Introduction

Another way to represent an improper fraction is to write it as a mixed number.

Let's look at the improper fraction \dfrac{7}{5}, shown below.

We can separate this improper fraction into "wholes" and "fractions" like so:

We see that we have \color{red}1 whole and a fraction of \color{blue}\dfrac 2 5. Therefore, this picture represents the mixed number

{\color{red}{1}}\,{\color{blue}{\dfrac 2 5}}\,.

It's important to realize that \dfrac 7 5 and 1\,\dfrac 2 5 represent the same number!

FLAG
Example: Representing Mixed Numbers Using Area Models

What mixed number is shown in the picture below?

EXPLANATION

There are \color{red}2 shapes completely shaded:

So, there are \color{red}2 wholes.

Additionally, one shape is partially shaded:

This shape has \color{blue}3 parts, and \color{blue}2 parts are shaded. So, \color{blue}\dfrac{2}{3} of this shape is shaded.

Therefore, the mixed number is {\color{red}2}\, {\color{blue}\dfrac{2}{3}}.

FLAG
Practice: Representing Mixed Numbers Using Area Models

What mixed number is shown in the picture above?

a
 $3\, \dfrac 18$
b
 $3\, \dfrac 17$
c
 $2\, \dfrac 78$
d
 $2\, \dfrac 18$
e
 $3\, \dfrac 78$
Practice: Representing Mixed Numbers Using Area Models

What mixed number is shown in the picture above?

a
 $6\dfrac{4}{6}$
b
 $6\dfrac{4}{1}$
c
 $4\dfrac{2}{6}$
d
 $4\dfrac{1}{6}$
e
 $4\dfrac{2}{8}$
Example: Selecting an Area Model Representing a Mixed Number

Draw a picture that represents the mixed number 2\dfrac{3}{7}.

EXPLANATION

The mixed number {\color{red}2}\dfrac{\color{blue}3}{\color{blue}7} means we must have

  • \color{red}2 entirely shaded shapes, and

  • an additional shape that represents \color{blue}\dfrac37.

Therefore, we could represent 2\dfrac{3}{7} using the following picture:

FLAG
Practice: Selecting an Area Model Representing a Mixed Number

Which of the following pictures represents the mixed number $1\dfrac{1}{4}?$

a
b
c
d
e
Practice: Selecting an Area Model Representing a Mixed Number

Which of the following pictures represents the mixed number $2\dfrac{1}{6}?$

a
b
c
d
e
Number Line Models for Mixed Numbers

We can represent mixed numbers with number lines.

For example, let's write the number shown on the number line below as a mixed number.

First, notice that the line segment from 0 to 1 is split into \color{blue}3 equal parts.

We can land on our point by making \color{red}1 whole step plus \color{blue}2 part steps (out of a possible {\color{blue}{3}}).

Therefore, the mixed number is {\color{red}1}{\color{blue}\dfrac{2}{3}}.

FLAG
Example: Representing Mixed Numbers Using Number Lines

What mixed number is shown on the number line?

EXPLANATION

The line segment from 0 to 1 is split into \color{blue}6 equal parts. Each part represents \dfrac{1}{\color{blue}6} of a whole.

Starting from zero, we land on our point by making \color{red}2 whole steps plus \color{blue}1 part step:

Therefore, the mixed number is {\color{red}2}{\color{blue}\dfrac{1}{6}}.

FLAG
Practice: Representing Mixed Numbers Using Number Lines

What mixed number is shown on the number line?

a
 $2\dfrac{1}{3}$
b
 $\dfrac{1}{2}$
c
 $2\dfrac{1}{2}$
d
 $3\dfrac{1}{2}$
e
 $7\dfrac{1}{2}$
Practice: Representing Mixed Numbers Using Number Lines

What mixed number is shown on the number line?

a
 $2\dfrac 23$
b
 $2\dfrac 12$
c
 $3\dfrac 13$
d
 $2\dfrac 13$
e
 $3\dfrac 12$
Flag Content
Did you notice an error, or do you simply believe that something could be improved? Please explain below.
SUBMIT
CANCEL