Dividing Fractions

Dividing fractions includes division of fractions. You must have learned about division performed in natural and whole numbers, which are easy to calculate. But, fractions are not integers and are represented in ratios, where both the numerator and denominator are integers and denominator is never equal to zero. So, the fractions are only divisible if and only if they rely on fractions condition. Also, in case of dividing decimals, we can convert them into fractions and then can simplify it. Let us solve some of the word problems and examples in this article to have a thorough knowledge. Division of fractions by direct method required more effort. Therefore, an alternative method was introduced to solve it. In this method, instead of performing division on fractions, we will perform multiplication on it, as it is easy than dividing them. Students can also reach to calculators for simplifying such problems. Here, we will learn the steps, how to divide fractions with some set of examples.

Table of Contents:

What is Meant by Dividing Fractions?

Dividing fractions is nothing but multiplying the fractions by reversing one of the two fraction numbers or by writing the reciprocal of one of the fractions. By reciprocal we mean, if a fraction is given as a/b, then the reciprocal of it will b/a. Thus, interchanging the position of numerator and denominator with each other.

How to Divide Fractions?

The division of fractions can be classified into three different ways. They are

  • Dividing fractions by a fraction
  • Dividing fractions by whole number
  • Dividing fractions by mixed fraction

Let us discuss all these three methods in a detailed way

Dividing Fraction by a Fraction

In three simple steps, we can solve the division of fractions by converting into the multiplication of fractions. Let us learn one by one.

  1. Write the reciprocal of the second fraction number and multiply it with the first fraction number
  2. Multiply the numerators and denominators of both fractions
  3. Simplify the fraction number

In general, if a/b is a fraction which is divided by c/d. Then we can solve the division as;

  • a/b ÷ c/d = a/b × d/c
  • a/b ÷ c/d = a×d / b×c
  • a/b ÷ c/d = ad/bc

You can see from the above expressions. The a/b is divided by c/d, then we can write it as a/b multiplied by d/c (reciprocal of c/d). And in the next step, we have to multiply both the numerator a & d and both the denominator, c & d. Hence, we can simplify the rest calculation.

Dividing Fraction by a Whole Number

While dividing the fractions with whole numbers, the process of division is very easy. Follow the procedure given below. 

Step 1: The whole number is converted into the fraction by applying the denominator value as 1

Step 2: Take the reciprocal of the number

Step 3: Now, multiply the fractional value by a given fraction

Step 4: Simplify the given expression

Example: Divide 6/5 by 10

Step 1: Convert 10 into a fraction: 10/1

Step 2: Take reciprocal: 1/10

Step 3: Multiply 6/5 and 1/10: (6/5)×(1/10)

Step 4: Simplify: 3/25

Dividing Fractions by a Mixed Fraction

The process of dividing fractions by a mixed fraction is almost similar to the dividing fraction by a fraction. The steps to perform the division of a fraction by a mixed fraction are as follows:

Step 1: Convert the mixed fraction into the improper fraction

Step 2: Now, take the reciprocal for the improper fraction

Step 3: Multiply the obtained fraction by a given fraction

Step 3: Simplify the fractions

Example: Divide ⅖ by 3½.

Step 1: Convert 3½ into an improper fraction, we get 7/2

Step 2: Take reciprocal for improper fraction: 2/7

Step 3: Multiply ⅖ and 2/7

Step 4: Simplify: 4/35

Dividing Decimals

We have learned to divide fractions using three simple steps. Now with the help of these steps let us learn how to divide decimals with examples.

Example: Divide 0.5 ÷ 0.2

Solution: To divide these decimal numbers, we have to convert both the decimal number into natural numbers by multiplying numerator and denominator by 10.

Therefore, 0.5 × 10 / 0.2 × 10

We get, 5/2 = 2.5

Also, we can use dividing fractions method to solve the above problem.

We can write 0.5 and 0.2 as 5/10 and 2/10.

So for 5/10 ÷ 2/10, we can use the same steps fraction’s division.

5/10 × 10/2

= 5 × 10 / 10 × 2

= 50/20

= 5/2

= 2.5

Note: These are the simple method of dividing decimals. You can also use the direct division method to divide decimals. The only difference is to place the decimal into the right place of the quotient. Let us take an example of this.

Example: Divide 13.2 ÷ 2

Solution: 2) 13.2 (6.6

    -12

—————

12

-12

—————

00

—————

Therefore, 13.2 ÷ 2 = 6.6

Dividing the natural numbers or whole numbers is an easy task but dividing the fractions is a little complex one. The operations performed on natural numbers and whole consist of simple calculations, which one can easily solve. But the operations performed on fractions are sometimes typical and also time-consuming. The simple division has four parts divisor, dividend, quotient and remainder. Also, know some of the divisibility rules for the whole number here.

Dividing Fractions Examples

Example 1: 

¼ ÷ ½

Solution:

Given, ¼ ÷ ½

Writing the reciprocal of the second fraction and multiply it with the first fraction.

¼ × 2/1

Multiplying both numerators and denominators

1×2/4×1

2/4

Simplifying the fraction;

2/4 = ½ = 0.5

Example 2:

⅗ ÷ ⅔

Solution:

Following the same steps:

  1. ÷ ⅔ = ⅗ × 3/2
  2. 3 × 3/ 5 × 2
  3. 9/10=0.9

One more method to divide fractions is to make the denominator equal and then dividing it.

Example 3:

¾ ÷ 3/2

Solution:

Given, ¾ ÷ 3/2

By making the denominator equal we get,

¾ ÷ 6/4

Now the denominators are the same, we can cancel both the denominator and write it as;

3/6 = ½ = 0.5

Frequently Asked Questions on Dividing Fractions

What is meant by dividing fractions?

In mathematics, the dividing fraction is the process of dividing a fraction by another fraction, which should result in a fraction

What are the basic arithmetic operations performed using fractions?

Adding fractions
Subtracting fractions
Multiplying fractions
Dividing fractions

How to divide fractions by a whole number?

First, convert the whole number into a fraction by using applying the denominator value as 1. Then take the reciprocal of the obtained fraction, and then multiply it by the given fraction. Finally, simplify the result, if required.

Why do we perform the reciprocal operation while dividing fractions?

We know that the inverse operation of division is multiplication. To perform multiplication operation by avoiding the division operation, we are taking the reciprocal of the divisor number.

Mention the steps performed in dividing fractions?

The step used in dividing fractions are:
Step 1: Take the reciprocal of the divisor value
Step 2: Multiply the given fraction by the reciprocated value
Step 3: Simplify the fraction.

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