Multiplying Fractions: Multiplication of fractions is very straightforward – just multiply the numerator and denominators and simplify the resulting fraction if needed. Multiplication by fraction does not increase the value of the product.

The product value depends upon the multipliers and it decreases with the decrease in multipliers value and increase with increase in multipliers value. Numerator of multipliers gives us an idea of how many times the numerator of the multiplicand is to be used as an added.

**Fundamental rule of multiplying fractions:**

Multiplying both numerator and denominator by the same number does not change the value of the fraction. It is one of the most important steps used in dealing with equating the fractions.

## Table of Contents

- Fractions
- Simplify Fractions
- Adding Fractions
- Multiplying Fractions
- Subtracting Fractions
- Dividing Fractions
- Proper Fractions
- Improper Fractions
- Mixed Fractions
- Like Fractions
- Unlike Fractions
- Fraction Calculator
- Fraction Simplifier
- Mixed Fraction Calculator
- Convert Fraction to Decimal
- Convert Decimal to Fraction

## How to Multiply Fractions

For multiplying two fractions, we follow three main steps which are show as follows:

- Multiply the top numbers (the numerators) of the given fractions.
- Multiply the bottom numbers (the denominators) of the given fractions.
- Simplify the fraction if needed.

When we have to multiply m and n, it means m is added to itself n times. We can perform multiplication of all the numbers and fractions. We can perform various operations on fractions, like addition, subtraction, multiplication and division. Let us see how we can multiply two fractions in detail.

Fraction is one of the most important concepts of mathematics. Fraction is defined as an equal amount of one whole object. It can be represented as a/b where ‘a’ denotes the value called numerator, b not equal to zero and ‘b’ denotes the value called denominator.

These fractions are primarily used for comparison between parts and whole. A fraction can be a part of an object or group of objects. Each group or share is better known as one half and this is same for other fractions as well.

## Multiplying Fractions Examples

Here are solved examples shown for you to understand how do you multiply fractions with step by step explanation:

Solution:

Step 1: Multiply the top numbers: (1 × 2) = 2.

Step 2: Multiply the bottom numbers: (2 × 5) = 10.

Put the product of the numerators on top of the product of the denominators => 2/10.

Step 3: Simplify the fraction: 2/10 , Now divide both numerator and denominator by 2. you will get 1/5.

**Correct answer is 1/5**

Solution:

Step 1: Multiply the numerators: (2 × 3) = 6

Step 2: Multiply the denominators: (9 × 12) = 108

Put the product of the numerators on top of the product of the denominators => (6/108)

Step 3: Simplify the Fraction 6/108. You will get 1/18

**Correct answer is 1/18**

Solution:

Step 1: Convert both to improper fractions

(3 1/4) x (3 1/3 ) = (13/4) x (10/3)

Step 2: Multiply

13/4 × 10/3 = 130/12

Step 3: Convert to a mixed number (and simplify):

130/12 = 10 10/12 = 10 5/6

**Correct answer is 10 5/6**

## Multiplying Fractions with Whole Numbers

For multiplying a whole number with a proper or an improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator same. The denominator and numerator together are called the fraction, a/b, the upper number in fraction, a, is numerator and lower number, b, is denominator.

**Solved Example:**

Solution:

Given 2/7 x 3

We rewrite 3 as 3/1

Now we multiply 2/7 x 3/1

= 2×3/7×1

= 6/7

## Multiplying Mixed Fractions with Whole Numbers

In multiplication of fractions, fraction is multiply by another fraction, multiplying a fraction by a mixed number, multiplying a fraction by a whole number, multiplication of mixed fractions with a whole number.

Here we learn the concept of multiplication of mixed fractions with whole numbers.

### How to Multiply Mixed Fractions With Whole Numbers

To multiply any mixed numbers and whole numbers, write the mixed numbers as a fractions. Write whole numbers over the denominator one. A mixed number is a whole number and a fraction expressed together.

**Steps for Multiply mixed Fractions With Whole Numbers:**

- Reduced mixed fraction and whole number to improper fraction.
- Multiply the numerators of the fractions.
- Multiply the denominators.
- Simplify the fraction if needed.

