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Math Lesson 3.3.4 - Comparing Improper Fractions and Mixed Numbers

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Welcome to our Math lesson on Comparing Improper Fractions and Mixed Numbers, this is the fourth 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 Improper Fractions and Mixed Numbers

So far, we have considered only proper fractions in all our examples. However, we may use the same approach when comparing improper fractions as well. However, this time we have an extra "weapon" available. We can convert improper fractions into mixed numbers and eventually compare only the whole parts without concerning ourselves with the fractional part of both mixed numbers. This saves us precious time in calculating the LCM of numerators or denominators. For example, if we want to compare 47/13 and 69/17, we write
47/13 = 47 ÷ 13 = 3 (8), so 47/13 = 3 8/13
and
69/17 = 69 ÷ 17 = 4 (1), so 69/17 = 4 1/17
Hence, considering only the whole part of the corresponding mixed numbers, we obtain

47/13 < 69/17 because 3<4

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. Let's consider an example to clarify this point.

Example 3

Which of the numbers below is the biggest?
24/11 22/7 17/9

Solution 3

First, we write all fractions as mixed numbers. We have
24/11 = 24 ÷ 11 = (22 + 2) ÷ 11 = 2 2/11
and
17/9 = 17 ÷ 9 = (9 + 8) ÷ 9 = 1 8/9
From here, we can immediately exclude the third fraction (17/9), as it is the smallest number from the list because the corresponding whole part is 1, while in the other two numbers the whole part is 2. Hence, comparing only the fractional part of the first two numbers, we obtain 2/11 and 2/7, where obviously the number with the fractional part 2/7 is the greatest. Hence, we can write
2 2/11 > 24/11 > 17/9

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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