How to Multiply Fractions [Step by Step]

There are three steps to multiply two fractions or more fractions.Look at the following examples to understand how to multiply fractions step by step.


●1/3 Times 1/3 


Step-1:Times means "×" sign


=1/3 × 1/3 


Step-2:

●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(1×1)/(3×3)


Step-3:

Now simplify the new fraction by canceling the common factors if needed.


=1/9 (Answer)


So,1/3 times 1/3  as a fraction in simplest form is 1/9.

Here is the second example of multiplying fractions that will help you to understand how to multiply two fractions:

●4/5 Times 1/6 


Step-1:Times means "×" sign


=4/5 × 1/6


Step-2:

●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(4×1)/(5×6)


Step-3:

Now simplify the new fraction by canceling the common factors if needed.


=4/30

So,4/5 times 1/6  as a fraction in simplest form is 2/15.

Here is the third example of multiplying fractions that will help you to understand how to multiply 4 fractions :

1/3 Times 1/3 Times 1/3 Times 1/3


Step-1:Times means "×" sign


=1/3 × 1/3 × 1/3 × 1/3


Step-2:

●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(1×1×1×1)/(3×3×3×3)


Step-3:

Now simplify the new fraction by canceling the common factors if needed.


=1/81(Answer)


So,1/3 times 1/3 times 1/3 times 1/3 as a fraction in simplest form is 1/81.

Here is the another example of multiplying two fractions that will help you to understand how to multiply  fractions with different denominators :

●5/6 Times 2/3 


Step-1:Times means "×" sign


=5/6 × 2/3 


Step-2:

●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(5×2)/(6×3)


Step-3:

Now simplify the new fraction by canceling the common factors if needed.

=(5×2)/(6×3)

=(5×2)/(3×2×3)

==5/(3×3)

=5/9 (Answer)

Here is the another example of multiplying fractions that will help you to understand how to multiply a fraction with Whole number :

●5/6 Times 2 


Step-1:Times means "×" sign


=5/6 × 2


Step-2:

●Rewrite the whole number as fraction considering 1 as a whole number.
=5/6 × 2/1

After that,
●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(5×2)/(6×1)


Step-3:

Now simplify the new fraction by canceling the common factors if needed.

=(5×2)/(6×1)

=(5×2)/(3×2×1)

【Cancel 2 from both sides】

=5/(3×1)

=5/3 (Answer)

Here is the another example of multiplying fractions that will help you to understand how to multiply whole numbers by fractions:

●7 Times 2 /5


Step-1:Times means "×" sign


=7 × 2/5


Step-2:

●Rewrite the whole number as fraction considering 1 as a whole number.
=7/1 × 2/5

After that,
●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(7×2)/(1×5)


Step-3:

Now simplify the new fraction by canceling the common factors if needed.

=(7×2)/(1×5)

=14/5

This is a improper fraction,.So we need to express this fraction as a mixed number by dividing numerator bt the denominator using long division method.

Here is the another example of multiplying  fractions that will help you to understand how to multiply mixed fractions  :

●1 2/6 Times 2 2/3 


Step-1:Times means "×" sign


=1 2/6 × 2 2/3 


Step-2:
Now convert mixed fractions to improper fractions.

Now,

●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(8×8)/(6×3)

Step-3:

Now simplify the new fraction by canceling the common factors if needed.

=(2×4×8)/(3×2×3)
【Cancel 2 from both sides】
=(4×8)/(3×3)

=32/9
This is an improper fraction.So,we need to convert this fraction to mixed fraction with long division.

So,3 5/9 is the answer.

Here is the another example of multiplying  fractions that will help you to understand how to multiply a mixed fraction by a whole number  :

●1 2/6 Times 2  


Step-1:Times means "×" sign


=1 2/6 × 2 


Step-2:
Now convert mixed fractions to improper fractions.

(1×6+2)/6  × 2

=(6+2)/6 ×2

=8/6  × 2 

Step-3:Now express the whole number as reaction.

8/6  × 2 

=8/6  × 2/1

Now,

●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(8×2)/(6×1)

This  is the new fraction.

Step-4:

Now simplify the new fraction by canceling the common factors if needed.

=(2×4×2)/(3×2×1)
【Cancel 2 from both sides】
=(2×4)/(3×1)

=8/3

This is an improper fraction.So,we need to convert this fraction to mixed fraction with long division.

So,2 2/3 is the answer.

Here is the another example of multiplying  fractions that will help you to understand how to multiply fractions with decimals:

● 2/6 Times 0.4 


Step-1:Times means "×" sign


= 1/6 × 0.4


Step-2:
Now convert decimal number to fraction.

1/6  × 4/10

Now,

●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(1×4)/(6×10)

This  is the new fraction.

Step-4:

Now simplify the new fraction by canceling the common factors if needed.

=(1×4)/(6×10)

=(1×2×2)/(3×2×5×2)
【Cancel 2 from both sides】

=1/(3×5)

=1/15

This is the answer.

Here is the another example of multiplying two fractions that will help you to understand how to multiply a negative fraction by another negative fraction.

●  -5/6 Times -2/3 

Step-1:Times means "×" sign


=-5/6 × -2/3 


Step-2:

●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(-5×-2)/(6×3)


Step-3:

Now simplify the new fraction by canceling the common factors if needed.

=(-5×-2)/(6×3)
Rule:【-1×-1=+1】

=10/(6×3)

=(5×2)/(3×2×3)

=5/(3×3)

=5/9 (Answer)

Here is the another example of multiplying two fractions that will help you to understand how to multiply a negative fraction by a positive fraction.

●  -5/6 Times 2/3 

Step-1:Times means "×" sign


=-5/6 × 2/3 


Step-2:

●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(-5×2)/(6×3)


Step-3:

Now simplify the new fraction by canceling the common factors if needed.

=(-5×2)/(6×3)
Rule:【-1×+1=-1】

=(-5×2)/(3×2×3)

=-5/(3×3)

=-5/9 (Answer)

Here is the another example of multiplying two fractions that will help you to understand how to multiply a negative fraction by a whole number.

●  -5/6 Times 2 

Step-1:Times means "×" sign


=-5/6 × 2


Step-2:Convert the whole number to a fraction.

=-5/6 × 2/1

Then,
●Multiply all top numbers.The obtained number will be the numerator of the new fraction.

●Multiply all bottom numbers.The obtained number will be the denominator of the new fraction.

=(-5×2)/(6×1)


Step-3:

Now simplify the new fraction by canceling the common factors if needed.

=(-5×2)/(6×1)
Rule:【(-1)×(+1)=-1】

=-10/(6×1)

=(-5×2)/(3×2)

=-5/3