 # Multiplying Fractions

Multiplying fractions is as simple as multiplying any numbers in the number systems. A fraction represents the division of the whole. The fraction is generally represented in the form “x/y”. Here “x” is the numerator and “y” is the denominator.  The concept of fractions is also used in our daily life. Like if we divide an apple into 4 equal parts, then the value of each part is ¼ and if we divide it into 8 equal parts, then the value of each piece is 1/8th of the whole apple. Here we are going to discuss how to multiply fractions with whole numbers or with fractions or with variables in a more detailed way.

## Multiplying Fractions Definition

Multiplying fractions is defined as the product of a fraction with a fraction or with an integer or with the variables. The procedure to multiply the fractions are:

• Multiply the numerator with numerator
• Multiply the denominator with denominator
• Simplify the fractions, if required

For example,

3/2 and ⅓ are the two fractions

The multiplication of two fractions is given by:

(3/2)× (⅓) = [3×1]/[2×3]

(3/2)× (⅓) = 3/6

Now, simplify the fraction, we get ½

Therefore, the multiplication of two fractions 3/2 and ⅓ is ½.

Simply, we can write the formula for multiplication of fraction as;

The product of Fraction = Product of Numerator/Product of Denominator Multiplying Fractions

Try This: Multiplying Fractions Calculator

### Fractions Parts and Types

If a fraction is written in the form of a/b, then a and b are the parts of the fraction, where a is called as numerator and b is called as the denominator.

For example,

Suppose ⅖ is a fraction, then 2 is the numerator and 5 is the denominator.

There are three main types of fractions which are proper fractions, improper fractions, and mixed fractions. Below is a brief explanation on each of the types.

• Proper fractions

When numerator of a fraction is less than the denominator.

Example: ½, ⅗, 7/9

• Improper fractions

When the numerator is greater than the denominator

Example: 3/2, 5/4, 8/3

• Mixed Fraction

We can also write the improper fraction in the combination of a whole number and a fraction. This type of fraction is called a mixed fraction.

Example: 13/4 =  3 ¼

21/5 =  4 ⅕ .

## Types of Fraction Multiplication

The fraction can be multiplied with different types of numbers. They are

• Multiplication of Fraction with Whole Numbers
• Multiplication of Fraction with another Fraction
• Multiplication of Fraction with Variables

### Multiplication of Fractions with Fractions

Example 1: Solve ⅔×½

Solution: ⅔×½ = 2×1/3×2 = 2/6 =

Therefore, from the above example, we can observe, by multiplying two fractions we get a fraction number. This is a proper fraction.

Example 2: Multiply ⅘×⅞

Solution: ⅘×⅞ = 4×7 / 5×8 = 28/40

We can further simplify it as;

28/40 = 7/10

If we have to multiply three fractions, then the above formula remains the same.

Example 3: Multiply ¼×⅖×⅛

Solution: Multiplying the given fraction ¼×⅖×⅛, we get

Product = 1×2×1 / 4×5×8

= 2 / 160

= 1 / 80

### Multiplying Fractions with Whole numbers

If a whole number or real number is multiplied with fraction, then it is equal to the real number times the fraction is added.

Example 4: Multiply 5×½

Solution: 5×½ means 5 times of ½

Means, if we add ½ for five times, we get the answer.

Therefore,

½ + ½ + ½ + ½ +½ = (1+1+1+1+1)/2 = 5/2 = 2.5

Example 5: Multiply 8/7×10

Solution: Given, 8/7×10

We can write it as 8×10/7

Therefore, 80/7 is the answer. In decimal, it is 11.42.

• Note: If we multiply a mixed fraction to a whole number or real number, then we get a fraction itself.

Example 6: Multiply $3\frac{1}{5}$×12

Solution: Simplifying the value $3\frac{1}{5}$ we get,

16/5×12 = 16×12 / 5 = 192 / 5 = 38.4

### Multiplying Fractions with Variables

Now, consider the fraction is multiplied with a variable, then the results or outcome will be as per below examples.

Example 7: Multiply 5x/2y × 2x/3z

Solution: Given, 5x/2y × 2x/3z

Therefore, we can solve the above-given expression as;

$\frac{5x\times 2x}{2y\times 3z} = \frac{10x^{2}}{6yz}$

### Practice Problems on Multiplying Fractions

1. What is the product of (½) and 6?
2. The product of (¾) and (12/6) is ______.
3. What is the product of 3 ½ and ⅔?
4. Find the area of a square farm whose side length is 10  ⅔ m.
5. There are f 50 students in a class, and ⅔ of them are girls. Find out how many boys are there?

### What is meant by fractions?

The fraction is defined as the ratio of two numbers. It generally represents the parts of the whole. The fraction can be written in the form “a/b”. Where, the top number “a” is called the numerator and the bottom number “b” is called the denominator.

### How to Multiply Fractions?

To multiply fractions, first simply the fraction to its lowest term. In the case of mixed fractions, simplify it. After simplifying the fraction, multiply the numerator with the numerator and denominator with the denominator. Then, the product of fractions is obtained in p/q form.

### How to Multiply a Fraction Times a Whole Number?

To multiply a fraction with a whole number, represent the whole number as a fraction by putting 1 in the denominator. Then, multiply the numerator with the numerator and the denominator with the denominator to get the product.

### Do you Need Common Denominators to Multiply Fractions?

No, there is no need for a common denominator to multiply fractions. Any two fractions can be multiplied in which numerators are multiplied with each other and the denominators are multiplied with each other.

### How to Multiply Fractions with Mixed Numbers?

If a fraction has to be multiplied with a mixed number (fraction), simplify the fraction first. Once the mixed fraction is in the form of p/q, multiply the numerators with numerators and denominators with denominators.

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