How to Multiply Fractions

Multiplication is the basic operations in elementary arithmetic and a fraction represents a part of a whole. To multiply fractions, multiply the numerators together and multiply the denominators together, not necessarily in that order, and then simplify the product if necessary, as to leave it in the simplest form.
Here we discussed about the multiplication of the fractions. To multiply signed fractions, we follow both the rules for multiplying fractions and those for multiplying signed integers.

There is more than one way to multiply with fractions:


  • Multiply fractions by whole numbers.
  • Multiply fractions by fractions.
  • Multiply fractions by mixed fractions. 

How to Multiply Fractions

To multiply fractions, multiplying the numerators with each other and the denominators with each other. Sometimes the fractions in a multiplication problem can be canceled. Cancelling is a shortcut to reduced the fraction before multiplying fractions. Before multiplying in order to avoid dealing with big, reduce fractions. All fractions can be multiplied by multiplying the numerators and then multiplying the denominators. While multiplying the fractions we don't need common denominators like adding and subtracting fractions.

Steps for Multiplying Fractions:

Step 1: Multiply the numerators.

Step 2: Multiply the denominators.

Step 3: Write the answer as a fraction, reduced it if possible.

Solved Examples

Question 1: Multiply $\frac{3}{5}$ and 7
Solution:
Step 1:

Write 7 as a fraction with a denominator of 1.

7 = $\frac{7}{1}$

Step 2: Multiply numerators together and denominators together

$\frac{3}{5}$ * $\frac{7}{1}$ = $\frac{3 * 7}{5 * 1}$

= $\frac{21}{5}$
 

Question 2: Multiply $\frac{6}{15}$ and $\frac{9}{2}$
Solution:
Step 1:

Multiply numerators together and denominators together

$\frac{6}{15}$ * $\frac{9}{2}$ = $\frac{6 * 9}{15 * 2}$

= $\frac{54}{30}$

Step 2: Reduced the fraction

$\frac{54}{30}$  = $\frac{2 * 3 * 3 * 3}{2 * 3 * 5}$

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

=
$\frac{9}{ 5}$

=>
$\frac{6}{15}$ * $\frac{9}{2}$ $\frac{9}{ 5}$
 

Question 3: Multiply $\frac{31}{4}$ and $\frac{5}{2}$
Solution:
Multiply numerators together and denominators together

$\frac{31}{4}$ * $\frac{5}{2}$ = $\frac{31 * 5}{4 * 2}$

= $\frac{155}{8}$

=> $\frac{31}{4}$ * $\frac{5}{2}$ = $\frac{155}{8}$
 

Multiplying Fractions

Multiply the numerators and denominators separately. While multiplying fractions with whole number or mixed fraction, convert the whole number and mixed fractions into the fraction. Then multiply the numerators together for a new numerator, and the denominators together for a new denominator. Mixed number must be reduced to improper fractions, and whole numbers to the form of fractions.

Solved Examples

Question 1: Solve $3\tfrac{4}{5}$ * $\frac{4}{5}$
Solution:
Step 1: Change mixed number to improper fraction

$3\tfrac{4}{5}$ = $\frac{19}{5}$

Step 2: Multiply numerators together and denominators together

$\frac{19}{5}$ * $\frac{4}{5}$ = $\frac{19 * 4}{5 * 5}$

= $\frac{76}{25}$

=>
$\frac{19}{5}$ * $\frac{4}{5}$ =  $\frac{76}{25}$
 

Question 2: Solve $2\tfrac{2}{3}$ * $\frac{8}{5}$
Solution:
Step 1: Change mixed number to improper fraction

$2\tfrac{2}{3}$ = $\frac{8}{3}$

Step 2: Multiply numerators together and denominators together

$\frac{8}{3}$ * $\frac{8}{5}$ = $\frac{8 * 8}{3 * 5}$

=
$\frac{64}{15}$

=>
$2\tfrac{2}{3}$ * $\frac{8}{5}$ =  $\frac{64}{15}$
 

Question 3: Multiply $\frac{10}{3}$ and $\frac{4}{7}$
Solution:
Multiply numerators together and denominators together

$\frac{10}{3}$ * $\frac{4}{7}$ = $\frac{10 * 4}{3 * 7}$

=
$\frac{40}{21}$

=> $\frac{10}{3}$ * $\frac{4}{7}$  = $\frac{40}{21}$