In algebra, the least to greatest is one of two kinds of ordering fractions. The other type is greatest to least. The ordering fraction is usually used to arrange the whole numbers, decimals, percentages, and fractions either in ascending or descending orders.
The ordering of fractions plays a vital role in algebra and central tendencies to solve various kinds of problems. In this article, we will go through the basics of ordering fractions along with solved examples.
What are the ordering fractions?
The ordering fractions is a general rule used to arrange the fractions, numbers, and percentages in ascending or descending orders. When the sequence starts in which the smallest term is in the first place and going up is said to be the ascending order.
It is also known as least to greatest because the terms are written from least and going to the greatest one. When the sequence starts in which the greater term is in the first place and going toward the smallest one is known as descending order.
It is also called greatest to least because the terms are written from greatest one to the least once. All kinds of fractions, numbers, and percentages can be arranged in ascending and descending orders.
Methods of ordering fractions
There are two well-known methods of ordering fractions in ascending and descending orders. Here are these methods:
- Making the same denominators (Making like fractions)
- Fractions to decimal conversion
Below is a brief introduction to methods of ordering fractions along with examples.
1. Making the same denominators (Making like fractions)
To arrange the fractions in ascending and descending orders, making like fractions is frequently used. According to this method, you have to find the LCM of the denominators of the fractions and make them like fractions. After that arrange them.
Follow the below steps to understand making like fractions to arrange the ordering fractions.
- First of all, take a list of fractions.
- After that, take the denominators of all the fractions.
- Then find the least common multiple of the denominators by using a list of multiples, prime fractions, or division method.
- Make all the denominators equal to the LCM of denominators.
- Then arrange the terms in ascending or descending orders according to the numerator of the fractions.
- In the last step, write the corresponding fractions.
Here is an example of this type of ordering fraction.
Example
Arrange the given fractions in ascending and descending orders by using the making like fraction method.
13/5, 5/9, 9/2, 15/6, 21/7, 22/8, 1/10
Solution
Step I: First of all, take a list of fractions.
13/5, 5/9, 9/2, 15/6, 21/7, 22/8, 1/10
Step II: Now take the denominators of all the fractions and find the least common multiple of the denominators.
Fraction’s denominators = 5, 9, 2, 6, 7, 8, 10
Now write the multiplication tables of the above numbers.
5 times table = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, …
9 times table = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, …
2 times table = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, …
6 times table = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, …
7 times table = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, …
8 times table = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, …
10 times table = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, …
LCM of 5, 9, 2, 6, 7, 8, 10 = 2520
Step III: Make all the denominators equal to the LCM of denominators.
13/5 = 13 * 504 / 5 * 504 = 6552/2520
5/9 = 5 * 280 / 9 * 280 = 1400/2520
9/2 = 9 * 1260 / 2 * 1260 = 11340/2520
15/6 = 15 * 420 / 6 * 420 = 6300/2520
21/7 = 21 * 360 / 7 * 360 = 7560/2520
22/8 = 22 * 315 / 8 * 315 = 6930/2520
1/10 = 1 * 252 / 10 * 252 = 252/2520
Step IV: Arrange the like fractions in ascending order and write their corresponding terms.
Ascending order = 252/2520, 1400/2520, 6300/2520, 6552/2520, 6930/2520, 7560/2520, 11340/2520
Their corresponding terms are:
Ascending order = 1/10, 5/9,15/6, 13/5, 22/8, 21/7, 9/2
Step V: Similarly, Arrange the like fractions in descending order and write their corresponding terms.
Descending order = 11340/2520, 7560/2520, 6930/2520, 6552/2520, 6300/2520, 1400/2520, 252/2520
Their corresponding terms are:
Descending order = 9/2, 21/7, 22/8, 13/5, 15/6, 5/9, 1/10
The arrangements of ordering fractions can also be done by using a least to greatest calculator.
Faction to decimal conversion
To find the order of fractions there is another method known as converting fractions into decimals. According to this method convert all the terms into decimals and arrange them.
Follow the below steps to understand converting fractions into decimals to arrange the ordering fractions.
- Take a list of fractions and percentages.
- Find the quotient of each fraction to convert the fraction into decimals.
- Then arrange the terms in ascending or descending orders according to the decimals of the fractions.
- In the last step, write the corresponding fractions.
Here is an example of this type of ordering fraction.
Example
Arrange the given terms in ascending and descending orders by using converting fraction in the decimal’s method.
140/8, 56/4, 18/48, 79%, 94%, 6 * 1/8, 4 * 2/9
Solution
Step I: Take the list of fractions and percentages.
14/8, 56/7, 180/50, 69%, 84%, 6 * 2/8, 5 * 2/10
Step II: First of all, convert the improper and proper fractions into decimals.
14/8 = 7/4 = 3.5/2 = 1.75
56/7 = 8/1 = 8
180/50 = 18/5 = 3.6
Step III: Now convert the percentages into a fraction and find the decimals.
69% = 69/100 = 0.69
84% = 84/100 = 42/50 = 0.84
Step IV: Deal with the mixed fractions and make them in form of fractions and find the decimal.
6 * 2/8 = 50/8 = 6.25
5 * 2/10 = 52/10= 5.2
Step V: Arrange the decimals from least to greatest and write the corresponding terms of each decimal value.
Ascending order = 0.69, 0.84, 1.75, 3.6, 5.2, 6.25, 8
The corresponding terms are:
Ascending order = 69%, 84%, 14/8, 180/50, 5 * 2/10, 6 * 2/8, 56/7
Step VI: Arrange the decimals from greatest to least and write the corresponding terms of each decimal value.
Descending order = 8, 6.25, 5.2, 3.6, 1.75, 0.84, 0.69
The corresponding terms are:
Descending order = 56/7, 6 * 2/8, 5 * 2/10, 180/50, 14/8, 84%, 69%
Summary
In this article, we have covered all the basics of ordering fractions along with methods and examples. Now you can grab all the basics of ordering fractions just by learning the above post.