6.1.8 Mixed Numbers

In most of the examples considered so far, you have been using fractions to describe part of a whole. The result is a positive number whose value is less than 1. Fractions in which the numerator (top number) is less than the denominator (bottom number), such as four divided by nine and one divided by six, are known as proper fractions.

A mixed number consists of a whole number and a proper fraction. Consider .

Mixed numbers can be represented on a number line by dividing each unit interval into parts. For example, to mark on the number line, the interval from 2 to 3 can be divided into thirds.

Then, can be marked at the point one third of the way along the interval from 2 to 3.

Activity symbol Activity: Fractions on the Number Line

Draw a number line from 2 to 5 in your math notebook. Plot the following fractions on the number line:

, , , and negative.

Hint symbol


Which two whole numbers does lie between? Into how many parts do you want to break the distance between these whole numbers if you have fourths?

Solution symbol


You can determine the position of a number by dividing the length between the two appropriate whole numbers on the scale into 2, 4, 8 or 5 equal parts (or pieces) as appropriate, and then plotting the fractions on it as shown below.

6.1.7 True or False?

6.1.9 Improper Fractions