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Math Lesson 3.2.6 - How to Convert a Mixed Number into Improper Fraction

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Welcome to our Math lesson on How to Convert a Mixed Number into Improper Fraction, this is the sixth lesson of our suite of math lessons covering the topic of Proper and Improper Fractions. Mixed Numbers, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

How to Convert a Mixed Number into Improper Fraction

We can convert a mixed number into an improper fraction by multiplying the whole part of the mixed number by the denominator and then adding the numerator. This only gives the numerator of the improper fraction as the denominator does not change. Math Tutorials: Proper and Improper Fractions. Mixed Numbers Example

For example,

5 2/3 = (5 × 3 + 2)/3 = (15 + 2)/3 = 17/3

Example 5

Convert the following mixed numbers into fractions.

2 4/7
7 1/3
11 5/9

Solution 5

We have

2 4/7 = (2 × 7 + 4)/7 = (14 + 4)/7 = 18/7

Likewise,

7 1/3 = (7 × 3 + 1)/3 = (21 + 1)/3 = 22/3

Also,

11 5/9 = (11 × 9 + 5)/9 = (99 + 5)/9 = 104/9

In this way, we can say that improper fractions and mixed numbers are two different methods of representation of the same amount.

More Proper and Improper Fractions. Mixed Numbers Lessons and Learning Resources

Fractions Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
3.2Proper and Improper Fractions. Mixed Numbers
Lesson IDMath Lesson TitleLessonVideo
Lesson
3.2.1Proper Fractions
3.2.2Improper Fractions
3.2.3Mixed Numbers
3.2.4How to Convert an Improper Fraction into Mixed Number
3.2.5How to Avoid the Confusion between Improper Fractions and Integers Expressed as Fractions
3.2.6How to Convert a Mixed Number into Improper Fraction
3.2.7Applications of Improper Fractions and Mixed Numbers in Practice

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  7. Continuing learning fractions - read our next math tutorial: Comparing Fractions. Ordering Fractions

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