Dividing Fractions

A fraction represents a portion of a total. This entire area can be considered a region or a collection. Fraction comes from the Latin word “fractio,” which literally means “to shatter.” The Egyptians were the first society to understand fractions, and they employed fractions to address their mathematical challenges, which included dividing food and supplies, as well as the lack of a bullion currency. The Fractions only written in Ancient Rome using the words to define a portion of the whole. In India, fractions were first written without a line, with one number above the other (numerator and denominator). 

The word “division” means the equitable distribution of the resource. There are two kinds of fractions: a numerator and a denominator. We multiply the first fraction by the reciprocal (inverse) of the second fraction to divide fractions.

To find the quotient, divide a whole number by the divisor. Now, the multiplication of a fraction by the reciprocal of the second fraction is the same as dividing a fraction by another fraction. The reciprocal of a fraction is a simple technique to swap the numerator and denominator of a fraction.

Fractions Divided by Fractions

We just learnt how to use the reciprocal to divide fractions. Let’s have a look at how to divide fractions by fractions using an example. Take a look at the following formula for dividing a fraction by a fraction. If 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

Now, if we need to divide 5 / 8 ÷ 15 / 16, we will substitute the numerators and denominators’ values.

5 / 8 ÷ 15 / 16 = 5 / 8 × 16 / 15 = 2 / 3

∴ 5 / 8 ÷ 15 / 16 = 2 / 3.

Fraction Division with Whole Numbers

We must multiply the denominator of the provided fraction with the given whole number to divide fractions with whole numbers. If x / y is a fraction and an is a whole number, then 

x / y  ÷ a = x / y x 1 / a = x / ya is the general form.

Fractional division using entire numbers

Let’s use 2 / 3 as an example and divide it by 4.

2 / 3 ÷ 4 = 2 / 3 × ¼ = 1 / 6

As a result, 2 / 3 ÷ 4 equals 1 / 6. This is how we divide whole numbers by fractions.

Using Decimals to Divide Fractions

We already know that decimal numbers are fractions with a basis of ten. We can represent the decimal in fractional form and divide from there. Given below are the instructions to divide fractions with decimals:

When converting a decimal to a fraction, use the formula below.

Divide the fractions in half.

Take the example of 4 / 5 ÷ 0.5. In this scenario,  0.5 can be expressed as 5 / 10 or 1 / 2 in fractional form. Divide 4 / 5 by 1 / 2 now. This means that 4 /  ÷ 5 1 / 2 = 4 / 5 x 2 / 1 = 8 / 5. The division of fractions with decimals is done in this manner.

Fractions and Mixed Numbers Division

We’ve learned how to divide improper fractions into mixed fractions. To divide fractions with mixed numbers, first convert the mixed fraction to an improper fraction, then divide them as if they were two fractions. Consider the following illustration.

3 / 4 ÷ 112

As a result, the first step is to change 112 to an incorrect fraction. 3 / 2 is exactly same as 112.

It can now be solved in the following manner:

3 / 4 ÷ 3 / 2

⇒ 3 / 4 × 2 / 3

⇒ 6 / 12 = 1 / 2

As a result, 3 / 4 ÷ 112 equal 1 / 2. If you want to divide a mixed number by a fraction, convert it to an improper fraction first and then follow the techniques outlined above.

Conclusion:

Dividing two fractions by the reciprocal of the first fraction is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step in splitting fractions is to get the reciprocal (reversing the numerator and denominator) of the second fraction. After that, multiply the two numerators together. Then combine the two denominators. Finally, simplify the fractions if necessary.