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Welcome to our Math lesson on How to Avoid the Confusion between Improper Fractions and Integers Expressed as Fractions, this is the fifth 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 Avoid the Confusion between Improper Fractions and Integers Expressed as Fractions
Sometimes, for specific purposes (for example when adding or subtracting fractions) we can have integers expressed as fractions. These integers may seem as improper fractions but when we divide the fraction's numerator by its denominator, we obtain a quotient without any remainder. In other words, when numerator of a fraction is a multiple of its denominator, we are dealing with an integer, not an improper fraction. For example, 32/8 is not an improper fraction but an integer instead. This is because 32 ÷ 8 = 4 (0).
Example 4
Identify the integers from the list of fractions given below.
68/17 81/18 58/16 65/13 96/6 102/34
Solution 4
We have
68/17 = 68 ÷ 17 = 4 (0). Since there is no remainder in the corresponding division, this fraction represents an integer. We have
81/18 = 81 ÷ 18 = 4 (9). Since the remainder in the corresponding division is 9, this fraction does not represent an integer. We have
58/16 = 58 ÷ 16 = 3 (10). Since the remainder in the corresponding division is 10, this fraction does not represent an integer. We have
65/13 = 65 ÷ 13 = 5 (0). Since there is no remainder in the corresponding division, this fraction represents an integer. We have
96/6 = 96 ÷ 6 = 16 (0). Since there is no remainder in the corresponding division, this fraction represents an integer. We have
102/34 = 102 ÷ 34 = 3 (0). Since there is no remainder in the corresponding division, this fraction represents an integer.
More Proper and Improper Fractions. Mixed Numbers Lessons and Learning Resources
Fractions Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 3.2 | Proper and Improper Fractions. Mixed Numbers | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 3.2.1 | Proper Fractions | | |
| 3.2.2 | Improper Fractions | | |
| 3.2.3 | Mixed Numbers | | |
| 3.2.4 | How to Convert an Improper Fraction into Mixed Number | | |
| 3.2.5 | How to Avoid the Confusion between Improper Fractions and Integers Expressed as Fractions | | |
| 3.2.6 | How to Convert a Mixed Number into Improper Fraction | | |
| 3.2.7 | Applications of Improper Fractions and Mixed Numbers in Practice | | |
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