Last modified on August 22nd, 2024

chapter outline

 

Fractions on a Number Line

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 13, the numerator is 1, and the denominator is 3.

As we know that 0 < 13 < 1, to put 13 on a number line, we divide the region from 0 to 1 into 3 equal parts as the denominator is 3. Then, we move towards the right, starting from 0 based on the value of the numerator (here, 1). So we mark the 1st part starting from 0 as 13.

Fractions on a Number Line 0 1

Here, 13 is a unit fraction as it has 1 as its numerator.

As a number line represents values in ascending order, the values of the fractions also increase from left to right, like  13  <  23

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.

Number Line Positive and Negative Fractions

The above figure divides the region between each pair of successive integers into two equal parts. The positive fractions 12, 32  are found to the right of 0, while the negative fractions 12, 32 lie to the left of 0.

Representing Fractions on a Number Line

We can represent different types of fractions on a number line.

Proper Fractions

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 56 on a number line, we mark the points (-1) and 0 on a number line.

Number Line Negative Proper Fraction Step 1

Then we divide the region from (-1) to 0 into 6 equal parts as the denominator is 6. Each part represents 16.

Number Line Negative Proper Fraction Step 2

Next, we move from right  to left  starting from 0 up to the 5th part as the numerator is 5 and mark it as 56

Number Line Negative Proper Fraction Step 3

Equivalent Fractions

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 13, 26, 39 on a number line:

To plot 13, we divide the region from 0 to 1 into 3 equal parts and mark the first part as 13

To plot26, we divide the region from 0 to 1 into 6 equal parts and mark the second part as 26

Similarly to plot 39 , we divide the region from 0 to 1 into 9 equal parts and mark the third part as 39

Equivalent Fractions on a Number Line

Mixed Fractions

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 425 on the number line.

We get the fraction 425 by adding its integer part 4 and the proper fraction part 25. To represent 425  on a number line, we first mark 4 and 5 on the number line as the integer part is 4 and 425 lies between 4 and 5.

Number Line Mixed Fraction Step 1

Next, we divide the above line segment into 5 equal parts, each representing 15 and go to the proper fractional part (here25) starting from 4.

Number Line Mixed Fraction Step 2

Thus we find the point representing 425 on the number line.

Improper Fractions

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 32 on a number line, we first convert it into a mixed fraction

32 = 112

Then, we mark 1 and 2 on the number line as the integer part is 1. As we know, 32 lies between 1 and 2; we divide the region from 1 to 2 into two equal parts, each representing 12 and move towards the proper fraction, here 12.

Fraction on a Number Line

Thus we find 32 on a number line.

Solved Examples

Represent the fraction 847  on the number line.

Solution:

To represent 847 on the number line, we follow the given steps:
In the fraction 847, the integer part is (-8) and the proper fraction part is 47. As 847 lies  between the integers (-8) and (-9), we divide the region from (-8) to (-9) in 7 equal parts and mark the 4th part starting from (-8).
Thus we get  847 on the number line.

Locate 94  on a number line.

Solution:

We first convert the improper fraction 94 into a mixed fraction.
Again, 94 = 214
Since 214 lies between (-2) and (-3). Next we divide the region from (-2) to (-3) into 4 equal parts each representing (14) and go to the 1st part starting from (-2) to get the answer.
Thus we find 94 on the number line.
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.

Fraction Number Line Chart 0 to 1

Last modified on August 22nd, 2024

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