Multiplication of Fractions

Multiplying fractions is an impressively easy topic!
In this article, you will learn in no time how to solve any fraction multiplication exercise.
Shall we start?

The method to solve fraction multiplications is - numerator by numerator and denominator by denominator.
Let's remember this method as this is how we will proceed in all the fraction multiplication exercises.

Important observations:

• The commutative property works - as it is a multiplication exercise, the commutative property acts the same way with fractions, and if we change the order of the parts of the exercise, the result will not be altered.
• If we come across the multiplication of a fraction by a whole number or by a mixed number, we will first convert that number to a fraction.

Let's start solving and, little by little, we will see all the possibilities along the way.

Fraction by fraction multiplication exercises are very simple and are solved by multiplying numerator by numerator and denominator by denominator.

$\frac{2}{3} \times \frac{3}{5}=\frac{6}{15}$

Solution:
We multiply the numerator $3$ by the numerator $2$ and obtained $6$ in the numerator.
We multiply the denominator $5$ by the denominator $3$ and obtained $15$ in the denominator.
We can simplify and arrive at $2 \over 5$

$\frac{1}{2} \times \frac{2}{9} \times \frac{1}{3}$
Solution:
We will multiply the numerator by the numerator by the numerator -> $1 \times 2 \times 1=2$
and the denominator by the denominator by the denominator $2 \times 9 \times 3=54$
We will obtain
$2 \over 54$
We can simplify and get to​ $1 \over 27$

Observe - Since this is a multiplication exercise we can apply the commutative property and change the order of the fractions writing them, for example, in the following way - >$\frac{1}{2}\times \frac{1}{3}\times \frac{2}{9}$, the result will not vary.

When we have an exercise with an integer that is multiplied by a fractional number, we will convert the integer to a fraction and then proceed to solve according to the method of numerator by numerator and denominator by denominator.
How do you convert an integer to a fraction? It's very easy!
You can convert any number to a fraction in the following way: write the given number in the numerator
and in the denominator write $1$.

$2=\frac{2}{1}$

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

Now let's practice this:
$3 \times \frac{2}{6}=$

Solution:
First, let's convert the whole number to a fraction:

$\frac{1}{3}=3$

Now let's write the exercise only with fractions:
$\frac{2}{6} \times \frac{3}{1}=$
Let's solve using the method we learned - Numerator by numerator and denominator by denominator, we will get: $6 \over 6$ that is, $1$.

We will solve multiplication exercises of fractions by mixed numbers like this:
We will convert the mixed number to a fraction.
Now we can solve using the method of numerator by numerator and denominator by denominator.
What is a mixed number?
A mixed number is, in fact, a fraction composed of a whole number and a fraction, like, for example $3 \frac{4}{5}$.
How do you convert a mixed number to a fraction?
Multiply the whole number by the denominator.
Then add the numerator, and this will be the number that will be written in the place of the numerator.

Convert the mixed number $4 \frac{2}{3}$ to a fraction.
Solution: We will multiply the whole number by the denominator and add the numerator
$4 \times 3+2=$
$12+2=14$
The obtained number ($14$) will be written in the numerator, while the denominator will not change.
This gives us:
$4 \frac{2}{3}=\frac{14}{3}$
Now let's practice multiplying a mixed number by a fraction:
$\frac{3}{4} \times 2\frac{2}{9}=$

Solution:
First, we will convert the mixed number to a fraction:
We will do it the way we learned $2 \times 9+2=20$
We will write the result in the numerator and the denominator will remain the same. We obtain: $9 \over 20$
Let's rewrite the exercise:
$\frac{3}{4} \times \frac{20}{9}=$

Multiply numerator by numerator and denominator by denominator, we will obtain:
$\frac{60}{36}=\frac{5}{3}$

To solve exercises of multiplying an integer by a mixed number, we will convert both numbers to simple fractions, then proceed according to the method of numerator by numerator and denominator by denominator.

$5 \times 1\frac{2}{3}$
Let's convert the whole number $5$ to a fraction -> $5 \over 1$
Let's convert the mixed number $12 \over 3$ to a fraction -> $5 \over 3$
Let's rewrite the exercise and solve by multiplying numerator by numerator and denominator by denominator:
$\frac{5}{1} \times \frac{5}{3}=\frac{25}{3}$