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Welcome to our Math lesson on Comparing Fractions with Different Numerators and Denominators, this is the third 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.
Comparing Fractions with Different Numerators and Denominators
If both numerators and denominators of two fractions are different, first we must transform them to have the same denominator or numerator (it is preferable to transform them to have the same denominator but sometimes it is more appropriate to have them written with the same numerator) and then make the comparison using the aforementioned rules. For example, if we want to compare
2/3 and
3/5, first we write both fractions with the same denominator (we find the LCM of 3 and 5, which is 15 through the known method explained in 1.5) and then, we use the equivalent fractions of the original ones which have the denominator 15 to make the comparison. We have
2/3 = (2 × 5)/(3 × 5) = 10/15
and
3/5 = (3 × 3)/(5 × 3) = 9/15
Now that we have the equivalent fractions of the original ones but with the same denominator, it is easy to compare them. Thus, we have
2/3 > 3/5 because 10/15 > 9/15
Sometimes it is more appropriate to convert both fractions with the same numerator, i.e. find the LCM of numerators, and then using the aforementioned comparison rules. For example, if we have to compare
8/13 and
12/19, it is better to find the LCM of 8 and 12 (which is 24) than that of 13 and 19 (which is 13 × 19 = 247). Thus, we have
8/13 = (8 × 3)/(13 × 3) = 24/39
and
12/19 = (12 × 2)/(19 × 2) = 24/38
Therefore, we have
12/19 > 8/13 because 24/38 > 24/39
Example 2
Compare the following pairs of fractions:
8/15 and 11/20
12/17 and 18/29
Solution 2
Here it is more appropriate to write both fractions with the same denominator. Since LCM (15 and 20) is 60, we obtain
8/15 = (8 × 4)/(15 × 4) = 33/60
and
11/20 = (11 × 3)/(20 × 3) = 33/60
Hence, we have
8/15 < 11/20 because 33/60 < 33/60
This time, it is better to write both fractions with the same numerator. Giving that LCM (12 and 18) is 36, we obtain
12/17 = (12 × 3)/(17 × 3) = 36/51
and
18/29 = (18 × 2)/(29 × 2) = 36/58
Hence,
12/17 > 18/29 because 36/51 > 36/58
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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