Online Subtraction of Fractions Calculator
How to use the ‘Subtraction of Fractions Calculator’?
Follow the steps below to use the subtraction of fractions calculator:
- Toggle the button if you wish to switch from ‘Fractions’ to ‘Mixed Numbers’.
When on ‘Fractions’, enter the fractions into the respective input boxes. Or When on ‘Mixed Numbers’, enter the mixed numbers or fraction into the respective input boxes.
Click on the ‘Solve’ button to obtain the difference or result.
Click on the ‘Show steps’ button to know the stepwise solution to find the difference. Steps can be seen using the three different methods, that are, ‘Use Model’ method, ‘Subtraction with Like Denominators’ method or ‘Number Line Method’.
Click on the
button to enter new inputs and start again.Click on the ‘Example’ button to play with different random input values and their difference.
Click on the ‘Explore’ button to see the representation of two fractions on number lines and find their difference with the use of a slider.
When on the ‘Explore’ page, click the ‘Calculate’ button if you want to go back to the calculator.
What is Fraction?
In mathematics, a fraction number is a way that represents part (s) of a whole. A fraction is a part of a whole, where the whole can be a number, a certain amount of money, or a given number of objects etc.
A fraction is represented by \( \frac{a}{b} \) where \( a \) is called numerator and \( b \) is called denominator.
Types of fraction:
Based the the value of numerators and denominators, fraction is mainly divided into two type:
Proper Fraction
Fractions that have a smaller numerator than their denominator are said to be proper fractions. Proper fractions include, for example, \( \frac{2}{3},~\frac{6}{11},~\frac{9}{14} \).
Improper Fraction
When the numerator of a fraction is more than or equal to the denominator, the fraction is said to be improper. It is equal or greater than a whole. For example, \( \frac{5}{3},~\frac{9}{7},~\frac{11}{6} \).
What are Mixed numbers?
An improper fraction can be represented as the sum of a whole number and a proper fraction, these are called mixed numbers. For example, \( 3\frac{2}{5},~1\frac{2}{7},~11\frac{22}{37} \)
Solved Examples
Example 1: Subtract \( \frac{4}{5}\) and \( \frac{3}{4}\).
Solution: Subtraction of fractions using the like denominators method.
\( \frac{4}{5}~-~\frac{3}{4}\)
\(\Rightarrow ~ \frac{4\times~4}{5\times~4}~-~\frac{3\times~5}{4\times~5}\)
\( \Rightarrow ~\frac{16}{20}~-~\frac{15}{20}\)
\( \Rightarrow ~\frac{1}{20}\)
So, \( \frac{4}{5}~-~\frac{3}{4}=\frac{1}{20}\)
Example 2: Subtract \(2\frac{1}{3}\) from \(3\frac{2}{5}\).
Solution:
\(3\frac{2}{5}~-~2\frac{1}{3}\)
Convert mixed numbers into fraction numbers.
\(\frac{17}{5}~-~\frac{7}{3}\)
\(\Rightarrow ~\frac{17\times~3}{5\times~3}~-~\frac{7\times~5}{3\times~5}\)
\(\Rightarrow ~\frac{51}{15}~-~\frac{35}{15}\)
\(\Rightarrow ~\frac{16}{15}=1\frac{1}{15}\)
So, \(3\frac{2}{5}~-~2\frac{1}{3}=1\frac{1}{15}\)
Example 3: Subtract \(\frac{5}{6}\) from \(\frac{3}{4}\) using the number line method.
Solution: Find equivalent fractions of both fractions such that the denominators are the least common multiples.
\(\frac{3}{4}~-~\frac{5}{6}\)
\(\Rightarrow ~\frac{3\times~3}{4\times~3}~-~\frac{5\times~2}{6\times~2}\)
\(\Rightarrow ~\frac{9}{12}~-~\frac{10}{12}\)
Start from 0 and represent \(\frac{9}{12}\) on the number line first. Now use \(\frac{9}{12}\) as the starting point and to take away \(\frac{10}{12}\) move towards the backwards on the number line.
The value from the 0 is the difference of \(\frac{3}{4}\) and \(\frac{5}{6}\).
So, \(\frac{3}{4}~-~\frac{5}{6}=-~\frac{1}{12}\)
Example 4: Find the difference of \(\frac{1}{2}\) and \(\frac{3}{8}\) using the bar models.
Solution:
Represent \(\frac{1}{2}\) and \(\frac{3}{8}\) using bar models.
Using equivalence,
\(\frac{1}{2}=\frac{4}{8}\)
Now take away three bars (numerator of the second fractional part) from the four shaded bars ( numerator of the equivalent of the first fraction) to find the difference.
So, \(\frac{1}{2}~-~\frac{3}{8}=\frac{1}{8}\)
Multiplying or dividing the numerator and denominator of a fraction with the same number gives the equivalent fractions.
The fraction with 1 as a numerator is called unit fraction.
The value of fraction with denominator as 0 is not defined.
Two or more fractions which represent the same value but have different numerator and denominator from each other are called equivalent fractions.
Fractions are all around us. Fractions are used in measurement, construction, needlework, and baking etc. Whether you realise it or not, fractions are all pervasive or all around you in our lives.