Online Addition of Fractions Calculator
How to use the ‘Addition of Fractions Calculator’?
Follow the steps below to use the addition 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 into the respective input boxes.
Click on the ‘Solve’ button to obtain the sum or result.
Click on the ‘Show steps’ button to know the stepwise solution to find the sum. Steps can be seen using the three different methods, that are, ‘Use Model method’, ‘Addition 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 sum
Click on the ‘Explore’ button to understand the addition of fractions or mixed numbers with the use of visuals.
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 is a number that represents part(s) 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 consistently equals or exceeds the whole. For example \( \frac{5}{3},~\frac{9}{7},~\frac{11}{6} \).
Solved Examples
Example 1: Add \( \frac{3}{5} \) and \( \frac{1}{4} \).
Solution: addition of fractions using the like denominators method.
\( \frac{3}{5}~+~\frac{1}{4} \)
\( \Rightarrow ~\frac{3~\times~4}{5~\times~4}~+~ \frac{1~\times~5}{4~\times~5}\)
\( \Rightarrow ~\frac{12}{20}~+~ \frac{5}{20}\)
\( \Rightarrow ~\frac{17}{20}\)
So, \( \frac{3}{5}~+~\frac{1}{4}=\frac{17}{20} \)
Example 2: Add \( 3\frac{2}{3}\) and \( 2\frac{4}{5}\).
Solution:
\( 3\frac{2}{3}~+~2\frac{4}{5}\)
Convert mixed numbers into fraction numbers.
\( \frac{11}{3}~+~\frac{14}{5}\)
\( \Rightarrow ~\frac{11~\times~5}{3~\times~5}~+~ \frac{14~\times~3}{5~\times~3}\)
\( \Rightarrow ~\frac{55}{15}~+~ \frac{42}{15}\)
\( \Rightarrow ~\frac{97}{15}=6 \frac{7}{15}\)
So, \( 3\frac{2}{3}~+~2\frac{4}{5}=\frac{97}{20}=6\frac{7}{15}\)
Example 3: Add \( \frac{5}{6}\) and \( \frac{4}{5}\) using the number line method.
Solution: Find equivalent fractions of both fractions such that the denominators are the least common multiples
\( \frac{5}{6}\) and \( \frac{4}{5}\)
\( \Rightarrow ~\frac{5~\times~5}{6~\times~5}\) and \( \frac{4~\times~6}{5~\times~6}\)
\( \Rightarrow ~\frac{25}{30}\) and \( \frac{24}{30}\)
Represent \( \frac{25}{30}\) on the number line first. And now represent the second fraction \( \frac{24}{30}\) using the ending of \( \frac{25}{30}\) as the starting point.
So, \( \frac{5}{6}~+~\frac{4}{5}=\frac{49}{30}\)
Example 4: Find the sum of \( \frac{1}{3}\) and \( \frac{2}{5}\) using a bar model.
Solution:
Represent \( \frac{1}{3}\) and \(\frac{2}{5}\) in bar models.
Using equivalence add the fractional part of both fractions to find the sum.
So, \( \frac{1}{3}~+~\frac{2}{5}=\frac{11}{15}\)
The fraction with 1 as a numerator is called unit fraction. Worksheets allow your child to see their processes and determine where they might be making conceptual or computational mistakes.
Two or more fractions which represent the same value but have different numerator and denominator from each other are called equivalent fractions.
The value of fraction with denominator as 0 is not defined.
Multiplying or dividing the numerator and denominator of a fraction with the same number gives the equivalent fractions.