Online Multiplication of Fractions Calculator
How to use the ‘Multiplication of Fractions Calculator’?
Follow the steps below to use the multiplication 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 product or result.
Click on the ‘Show steps’ button to know the stepwise solution to find the product. Steps can be seen using the two different methods, that are, ‘Use unit fraction’ and ‘Multiply fractions’ 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 product.
Click on the ‘Explore’ button to understand the multiplication of fractions 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. In real life usage of fractions 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 equals or is bigger than a whole. For example \(\frac{5}{3},~\frac{9}{7},~\frac{11}{6}\).
An improper fraction can be represented as sum of a whole number and a proper fraction, called mixed numbers.
Solved Examples
Example 1: Multiply \(\frac{2}{7}\) and \(\frac{3}{5}\).
Solution:
\(\frac{2}{7}\times~\frac{3}{5}\)
\(\Rightarrow \frac{2\times~3}{7\times~5}\)
\(\Rightarrow \frac{6}{35}\)
So, \(\frac{2}{7}\times~\frac{3}{5}=\frac{6}{35}\)
Example 2: Find \(4\frac{3}{5}\times~1\frac{2}{5}\).
Solution:
\(4\frac{3}{5}\times~1\frac{2}{5}\)
Convert mixed numbers into fraction form.
\(\frac{23}{5}\times~\frac{7}{5}\)
\(\Rightarrow \frac{23\times~7}{5\times~5}\)
\(\Rightarrow \frac{161}{25}=6\frac{11}{25}\)
So, \(4\frac{3}{5}\times~1\frac{2}{5}=\frac{161}{25}=6\frac{11}{25}\)
Example 3: Multiply \(\frac{5}{7}\) and 7.
Solution:
\(\frac{5}{7}\times~7=\frac{5}{7}\times~\frac{7}{1}\)
\(\Rightarrow \frac{5\times~7}{7\times~1}\)
\(\Rightarrow \frac{5}{1}=5\)
So, \(\frac{5}{7}\times~7=5\)
Example 4: Multiply \(2\frac{5}{8}\) and \(\frac{2}{3}\).
Solution:
\(2\frac{5}{8}\times~\frac{2}{3}\)
Convert mixed numbers into fraction form.
\(\frac{21}{8}\times~\frac{2}{3}\)
\(\Rightarrow \frac{21\times~2}{8\times~3}\)
\(\Rightarrow \frac{7}{4}=1\frac{3}{4}\)
So, \(2\frac{5}{8}\times~\frac{2}{3}=\frac{7}{4}=1\frac{3}{4}\)
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.
A mixed number consists of a whole number and a fraction. Multiply the denominator of fraction with whole number and add it to the numerator of fraction. The sum is numerator of improper fraction and the denominator remains the same.
The value of fraction with denominator as 0 is not defined.
No, the product of two smaller number is always less than that of two bigger numbers. Hence, the product of two proper fraction will have smaller number in denominator and bigger in denominator. So, it is always a proper fraction.
Multiplying or dividing the numerator and denominator of a fraction with the same number gives the equivalent fractions.