**Multiply a Fraction and a Whole Number:**

Multiply 4/5 and 3

Step 1: Change the whole number to a fraction.

The number 3 is the fraction 3/1.

Step 2: Multiply the two fractions.

4/5 x 3/1 = 4×3/5×1 = 12/5

### Multiplying Mixed Fractions with Whole Numbers Examples

Solution:

Given 3 5/6 x 7

Step 1: Reduce 3 5/6 and 7

3 5/6 = 23/6

and

7 = 7/1

Step 2: Multiply the numerators of both the fractions

23 x 7 = 161

Step 3: Multiply the denominators

6 x 1 = 6

Step 4:

23×7/6×1 = 161/6

Solution:

Given 5 x 2 5/7

Step 1: Reduce 5 and 2 5/7

5 = 5/1

and

2 5/7 = 19/7

Step 2: Multiply the numerators of both the fractions

5 × 19 = 95

Step 3: Multiply the denominators

1 × 7 = 7

Step 4:

5×19/1×7 = 95/7

Solution:

Given 9 1/3 x 4

Step 1: Reduce 9 1/3 and 7

9 1/3 = 28/3

and

4 = 4/1

Step 2: Multiply the numerators of both the fractions

28 × 4 = 112

Step 3: Multiply the denominators

3 × 1 = 3

Step 4:

28×4/3×1 = 112/3

Solution:

Given 3 3/2 × 6

Step 1: Reduce 3 3/2 and 6

3 3/2 = 9/2

and

6 = 6/1

Step 2: Multiply the numerators

9 × 6 = 54

Step 3: Multiply the denominators

2 × 1 = 2

Step 4:

9×6/2×1 = 54/2

= 27

## Multiplying Fractions with Unlike Denominators

Unlike denominators means the denominator terms are consists of different numbers. For example, 1/2 x 3/5, this is called the multiplication of fractions with unlike denominators.

### How to Multiply Fractions With Unlike Denominators

**Steps for multiplying fractions with unlike denominators:**

- In the first step, we have to write the given fraction numbers for the multiplication.
- In the next step, we have to check the denominator terms.
- According to that denominator, we have to multiply the given fraction numbers.

### Multiplying Fractions with Unlike Denominators Examples

Solution:

Step 1: Write the given fraction with unlike denominator,

2/3 x 4/5

Step 2: In the next step, we have to multiply the numerators,

2 x 4 = 8

Step 3: In the next step, we have to multiply denominator terms, we get,

3 x 5 = 15

Step 4: Now, we have to combine the obtained result,

8/15

This is the required solution for multiplying the fractions with unlike denominators.

Solution:

Step 1: Write the given fraction with unlike denominator,

3/6 x 9/3

Step 2: In the next step, we have to multiply the numerators,

3 x 9 = 27

Step 3: In the next step, we have to multiply denominator terms, we get,

6 x 3 = 18

Step 4: Now, we have to combine the obtained result,

27/18

= 3/2

## Multiplying Negative Fractions

Multiplying negative fractions are nothing but it is multiplication operation with negative integers.

**Solved Examples:**

Solution:

Given we need to multiply the fractions −2/3 and −4/5

Fractions to multiplied using the formula a∗c/b∗d

Here a = -2, b = 3, c = -4, d = 5.

= a∗c/b∗d

= (−2)x(−4)/3×5 by solving it we get

= 8/15

Solution:

Given we need to multiply the fractions 6/7 and −8/10

Here a = 6 b = 7, c = -8, d = 10.

= a∗c/b∗d

= (+6)×(−8)/7×10 by solving it we get

= −48/70

## Multiplying Fractions Word Problems

Below you could see multiplying fractions word problem.

Solution:

Emma reads a book for 1 3/4 hours per day.

For 6 days, Emma required to read ,

1 3/4 x 6

Convert mixed fraction into simple fraction.

1 3/4 = 1 + 3/4

= 1/1 + 3/4

= 1/1 x 4/4 + 3/4

= 4/4 + 3/4

= (4+3)/4

= 7/4

Thus for 6 days, 6 x 7/4

= (6×7)/4

= 42/4