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In addition to the revision notes for Comparing Fractions. Ordering Fractions on this page, you can also access the following Fractions learning resources for Comparing Fractions. Ordering Fractions
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 3.3 | Comparing Fractions. Ordering Fractions |
In these revision notes for Comparing Fractions. Ordering Fractions, we cover the following key points:
If two or more fractions have the same denominator, the fraction with the biggest numerator, is the greatest. The condition for comparison of fractions is that they must represent the same type of item.
On the other hand, if two or more fractions have the same numerator, the fraction with the smallest denominator, is the greatest.
If both numerators and denominators of two fractions are different, first we must change 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 according to the rules above. For this, we need to find the LCM of numerators or denominators involved in the operations.
We can convert improper fractions into mixed numbers and eventually compare the whole parts without concerning ourselves with the fractional part of both mixed numbers. This avoids calculation of the LCM of numerators or denominators. Even in the case when the whole part is equal in two improper fractions, it is more appropriate to have them written as mixed numbers because we can compare the two corresponding proper fractions instead of the entire fractions.
When the same number is added to both numerator and denominator of a proper fraction, its value increases, when this occurs to an improper fraction, its value decreases. In symbols we have
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 either by changing all fractions to have the same denominator or numerator and then using the known methods of comparison or putting them in a number line to check which fraction is more on the left (it is the smallest) as fractions in the number line increase from left to right.
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