# How to Multiply Mixed Fractions

## Introduction:

We know that the fractions are of three different types. They are proper fractions, improper fractions and mixed fractions.
Proper fractions are those which lie between 0 and 1 on the number line and the improper fractions are those which are equal to 1 or greater than 1. Improper fractions can be written as the combination of whole number and proper fraction. In this section let us see how we  multiply mixed fractions.

## Multiplication of Mixed Fractions:

Let us study the following figure before we discuss the method of multiplying mixed fractions.   In the above figure , we have

$1\frac{2}{3}$ + $1\frac{2}{3}$ + $1\frac{2}{3}$ = $1\frac{2}{3}\times 3$

=$\frac{5}{3}\times 3$

= $\frac{5\times 3}{3}$

= $\frac{15}{3}$

= 5
If we count the total number of shaded region we see that there are 15 one-thirds, which is 5 whole.
This is shown in the following figure. The following steps are followed when we multiply 2 or more mixed fractions:

Step 1: Convert the mixed fractions to improper fractions.
Step 2: Group the numerators and multiply them.
Step 3: Group the denominators and multiply them.
Step 4: Find the Highest Common factor of the numerator and denominator of the fraction obtained in steps 2 and 3.
Step 5: Divide the numerator and Denominator by the HCF obtained in step 4.
Step 6: The result obtained will be an improper fraction in the simplest form.
Step 7: Convert this into mixed fraction, which will be the final answer.
Let us discuss the following example:

#### Example :  $2\frac{1}{3}\times1\frac{5}{7}$

Solution: We have , $2\frac{1}{3}\times1\frac{5}{7}$

= $\frac{7}{5}\times \frac{12}{7}$ [ converting the mixed fractions into improper fractions ]

=$\frac{7\times 12}{5\times 7}$ [ grouping the numbers in the numerator and the denominator ]

=$\frac{84}{35}$ [ multiplying the numbers in the numerator and denominator separately ]

=$\frac{84\div 7}{35\div 7}$[ dividing the numerator and the denominator by the common factor]

= $\frac{12}{5}$ [ simplest form ]

=$2\frac{2}{5}$ Final Answer in mixed form.

## Practice Questions:

Multiply the following  and express your answer in mixed fraction.

1. $2\frac{1}{5}\times 3\frac{10}{17}$

2. $3\frac{2}{3}\times 4\frac{1}{5}$

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