Mixed numbers or mixed fractions

A mixed number is a number containing a whole number and a proper fraction. For example, 3¹⁄₂, 2¹⁄₄, 5⁶⁄₇  are mixed numbers.

The fraction of a mixed number is always a proper fraction (a fraction where the numerator is less than the denominator). Mixed numbers are also called mixed fractions or mixed numerals.

Content:

• Definition
• Example 1
• Example 2
• Videos
• References

1) Draw a figure to model the mixed number 2³⁄₄:

To model a mixed number, first we are going the model the whole number and the proper fraction. In the diagram below, each circle represents one whole. To represent 2 wholes, we are going to draw 2 whole circles and shade them completely. To represent ³⁄₄ we are going to draw another circle, then, and shade 3 out of 4 equal parts.  

Recall that it is not necessary to use circles, you can also use squares, rectangles or other geometric figures.

2) Use a model to rewrite the mixed number 4²⁄₃ as an improper fraction:

First, we are going to represent 4 wholes drawing 4 whole rectangles and shading them completely. After that, we are going to draw another rectangle, and shade 2 out of 3 equal parts.

Next, we are going to rewrite the mixed number 4²⁄₃ as an improper fraction using the model. Given that the denominator of the improper fraction is 3, we are going to divide each rectangle that represents the 4 wholes into 3 equal parts. Each part represents one third of a rectangle or one thirds of a whole. Finally, we just need to count how many thirds we have in the diagram. In total we have 14 thirds.

Note from the diagram above that the mixed number 4²⁄₃ and the improper fraction ¹⁴⁄₃ both represent the shaded part of the rectangles, therefore, 4²⁄₃ = ¹⁴⁄₃.

There is a faster method to obtain the same answer with far less work. To change the mixed number 4²⁄₃ to an improper fraction, we simply multiply the denominator (3) by the whole number (4) and then, add the numerator (2). Next, we add that sum as the numerator of the improper fraction over the original denominator (3).

Videos

In the following videos, we will review examples about mixed numbers.

And here you will find more examples:

References

For this lesson, we have used these books:

• Aufmann, R. and Lockwood, J. (2014). Basic College Mathematics (10th ed, pp. 70-71). Cengage Learning.
• Tussy, K., Gustafson, D. and Koenig, D. (2013). Prealgebra (4th ed.; pp. 360-362). Cengage Learning.
• Martin-Gay, E. (2020). Basic college mathematics with early integers (4th ed; pp. 218, 221). Pearson.
• McGraw-Hill Education (2018). Math grade 4 (2th ed.; p. 72).