In mathematics, the ordering fractions is a wide concept used to arrange the fractions, numbers, percentages, and whole numbers in ascending or descending order. These arrangements can be from least to greatest or greatest to least is very important in mathematics and statistics.
These terms are used to find the correct arrangement of numbers to solve various algebraic and central tendencies problems. In this post, we’ll discuss the methods and concepts of ordering fractions.
Table of Contents
What is ordering fractions?
The ordering fractions is a method to arrange the terms in ascending and descending orders to find the sequence of terms either from least to greatest and greatest to least. The ascending order is the arrangement of fractions, numbers, and terms from least to greatest.
While the descending order is the arrangement of terms, fractions, and numbers from greatest to least. The proper, improper, and mixed fractions, percentages, natural numbers, & integers can be arranged in ascending and descending orders.
As we know that the terms written in the form of u/v where u & v are integers and v is not equal to zero are said to be the fraction. U is said to be the numerator and v is said to be the denominator. The terms written with a “%” symbol are said to be the percentage terms.
The percentage terms can be written in the form of fractions by putting 100 in the denominator of each term, for example, 79% can be written as 79/100 in fractional form. The decimal terms are those terms that are written with a point among the digits.
The concept of ascending and descending orders can be understood by taking a real-life example such as the ascending order like climbing the stairs of a house or apartment while the term descending order is coming down from the upper step of the stair to the lower step.
Methods of arranging fractions
The ordering fractions has two ways to arrange the fractions either from least to greatest or greatest to least. These methods are:
- Making like fractions (making the same denominators)
- Fractions to decimal conversion
The arrangements of ordering fractions can also be done by using a least to greatest calculator. Let us study the above methods of ordering fractions briefly.
Making like fractions (making the same denominators)
In this method, find the least common multiple of the denominators of each given fraction and make the like fractions. Then arrange the fractions in ascending or descending orders. The arrangement of the fraction by using this method can be done by following the below steps.
- Take the given fractions
- Take the fraction’s denominators.
- Determine the LCM of taken denominators of fractions.
- After finding the least common multiples, make the denominator of each fraction that is equivalent to the calculated LCM.
- After making the same denominators, arrange the numerators from least to greatest or
greatest to least. - In the end, write the corresponding terms.
Follow the below example to understand the above method of ordering fractions more accurately.
Example
Find the ascending and descending orders of 18/2, 25/4, 19/10, 11/5, 25/6, 19/8, 2/11, 1/3 by using like fraction methods.
Solution
Step-I: First of all, take the given list of fractions.
18/2, 25/4, 19/10, 11/5, 25/6, 19/8, 2/11, 1/3
Step-II: Now to find the like fractions take the denominators of each fraction and find the least common multiple by using the list of multiples method.
Denominators of fractions = 2, 4, 10, 5, 6, 8, 11, 3
Least common multiple of 2, 4, 10, 5, 6, 8, 11, 3 = 1320
Step-III: Make the same denominators of each fraction equivalent to the LCM.
18/2 = 18 * 660 / 2 * 660 = 11880/1320
25/4 = 25 * 330 / 4 * 330 = 8250/1320
19/10 = 19 * 132 / 10 * 132 = 2508/1320
11/5 = 11 * 264 / 5 * 264 = 2904/1320
25/6 = 25 * 220 / 6 * 220 = 5500/1320
19/8 = 19 * 165 / 8 * 165 = 3135/1320
2/11 = 2 * 120 / 11 * 120 = 240/1320
1/3 = 1 * 440 / 3 * 440 = 440/1320
Step-IV: Arrange the like fractions from least to greatest and write their corresponding terms.
Ascending order = 240/1320, 440/1320, 2508/1320, 2904/1320, 3135/1320, 5500/1320, 8250/1320, 11880/1320
The equivalent terms are:
Least to greatest = 2/11, 1/3, 19/10, 11/5, 19/8, 25/6, 25/4, 18/2
Step-V: Similarly, Arrange the like fractions from least to greatest and write their corresponding
terms.
Descending order = 11880/1320, 8250/1320, 5500/1320, 3135/1320, 2904/1320, 2508/1320, 440/1320, 240/1320
The equivalent terms are:
Greatest to least = 18/2, 25/4, 25/6, 19/8, 11/5, 19/10, 1/3, 2/11
Faction to decimal conversion
The second method of ordering fractions is to convert the given fractions into decimals. The arrangement of a fraction by using this method can be done by following the below steps.
- Take the given fractions and percentages.
- Divide the numerator by the denominator to find the decimal result of the fractions.
- After finding the decimals arrange them either in ascending order or descending order.
- In the end, write the corresponding terms.
Follow the below example to understand the above method of ordering fractions more
accurately.
Example
Find the ascending and descending orders of 140/8, 56/4, 18/48, 79%, 94%, 6 * 1/8, 4 * 2/9 by using the fraction to decimal conversion method.
Solution
Step-I: Take the given fractions and percentages.
140/8, 56/4, 18/48, 79%, 94%, 6 * 1/8, 4 * 2/9
Step-II: First of all, convert the improper and proper fractions into decimals.
140/8 = 70/4 = 35/2 = 17.5
56/4 = 28/2 = 14/1 = 14
18/48 = 9/24 = 3/8 = 0.375
Step-III: Now convert the percentages into a fraction and find the decimals.
79% = 79/100 = 0.79
94% = 94/100 = 47/50 = 0.94
Step-IV: Deal with the mixed fractions and make them in form of fractions and find the decimal.
6 * 1/8 = 49/8 = 6.125
4 * 2/9 = 38/9 = 4.22
Step-V: Arrange the decimals according to the ascending order and write the corresponding
terms of each decimal value.
Ascending order = 0.375, 0.79, 0.94, 4.2, 6.125, 14, 17.5
The equivalent terms are:
Least to greatest = 18/48, 79%, 94%, 4 * 2/9, 6 * 1/8, 56/4, 140/8
Step -VI: Arrange the decimals according to the ascending order and write the corresponding
terms of each decimal value.
Descending order = 17.5, 14, 6.125, 4.2, 0.94, 0.79, 0.375
The equivalent terms are:
Greatest to least = 140/8, 56/4, 6 * 1/8, 4 * 2/9, 94%, 79%, 18/48
Conclusion
In this post, we’ve discussed all the concepts of ordering fractions along with examples. Now after reading the above post, you can easily solve the problems of ordering fractions easily. Once you grab the basics of ordering fractions, you’ll master it.