Part 4: Division

# 4.3: Improper fractions and mixed numbers

Notes

In the following, “A/B” represents the fraction “A over B.” For example, “4/3” refers to the fraction “4 over 3” or “four-thirds.”

##### Express an improper fraction as a mixed number

An *improper fraction* is a fraction that is greater than or equal to 1, i.e., its numerator is greater than or equal to its denominator. We can express an improper fraction as a *mixed number* (or *mixed fraction*) by thinking of the fraction in terms of dividing integers. For example,

- Express 13/5 (thirteen-fifths) as a mixed number.
- Think of 13/5 as 13 divided by 5.
- How many times does 5 go into 13?
- 2 times with remainder 3 (since 2 x 5 = 10 and 13 – 10 = 3).

- Therefore, 13/5 = 2 + 3/5 = 2 3/5 (two and three-fifths).

##### Express a mixed number as an improper fraction

We can express a mixed number as an improper fraction by expressing the whole number part of the mixed number as a fraction and adding it to the fraction part using 2.5: Adding and subtracting fractions. For example,

- Express 2 3/5 (two and three-fifths) as an improper fraction.
- Think of 2 3/5 as 2/1 + 3/5.
- A common denominator for 1 and 5 is 5.
- So, 2/1 + 3/5 = (2×5)/(1×5) + 3/5 = 10/5 + 3/5 = 13/5
- Therefore, 2 3/5 = 13/5 (thirteen-fifths).

The video below works through some examples of expressing an improper fraction as a mixed number and vice versa.

Video Tips

Practice Exercises

Do the following exercises to practice expressing an improper fraction as a mixed number and vice versa.