How to divide fractions

Division of Fractions

Divide implies to distribute anything evenly. After learning about whole number division, let’s move on to fraction division. The numerator and the denominator are the two components of a fraction. Fractional division is almost the same as fractional multiplication. When dividing fractions, we multiply the smaller of the two fractions by their reciprocals. In this tutorial, let’s learn more about how to divide fractions.

How to Divide Fractions?

We are aware that division is a strategy for distributing equitably and forming equal groupings. To obtain the quotient, we divide a whole integer by the divisor. Now, multiplying a fraction by the reciprocal of the second fraction is equivalent to dividing it by another fraction. A straightforward method for switching the numerator and denominator of a fraction is to find its reciprocal. To learn a straightforward rule for splitting fractions, look at the following illustration.

How to divide fractions - KS3 Maths - BBC Bitesize - BBC Bitesize

The division of fractions by fractions, whole numbers, decimals, and mixed numbers will be covered in the parts that follow. We shall always divide fractions according to the same rule as described earlier. Let’s start!

Dividing Fractions by Fractions

Our most recent fraction division lesson involved taking the reciprocal. Let’s now look at an example of how to divide fractions by fractions. Look at the formula for dividing a fraction by a fraction that is provided below. When x/y is divided by a/b, it follows that

x/y ÷ a/b

⇒ x/y × b/a (reciprocal of a/b is b/a)

⇒ xb/ya

We will now substitute the values of the provided numerators and denominators if we need to divide: 5/8 15/16.

5/8 ÷ 15/16 = 5/8 × 16/15 = 2/3

The result of 5/8/15/16 is 2/3.

Division of Fractions with Whole Numbers

We must multiply the denominator of the provided fraction by the supplied whole number in order to divide fractions by whole numbers. If an is a whole number and x/y is a fraction, then x/y a = x/y 1/a = x/ya in the general form.

Let’s use a division example and multiply 2/3 by 4.

2/3 ÷ 4 = 2/3 × 1/4

= 1/6

As a result, 2/3 x 4 equals 1/6. Fractions and whole numbers are divided in this manner.

Dividing Fractions with Decimals

We are aware that decimal numbers themselves are a base-10 fraction. The division can be done once the decimal is represented in fractional form. Follow the instructions below to divide fractions by decimals:

  • Put the given decimal into fraction form.
  • Split the two fractions in half.

Think about the case 4/5 0.5. In this case, 0.5 can be expressed as a fraction as 5/10 or 1/2. Divide 4/5 by 1/2 now. Thus, 4/5 x 1/2 = 4/5 x 2/1 = 8/5 is implied. The division of fractions with decimals is done in this manner. Let’s now examine the division of fractions by mixed numbers.

Division of Fractions and Mixed Numbers

We know how to change mixed fractions into incorrect fractions. To divide fractions containing mixed numbers, first change the mixed fraction to an improper fraction, and then divide the improper fraction as you would any other two fractions.