# Multiplying Fractions

In the post we will learn methods to multiply two or more fractions.

## How to multiply fractions?

There are different scenarios possible in fraction multiplication.

(a) Multiplication of two or more fraction
(b) Multiplication of fraction with whole number
(c) Multiplication of fraction with mixed number.

We will learn all these cases in detail.

### Multiplication of two or more fractions

Suppose a/b and c/d are the given fractions.

To multiply the fractions follow the below steps;

(a) Multiply the numerators ( a. c )

(b) Multiply the denominators (b. d)

(c) If possible, simplify the fraction.

Let us see some examples for our understanding.

Example 01
Multiply the fraction 2/3 and 4/5

Solution
Multiply the numerator and denominator separately as shown in below image.

The fraction 8/15 cannot be simplified further.
Hence, 8/15 is the solution.

Example 02
Multiply the fractions 6/10 x 5/3 x 3/7

Solution
Multiply the numerators and denominators separately

Note that there are many common factors in numerators and denominators.

⟹ Number 3 is present in both numerator and denominator and can be cancelled out.

⟹ Number 5 in numerator can divide 10 in denominator and leaves quotient 2.

⟹ Number 2 in denominator can divide 6 in numerator leaving 3.

Now no common factors are left in numerator and denominator.
The final numbers are:

Hence, 3/7 is the final solution of multiplication.

Example 03
Multiply the fractions 2/15 x 5/20

Solution
Multiply the numerators and denominator separately.

There are common factors present in numerator and denominator.
Removing the common factors.

⟹ Number 2 in numerator can divide number 20 in denominator leaving 10 as quotient.

⟹ Number 5 in the numerator can divide number 10 in the denominator leaving quotient 2.

Now there is no common factors left.

Multiplying the remaining numbers we get.

Hence 1/20 is the solution of the given multiplication.

### Multiplication of fraction with whole number

When multiplying fraction with whole number, follow the below steps;

(a) First convert the whole number into fraction by showing denominator 1

(b) Multiply the numerator and denominator separately.

(c) if possible, simplify the fraction.

Given below are solved examples for further understanding;

Example 01
Multiply 3/13 x 8

Solution
Convert the fraction into whole number by showing denominator 1

Multiply the numerator and denominator separately.

There is no common factor between numerator and denominator, so further simplification is not possible.

Hence, 24/13 is the final solution.

Example 02
Multiply 50 x (6/25)

Solution
Convert the whole number into fraction by showing 1 as denominator.

Now multiply the numerator and denominator separately.

⟹ Number 25 in the denominator can divide number 50 in numerator and leave quotient 2

Multiplying the remaining number we get;

Hence, number 12 is the solution of above problem.

Example 03
Multiply 40 x (9/24)

Solution
Convert the whole number into fraction by showing 1 as denominator.

Multiply the numerator and denominator separately

⟹ Number 40 in numerator and 24 in denominator can be divided by 8 and will leave remainders 5 and 3 respectively.

Hence, dividing numerator and denominator by 8, we get;

⟹ Number 3 in denominator can divide number 9 in numerator and leave quotient 3

Multiplying the remaining numbers we get;

Hence, number 15 is the solution of above multiplication.

### Multiplication of fraction with mixed number

To multiply mixed number with fraction, follow the below steps;

(a) Convert mixed number into fraction.

(b) Multiply the numerator and denominator.

(c) If possible, simplify the fraction.

Given below are some solved problems for your understanding.

Example 01
Multiply \mathtt{\frac{24}{5} \ \times \ 2\frac{2}{4}}

Solution
First convert the mixed number into fraction.

The mixed fraction is converted into fraction value 10/4.

Now multiplying the numerator and denominator separately.

⟹ Number 5 in the denominator can divide number 10 in numerator leaving 2 as quotient.

⟹ Number 4 in the denominator can divide 24 in numerator and leave 6 as quotient.

Multiplying the remaining numbers.

Hence, 12 is the solution of above multiplication.

Example 02
Multiply \mathtt{\frac{7}{25} \ \times \ 7\frac{3}{6}}

Solution
Convert the mixed fraction into simple fraction.

The mixed fraction is converted into fraction 45/6

Now multiply the numerator and denominator separately.

⟹ The numerator number 45 and denominator number 25 are both divisible by 5 leaving quotient 9 and 5 respectively.

So dividing numerator and denominator by 5 we get;

⟹ The numerator number 9 and denominator 6 is divisible by 6 leaving 3 and 2 as quotient respectively.

So, dividing numerator and denominator by 3 we get;

Now multiply the remaining numbers we get;

Hence, 21/10 is the solution for given multiplication.

Example 03
Multiply the fractions \mathtt{\frac{10}{21} \ \times \ 3\frac{6}{10}}

Solution
First convert the mixed number into simple fraction.

Hence, the mixed fraction is converted into 36/10.

Now multiply the numerator and denominator separately.

⟹ Cancel the number 10 from numerator and denominator.

⟹ The number 36 in numerator and 21 in denominator is divisible by 3 leaving quotient 12 and 7 repsectively.

So dividing numerator and denominator by 3.

12/7 is the number left at the end.
Hence, it is the final solution.