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Welcome to our Math lesson on Ordering Fractions, this is the sixth lesson of our suite of math lessons covering the topic of Comparing Fractions. Ordering Fractions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Ordering Fractions
Ordering fractions means writing a number of fractions from the smallest to the biggest (ascending order) or from the biggest to the smallest (descending order). This is done after changing all the fractions to the same denominator or numerator, as explained at the beginning of this tutorial.
Example 6
Write the following fractions in the ascending order.
3/7; 2/5; 5/11; 6/13; 10/23
3/5; 8/15; 11/20; 17/30; 7/12
Solution 6
In this case, it is more appropriate to change all fractions to have the same numerator. Since LCM (3, 2, 5, 6 and 10) is 30, we have
3/7 = (3 × 10)/(7 × 10) = 30/70
2/5 = (2 × 15)/(5 × 15) = 30/75
5/11 = (5 × 6)/(11 × 6) = 30/66
6/1 3= (6 × 5)/(13 × 5) = 30/65
10/23 = (10 × 3)/(23 × 3) = 30/69
From theory, we know that if two or more fractions have the same numerator, the smallest fraction is the one with the biggest denominator. Hence, when written in ascending order, the equivalent fractions of the original ones are:
30/75 < 30/70 < 30/69 < 30/66 < 30/65
which corresponds to the following ascending order of the original fractions:
2/5 < 3/7 < 10/23 < 5/11 < 6/13
This time is it better to have all fractions written at the same denominator. Since LCM (5, 15, 20, 30 and 12) is 60, we can write
3/5 = (3 × 12)/(5 × 12) = 36/60
8/15 = (8 × 4)/(15 × 4) = 33/60
11/20 = (11 × 3)/(20 × 3) = 33/60
17/30 = (17 × 2)/(30 × 2) = 34/60
7/12 = (7 × 5)/(12 × 5) = 35/60
Since in a list of fractions with the same denominator the smallest fraction is the one that has the smallest numerator, we can write
33/60 < 33/60 < 34/60 < 35/60 < 36/60
which correspond to the following ascending order of the original fractions:
8/15 < 11/20 < 17/30 < 7/12 < 3/5
More Comparing Fractions. Ordering Fractions Lessons and Learning Resources
Fractions Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 3.3 | Comparing Fractions. Ordering Fractions | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 3.3.1 | Comparing Fractions with the Same Denominator | | |
| 3.3.2 | Comparing Fractions with the Same Numerator | | |
| 3.3.3 | Comparing Fractions with Different Numerators and Denominators | | |
| 3.3.4 | Comparing Improper Fractions and Mixed Numbers | | |
| 3.3.5 | Adding or Subtracting the Numerator or Denominator of a Fraction by the Same Number | | |
| 3.3.6 | Ordering Fractions | | |
| 3.3.7 | Ordering Fractions in the Number Line | | |
| 3.3.8 | Applications of Fractions Comparison in Practice | | |
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