## Multiplying fractions is easy

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.

### Multiplication of Fraction by Fraction

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

#### For example

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

**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 $2 \over 5$

#### Another exercise

$\frac{1}{2} \times \frac{2}{9} \times \frac{1}{3}$

**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.

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### Multiplication of an Integer by a Fraction

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 $1$.

#### For example

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

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

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, $1$.

### Fraction by mixed number

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.

#### For example

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:

$\frac{60}{36}=\frac{5}{3}$

Do you know what the answer is?

### Multiplication of an Integer by a Mixed Number

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.

#### Example

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

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:

$\frac{5}{1} \times \frac{5}{3}=\frac{25}{3}$