Fractions on Number Line

Fractions are expressions that represent parts of a whole. A fraction has two parts, the numerator and the denominator. It is expressed in the form a/b, where a is the numerator and b is the denominator and b ≠ 0. In other words, a fraction represents the portion occupied out of the whole.

To plot fractions on a number line, use the steps listed below:

• Draw a horizontal number line.
• Determine whether the fraction is proper, improper, or mixed.
   

For proper fractions:

• Draw a number line from 0 to 1 and divide it into as many parts to find out those proper fractions lying between 0 and 1.

For mixed fractions:

• Start plotting from the whole number (quotient) part of the mixed fraction.

• Then, divide the remaining part based on the denominator.

For improper fractions:

• For converting the improper fraction into a mixed fraction, plot it on the number line.

• Count from left to right on the number line and mark the points.
   

There are different ways to represent fractions on a number line based on their type:

To represent equivalent fractions on a number line, follow the steps below:

• Express all the given fractions in their simplest form.

• Check if the fractions have the same simplest form to confirm they are equivalent.

• Now, we plot the fractions on the number line.

• Equivalent fractions occupy the same position on the number line, even though they may look different.
   

Represent proper fractions on a number line using the following steps:

• Since the numerator is less than the denominator, we represent it on a number line between 0 and 1.

• Divide the section between 0 and 1into equal parts based on the denominator.

• We now count to the numerator from the left to represent the proper fraction on the number line.
   

Represent mixed fractions on a number line using the following steps:

• Identify the fractional part and whole part of the mixed fraction.

• The plotting should start from the whole number part of the mixed fraction.

• Based on the denominator of the fractional part, divide the number line into equal parts.

• Now, mark the given mixed fraction on the number line.
   

Represent improper fractions on a number line using the following steps:

• If the given fraction is an improper fraction, convert it into a mixed fraction.

• Then, plot the mixed fraction on a number line.

• Improper fractions have a numerator greater than or equal to the denominator.

• If the numerator and denominator are equal, the fraction equals 1 and should be represented on the number line.

• When the numerator is greater than the denominator, the fraction needs to be converted into its equivalent mixed fraction before plotting.
   

Fractions play an important role in our everyday life. Visualizing fractions on a number line helps us measure the accurate portion of a whole amount. Here, we will look at a few real-life examples of fractions:

• While cooking, we use fractions to measure the quantity of ingredients, such as 1/2 cup of sugar.

• We can use fractions to manage time by dividing it into sections. For example: 30 minutes = ½ of an hour.

• With a fraction number line, students can determine the distance traveled and the distance remaining during a travel journey.

• When shopping, we may come across discounts that involve fractions. For example: ½ off an item.

• Fractions on a number line help us measure the remaining time or distance in a fitness routine. 
  For example: ¼ of the workout routine.