Online Division of Fractions Calculator
How to use the ‘Division of Fractions Calculator’?
Follow the steps below to use the division of fractions calculator:
Step 1: Toggle the button if you wish to switch from ‘Fractions’ to ‘Mixed Numbers’.
Step 2: 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.
Step 3: Click on the ‘Solve’ button to obtain the result.
Step 4: Click on the ‘Show steps’ button to know the stepwise solution to find the result.
Step 5: Click on the button to enter new inputs and start again.
Step 6: Click on the ‘Example’ button to play with different random input values and their division.
Step 7: Click on the ‘Explore’ button to understand the various division visually:
- Division of fractions and whole number
- Division of fractions and fraction
- Division of mixed numbers and fraction
Step 8: 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: Divide \(\frac{3}{20}\) by \(\frac{3}{5}\).
Solution:
\(\frac{3}{20} \div \frac{3}{5}\)
\(\Rightarrow \frac{3}{20}\times \frac{5}{3}\)
\(\Rightarrow \frac{1}{4}\)
So, \(\frac{3}{20} \div \frac{3}{5}=\frac{1}{4}\)
Example 2: Divide \(2\frac{1}{5}\) by 3\(\frac{1}{4}\).
Solution:
\(2\frac{1}{5} \div 3\frac{1}{4}\)
Convert mixed numbers into fraction numbers.
\(\frac{11}{5} \div \frac{13}{4}\)
\(\Rightarrow \frac{11}{5}\times \frac{4}{13}\)
\(\Rightarrow \frac{44}{65}\)
So, \(2\frac{1}{5} \div 3\frac{1}{4}=\frac{44}{65}\)
Example 3: Find the value of \(\frac{6}{7}\div 3\)
Solution:
\(\frac{6}{7}\div \frac{3}{1}\)
\(\Rightarrow \frac{6}{7}\times \frac{1}{3}\)
\(\Rightarrow \frac{2}{7}\)
So, \(\frac{6}{7}\div 3=\frac{2}{7}\)
Example 4: Find the value of \(3\div 1\frac{1}{6}\).
Solution:
\(3\div 1\frac{1}{6}\)
Convert mixed number into fraction numbers.
\(\frac{3}{1}\div 1\frac{1}{6}\)
\(\frac{3}{1}\div \frac{7}{6}\)
\(\Rightarrow \frac{3}{1}\times \frac{6}{7}\)
\(\Rightarrow \frac{18}{7}\)
So, \(3\div 1\frac{1}{6}=\frac{18}{7}=2\frac{4}{7}\)
Example 5: Find the value of \(2\frac{1}{2}\div 5\)
Solution:
\(2\frac{1}{2}\div 5\)
Convert mixed numbers into fraction numbers.
\(\frac{5}{2}\div \frac{5}{1}\)
\(\Rightarrow \frac{5}{2}\times \frac{1}{5}\)
\(\Rightarrow \frac{1}{2}\)
So, \(2\frac{1}{2}\div 5=\frac{1}{2}\)
The value of fraction which denominator as zero, is not defined.
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.
Two or more fractions which represent the same value but have different numerator and denominator from each other are called equivalent fractions.
The fraction obtained by flipping the fraction, that is, interchanging the numerator and denominator with each other is called reciprocal of fraction. For example, 6/7 is the reciprocal of 7/6.
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.