Order of fractions is used to arrange the set of fractions either in increasing or decreasing order. It is helpful to realize the fact that in fractions, we can’t use ordering rules like natural numbers.
For example, 1/3 is greater than 1/5 but the natural number 5 is greater than 3. In this post, we will learn how to order fractions with a lot of examples.
What is the order of fractions?
First of all, you must know about the fractions to arrange the fractions. Fractions are those terms that are written in the form of numerator and denominator having “/” sign. The fractions are of various types, some fractions have the same denominator while some have different. Similarly, some fractions have smaller numerators while some have greater numerators.
Order of fraction means to write the fractions from least to greatest or greatest to least. There are two ways to order the fractions.
- Ascending order
- Descending order
The fractions that are arranged from least to greatest are known as ascending order. On the other hand, if the fractions are arranged from greatest to least are known as descending order. There are two methods for the arrangement of the fractions.
- Make like fractions
- Make decimals
If the group of fractions is given, you can arrange that group either by making the denominator the same, if they are different or by dividing the fractions to get the decimal result. By using these two methods, you can easily arrange the fractions either in ascending order or descending order.
How to arrange fractions?
To understand how to arrange fractions let us take some examples.
Example 1: For arranging the fractions from least to greatest
Arrange the given fractions from least to greatest, 2/3, 3/9, 3/6, 7/2, 3/12.
Solution
Step 1: Write the given fractions.
2/3, 3/9, 3/6, 7/2, 3/12
Step 2: Now take the denominators of the given fractions.
Denominators = 3, 6, 9, 2, 12
Step 3: Now take the LCM of the denominators.
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 …
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …
Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36 …
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, …
Similar multiples = 36, 72, …
LCM of 3, 6, 9, 2, and 12= 36
Step 4: Now make the denominators 36 for making like fractions.
2/3 = 2 x 12 / 3 x 12 = 24/36
3/9 = 3 x 4 / 9 x 4 = 12/36
3/6 = 3 x 6 / 6 x 6 = 18/36
7/2 = 7 x 18 / 2 x 18 = 126/36
3/12 = 3 x 3 / 12 x 3 = 9/36
Step 5: Now arrange the numerators from least to greatest.
9/36, 12/36, 18/36, 24/36, 126/36
Step 6: Now take the corresponding fractions.
3/12, 3/9, 3/6, 2/3, 7/2
Hence, we arranged the given fractions from least to greatest.
Example 2
Arrange the given fractions from least to greatest, 1/2, 2/9, 5/6, 9/2, 2/12.
Solution
Step 1: Write the given fractions.
1/2, 2/9, 5/6, 9/2, 2/12
Step 2: Now divide the fractions to find the decimal result.
1/2 = 0.5
2/9 = 0.222
5/6 = 0.833
9/2 = 4.5
2/12 = 1/6 = 0.167
Step 3: Now arrange the decimals from least to greatest.
0.167, 0.222, 0.5, 0.833, 4.5
Step 4: Now take the corresponding fractions.
2/12, 2/9, 1/2, 5/6, 9/2
Hence, we arranged the given fractions from least to greatest. You can also use the ordering fractions calculator to avoid such calculations and get the result in a short time.
Example 3: For arranging the fractions from greatest to least
Arrange the given fractions from greatest to least, 7/6, 11/27, 13/18, 7/9, 3/15.
Solution
Step 1: Write the given fractions.
7/6, 11/27, 13/18, 7/9, 3/15
Step 2: Now take the denominators of the given fractions.
Denominators = 6, 27, 18, 9, 15
Step 3: Now take the LCM of the denominators.
Prime factors of 6 = 2 x 3
Prime factors of 27 = 3 x 3 x 3
Prime factors of 18 = 2 x 3 x 3
Prime factors of 9 = 3 x 3
Prime factors of 15 = 3 x 5
Now take the similar and non-similar factors.
Common factors of 6, 27, 18, 9, and 15 = 2 x 3 x 3 = 18
Non-common factors of 6, 27, 18, 9, and 15 = 3 x 5 = 15
Now evaluate the LCM by multiplying the similar and non-similar factors.
LCM = 18 x 15
LCM = 270
Step 4: Now make the denominators 270 for making like fractions.
7/6 = 7 x 45 / 6 x 45 = 315/270
11/27 = 11 x 10 / 27 x 10 = 110/270
13/18 = 13 x 15 / 18 x 15 = 195/270
7/9 = 7 x 30 / 9 x 30 = 210/270
3/15 = 3 x 18 / 15 x 18 = 54/270
Step 5: Now arrange the numerators from greatest to least.
315/270, 210/270, 195/270, 110/270, 54/270
Step 6: Now take the corresponding fractions.
7/6, 7/9, 13/18, 11/27, 3/15
Hence, we arranged the given fractions from greatest to least.
Example 4
Arrange the given fractions from greatest to least, 7/9, 5/11, 15/7, 19/3, 3/13.
Solution
Step 1: Write the given fractions.
7/9, 5/11, 15/7, 19/3, 3/13
Step 2: Now divide the fractions to find the decimal result.
7/9 = 0.778
5/11 = 0.455
15/7 = 2.143
19/3 = 6.333
3/13 = 0.231
Step 3: Now arrange the decimals from greatest to least.
6.333, 2.143, 0.778, 0.455, 0.231
Step 4: Now take the corresponding fractions.
19/3, 15/7, 7/9, 5/11, 3/13
Hence, we arranged the given fractions from greatest to least.
Summary
The ordering of fractions is not a tough topic. Once you grab all the concepts of the order of fractions, you can easily arrange fractions in any order. Start practicing now by following the above examples and you will arrange fractions like a pro.
