Today we will learn how to locate mixed numbers on the number line. This is helpful to visualize mixed numbers and understand their values.
Content:
Don’t forget that a mixed number is a number containing a whole number and a proper fraction (a fraction whose numerator is less than its denominator).
1) Locate 31/2 on the number line
The mixed number 31/2 contains 3 wholes and the proper fraction 1/2, so first, we need to locate 3 on the number line.
Then, since the denominator is 2, we divide the portion of the number line between 3 and its successor 4 into 2 equal parts (halves).
Finally, since the numerator is 1, starting from 3, we move 1 part to the right.
After locating the position of the mixed number on the number line, do not forget to draw a bold dot.
Steps for locating a mixed number on the number line
To locate a mixed number on the number line, follow these steps:
- Locate the whole number on the number line.
- Then, divide the portion of the number line between the whole number from the previous step and its successor into as many equal parts as the denominator indicates. For example, if the denominator is 2, divide the portion of the number line into 2 equal parts.
- Starting from the whole number of the first step, jump to the right as many parts as the numerator indicates. For instance, if the numerator is 1, jump 1 part to the right. At that location, draw a bold dot.
One more example will clear these steps. Don’t forget that this procedure works perfectly for positive mixed numbers, however if you are working with negative mixed numbers, just jump to the left in the last step.
2) Locate 23/4 on the number line
This mixed number contains 2 wholes and the proper fraction 3/4. So first, we need to locate 2 on the number line.
Next, given that the denominator is 4, we divide the segment line between 2 and its successor 3 into 4 equal parts.
At last, given that the numerator is 3, starting from 2, we jump 3 parts to the right. Recall drawing a bold dot at that location.
Challenge
Find the mixed number represented on the number line.
Answer: 13/5.
Videos
In the next video, we will see more examples of how to plot a mixed number on a number line.
And here you will find more examples.
References
For this lesson, we have used these books:
- Tussy, K., Gustafson, D. y Koenig, D. (2013). Prealgebra (4th ed.; pp. 363-364). Cengage Learning.
- OpenStax (2020). Prealgebra 2e (pp. 288-291). Rice University.