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Math Lesson 3.3.2 - Comparing Fractions with the Same Numerator

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Welcome to our Math lesson on Comparing Fractions with the Same Numerator, this is the second 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 the Same Numerator

When two fractions have the same numerator, this means we are considering the same number of parts of a whole but this doesn't mean we have the same amount from the whole because the denominator is different. This means we have used different methods of division for the whole. In these situations, the greatest fraction is the one with the smallest denominator. This is because the bigger the denominator the tinier the partitions are. Hence, when we consider the same number of partitions in two fractions with different denominators, the fraction with the least number of partitions (with the smaller denominator therefore) represents a larger part from the whole. For example,
3/4 > 3/5
because 4 < 5. In simpler words, the fraction 3/4 is the greatest as we have taken 3 parts of the whole out of 4, while in the fraction 3/5 we have taken 3 parts of the whole out of 5. Look at the figure below. Math Tutorials: Comparing Fractions. Ordering Fractions Example

Example 1

Which fraction is the greatest?
6/9 or 8/9
5/7 or 5/11

Solution 1

We have two fractions with the same denominator, 9. Therefore, the greatest one is the fraction with the greatest numerator (the second one). We can write
8/9 > 6/9
We have two fractions with the same numerator, 5. Therefore, the greatest one is the fraction with the smallest denominator (the first one). We can write
5/7 > 5/11
This is obvious as the first fraction represents more than half of the whole (5 parts out of 7), while the second fraction represents less than half of the whole (5 parts out of 11).

More Comparing Fractions. Ordering Fractions Lessons and Learning Resources

Fractions Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
3.3Comparing Fractions. Ordering Fractions
Lesson IDMath Lesson TitleLessonVideo
Lesson
3.3.1Comparing Fractions with the Same Denominator
3.3.2Comparing Fractions with the Same Numerator
3.3.3Comparing Fractions with Different Numerators and Denominators
3.3.4Comparing Improper Fractions and Mixed Numbers
3.3.5Adding or Subtracting the Numerator or Denominator of a Fraction by the Same Number
3.3.6Ordering Fractions
3.3.7Ordering Fractions in the Number Line
3.3.8Applications of Fractions Comparison in Practice

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