 x 273 = 3549/4368
2/14 = 2 x 312 / 14 x 312 = 624/4368
Step 5: Now arrange the numerators according to ascending order.
624/4368, 2912/4368, 3549/4368, 4032/4368, 9828/4368
Step 6: Now take the corresponding fractions and the result must be least to greatest.
Ascending order = 2/14, 2/3, 13/16, 12/13, 9/4
Step 7: Now write the above data according to descending order.
Descending order = 9/4, 12/13, 13/16, 2/3, 2/14
Example 2: For whole numbers
Arrange 1.2, 0.33, 18.2, 0.0012, 19.7, 12.4 according to ascending and descending order.
Solution
Step 1: Write the given whole numbers.
1.2, 0.33, 18.2, 0.0012, 19.7, 12.4
Step 2: Arrange the whole numbers from greatest to least to get the result according to descending order.
Greatest to least = 19.7, 18.2, 12.4, 1.2, 0.33, 0.0012
Step 3: Arrange the whole numbers from least to greatest to get the result according to ascending order.
Least to greatest = 0.0012, 0.33, 1.2, 12.4, 18.2, 19.7
You can also use a least to the greatest calculator to reduce the difficulty of larger calculations. By using this calculator, you have to simply input the comma-separated values and hit the “calculate” button to get the step-by-step conclusion. The result will come in a couple of seconds below the calculate button.
You can also click on the “show steps” button to get the step-by-step solution to the given problems.
Example 3: For percentages
Arrange 10%, 15%, 39%, 12%, 80%, 5% according to ascending and descending order.
Solution
Step 1: Write the given percentages.
10%, 15%, 39%, 12%, 80%, 5%
Step 2: Now convert the percentages into fractions by taking 100 as a denominator.
10/100, 15/100, 39/100, 12/100, 80/100, 5/100
Step 3: Now convert the above fractions into decimal numbers.
10/100 = 1/10 = 0.1
15/100 = 3/20 = 0.15
39/100 = 0.39
12/100 = 3/25 = 0.12
80/100 = 8/10 = 2/5 = 0.8
5/100 = 1/20 = 0.05
Step 4: Now write the decimals from least to greatest.
0.05, 0.1, 0.12, 0.15, 0.39, 0.8
Step 5: Now write the corresponding percentages.
Ascending order = 5%, 10%, 12%, 15%, 39%, 80%
Step 6: Now arrange the percentages from greatest to least.
Descending order = 80%, 39%, 15%, 12%, 10%, 5%
Example 4: For mixed numbers
Arrange 34/12, 30%, 0.34, 3 * 1/4, and 13/48 in ascending and descending order.
Solution
Step 1: Write the given mixed numbers.
34/12, 30%, 0.34, 3 * 1/4, 13/48
Step 2: Now convert the percentage number into a fraction.
30% = 30/100 = 3/10
34/12, 3/10, 0.34, 3 * 1/4, 13/48
Step 3: Convert the mixed fraction into an improper fraction.
3 * 1/4 = 13/4
34/12, 3/10, 0.34, 13/4, 13/48
Step 4: Now convert all the fractions into decimals.
34/12 = 17/6 = 2.83
3/10 = 0.3
13/4 = 3.25
13/48 = 0.27
Step 5: Now arrange the decimals from least to greatest and greatest to least.
Least to greatest = 0.27, 0.3, 0.34, 2.83, 3.25
Greatest to least = 3.25, 2.83, 0.34, 0.3, 0.27
Step 6: Now write the corresponding numbers.
Ascending order = 13/48, 30%, 0.34, 17/6, 13/4
Descending order = 13/4, 17/6, 0.34, 30%, 13/48
Summary
In this article, we have learned about the ordering of fractions and how to arrange various numbers from least to greatest or vice versa. By following the above-mentioned examples, and calculators you can easily arrange any number either in ascending or descending order.
