Dividing Fractions

You must have learned about division performed in natural and whole numbers or dividing whole numbers and natural numbers. Dividing fractions includes division of fractions. Fractions are not integers. As we know integers include all the positive and negative whole numbers, but they don’t include fractions or decimal numbers. Fractions 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.

Fractions are usually denoted by a numerator or denominator, but mixed fraction has an extra term attached to it. A mixed fraction is also called an improper fraction, whereas the simple fraction is called a proper fraction.

Dividing the natural numbers or whole numbers are is an easy task but dividing fractions are a little complex one. The operations performed on natural numbers and whole consist of simple calculations, which one can easily solve. But the operation performed on fractions are sometimes typical and also time-consuming. The simple division has four parts divisor, dividend, quotient and remainder, but we don’t deal with the division of fractions in the same way.

Dividing fractions by direct method required more effort. Therefore, an alternative method was introduced to solve the division of fractions. In this method, instead of performing division on fractions, we will perform multiplication on it, because multiplication of fractions 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.

How to Divide 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.

In three simple steps, we can solve the division of fractions by converting into 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.

Now let us take some dividing fractions examples, to understand the above steps.

Example: 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: 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 fractions.

Example: 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

How to Divide 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 for dividing fractions.

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

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Practise This Question

The points (2, –1), (3, 4), (–2, 3) and (–3, –2) taken in the order from the vertices of _________________