Fractions on Number Line : Representation , Examples and Practice problems

Fractions on Number Line: To draw fractions on the number line we split the number line according to the denominator of the given fraction with each part of the same size. Then, start from the start point and count the numbers equal to the number in the numerator. After counting mark, the point that represents the required fraction on a number line. ,

What are Fractions?

Fractions are expressions used to represent the parts of whole numbers. It has two parts, numerator and denominator. It is written as a/b where a is called the numerator and b is called the denominator. It can be also defined as the number of parts taken to the total number of parts.

How to Plot Fractions on Number Line

To represent a fraction on a number line we follow the below steps.

• First, draw a number line.
• Then, identify the fraction type i.e., proper, improper, or mixed.
• If the fraction is proper fraction draw number line between 0 and 1 and divide it into equal parts w.r.t denominator until it becomes 1.
• If the fraction is mixed fraction, then start plotting the number line from the quotient value of mixed fraction and divide further according to the remainder part of mixed fraction.
• If the fraction is improper fraction, first convert it into mixed fraction and then represent it in a number line.
• Start from left and count according to the numerator.
• Mark the point to represent the desired fraction.

Absolute Value and Number Line

The number line represents the integers where, the positive numbers are in right of zero and the negative numbers are in the right of zero. The distance between the position of given number and zero is referred to as the absolute value. The absolute value can be represented by |number|. The absolute value is always positive or can be zero.

Comparing Fractions on Number Line

Comparing fractions on number line is easy as the number line represents the fractions in ascending order. So, if we have to compare two fractions, we first plot the fractions on different number lines and then, check which fraction is on the left. The fraction on the left is smaller and the fraction on the left is larger.

Representation of Fractions on Number Line

The different fractions can be represented in different ways on a number line.

• Equivalent Fractions on Number Line
• Proper Fractions on Number line
• Mixed Fractions on Number Line
• Improper Fractions on Number Line

Equivalent Fractions on Number Line

The steps to represent an equivalent fraction on number line are given below.

• First, find the simplest form of all the given fractions.
• If the simplest form of fractions is same, they are equivalent fractions.
• Then, plot the fractions in the number line.
• When we plot these fractions on different number line, we can see that the equivalent fractions are in the same position on the number line.

Proper Fractions on Number Line

The steps to represent a proper fraction on number line are given below.

• First, we represent it between 0 and 1 as in proper fraction numerator is less than the denominator.
• Divide the number line between 0 and 1 in equal parts according to the denominator until it reaches 1.
• Count the number of times equal to the numerator from the left to get the representation of the given proper fraction on number line.

Mixed Fractions on Number Line

The steps to represent a mixed fraction on a number line are given below.

• First, we first observe the whole part and the fraction part of the mixed part.
• Start the number line from the whole part of the mixed fraction, then divide the number line into equal parts according to the denominator in the fraction part.
• Now, count the number of points from left until it is equal to the numerator of fraction part.
• Mark the point to represent the given mixed fraction on a number line.

Improper Fractions on Number Line

The steps to represent an improper fraction on number line are given below.

• First, we convert the given improper fraction into mixed fraction.
• Then follow the representation of mixed fraction on a number line.
• The improper fractions are fractions with numerator greater than or equal to the denominator.
• If the numerator is equal to denominator, it represents whole number that can be easily represented on a number line.
• If the numerator is greater than the denominator then the improper fraction is converted into its equivalent mixed fraction.

Examples of Fractions on Number Line

1: Plot fraction 4/5 on the number line.

The given fraction 4/5 is proper fraction so, we divide number line between 0 and 1.

According to denominator, we divide number line as 0, 1/5, 2/5, 3/5, 4/5 and 5/5.

The fraction 4/5 is highlighted in the above number line.

2: Plot fraction 3\bold{\frac{2}{5}} on the number line.

The given fraction is mixed fraction, so we start the number from whole number part i.e., 3.

Now, divide the number line according to the denominator of fraction part i.e., 3, 3\frac{1}{5}, 3\frac{2}{5}, 3\frac{3}{5}, 3\frac{4}{5}, 4.

The mixed fraction 3\bold{\frac{2}{5}} is highlighted on the number line.

3: Plot fraction 26/3 on number line.

The given fraction is improper fraction. So, first convert it into mixed fraction

26/3 = 8\frac{2}{3}

Now, plot mixed fraction 8\frac{2}{3} on number line.

Practice Questions on Fractions on Number Line - Unsolved

Q1. Plot fraction 7/9 on the number line.

Q2. Plot fraction 5\bold{\frac{4}{3}} on the number line.

Q3. Plot fraction 63/5 on number line.

Q4. Compare two fractions 3/8 and 2/7 using number line.

Q5. Represent fraction 12/17 on number line.

Q6. Represent fraction 14/5 on number line.

Q7. Represent fraction 10\bold{\frac{1}{9}} on the number line.

Q8. Compare fractions 4/9 and 7/9.