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\(\frac{a}{b} \), 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:

• Proper Fractions: These fractions are less than 1. They are placed between 0 and 1 on the number line.
   
• Improper Fractions: These are greater than or equal to 1. They appear to the right of 1 on the number line.
   
• Mixed Fractions: These consist of a whole number and a proper fraction. They are plotted by marking the whole number first, then moving ahead by the fractional part.
   
• Equivalent Fractions: Fractions that represent the same value appear at the same position on the number line. 

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 1 into 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.

• Start plotting 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.

• Next, plot the mixed fraction on the 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 on a number line are a complex topic in mathematics. Therefore, some tips and tricks are mentioned below to help us master the topic.
 

• Understand Equal Intervals: Always divide the space between two whole numbers into equal parts based on the denominator. For example, to plot \(\frac{3}{4} \)divide the section between 0 and 1 into four equal parts.
   
• Use the Numerator as a Counter: The numerator tells you how many parts to move from 0. For \(\frac{3}{4} \)​, move 3 parts to the right after dividing the segment into 4 equal intervals.
   
• Convert Improper Fractions to Mixed Numbers: Before plotting an improper fraction like \(\frac{3}{4} \)​, convert it into a mixed number 1\(\frac{3}{4} \)to easily locate it between 1 and 2 on the number line.
   
• Remember Negative Fractions Move Left: For negative fractions, move the same number of equal parts to the left of 0. For instance, \(\frac{-3}{4} \) lies three parts to the left of 0.
   
• Practice with Benchmarks: Use common fractions like \(\frac{1}{2} \), \(\frac{1}{3} \)and \(\frac{3}{4} \) as reference points. These help you quickly estimate where other fractions fall on the number line.

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\(\frac{1}{2} \)cup of sugar.

• We can use fractions to manage time by dividing it into sections. For example: 30 minutes = \(\frac{1}{2} \) 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: \(\frac{1}{2} \) off an item.

• Fractions on a number line help us measure the remaining time or distance in a fitness routine. 
  For example: \(\frac{1}{4} \) of the workout routine.