Table of Contents
Graphing fractions on a number line helps us represent and compare fractions, like plotting whole numbers and integers. Fractions represent a part of a whole.
For representing a fraction on a number line, its two immediate whole numbers are marked at both ends. The total distance is divided into a total number of equal parts according to the value of the denominator. The numerator represents its distance from 0.
For example, in the fraction
As we know that 0 <
Here,
As a number line represents values in ascending order, the values of the fractions also increase from left to right, like
As we know, while representing fractions on a number line, it appears between two integers. Thus, positive fractions lie at the right of 0 and between two positive integers, while the negative ones lie at the left of 0 and between two negative integers on a number line.
The above figure divides the region between each pair of successive integers into two equal parts. The positive fractions
We can represent different types of fractions on a number line.
We can plot positive and negative proper fractions easily on a number line. As a proper fraction has its numerator always less than the denominator (comparing only the numeric values of the numerator and the denominator), a positive proper fraction always lies between 0 and 1 on a number line. Similarly, a negative proper fraction lies between (-1) and 0.
In the first diagram, we have shown plotting a positive proper fraction.
Similarly, we can represent a negative proper fraction on a number line by marking the points (-1) and 0 and dividing the region into equal parts based on the denominator. Then we move from right to left, starting from 0 according to the numerator.
For example, to show
Then we divide the region from (-1) to 0 into 6 equal parts as the denominator is 6. Each part represents
Next, we move from right to left starting from 0 up to the 5th part as the numerator is 5 and mark it as
Equivalent fractions are located at the same point on a number line because they represent the same value when it is reduced to its simplest form despite having different denominators and numerators.
Let us represent the equivalent fractions
To plot
To plot
Similarly to plot
To represent a mixed fraction on a number line, we first identify its integer and proper fraction parts separately. Next, we mark those two integers on the number line between which the mixed fraction lies and move the number of steps right or left according to the proper fraction part.
Let us represent the mixed fraction
We get the fraction
Next, we divide the above line segment into 5 equal parts, each representing
Thus we find the point representing
Representing improper fractions (positive and negative) on a number line is similar to graphing proper fractions. Positive improper fractions are always greater than 1 and lie between 1 and a positive integer. Similarly, negative improper fractions being less than (-1), lie between (-1) and a negative integer.
We can represent improper fractions on a number line by converting them into a mixed fraction and following the same procedure as above.
For example, to plot
Then, we mark 1 and 2 on the number line as the integer part is 1. As we know,
Thus we find
Represent the fraction
To represent
In the fraction
Thus we get
Locate
We first convert the improper fraction
Again,
Since
Thus we find
We have provided a printable fraction number line chart from 0 to 1 for your use.
We have provided a printable fraction number line chart from 0 to 1 for your use.
Last modified on August 22nd, 2024