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How to Divide Fractions

In arithmetic, dividing fractions is much tricky but not difficult. If we ignore the reciprocal it is similar to the multiplication of fractions. In this section, we will learn how to divide fractions.

We can also divide a fraction by applying the division symbol (÷) between dividend and divisor. The fraction that is left of the division symbol is called the dividend, and the fraction that is right to the division symbol is called the divisor.

How to Divide Fractions

Methods of Dividing Fractions

There are two methods to divide fractions.

  • Invert and Multiply Method
  • Common Denominator Method

We can use both the methods in the following cases:

  • when the denominators are the same
  • when the denominators are different

Invert and Multiply Method

It is the easiest and commonly used method to divide fractions. In this method, first, we find the reciprocal (invert) of the divisor. After that multiply the dividend by the reciprocal. Do not use this for a complex problem.

  • Find the reciprocal of the divisor fraction by swapping the numerator and denominator.
  • Multiply the dividend fraction by the reciprocal.
  • Simplify the fraction if required.

Suppose, How to Divide Fractions and How to Divide Fractions are two fractions and we want to divide How to Divide Fractions by How to Divide Fractions then:

How to Divide Fractions

Suppose, How to Divide Fractions and How to Divide Fractions are two fractions and we want to divide How to Divide Fractions by How to Divide Fractions then:

How to Divide Fractions

It is because if we find the reciprocal of the divisor, we get How to Divide Fractions. Now multiply the dividend by the reciprocal, we get:

How to Divide Fractions
How to Divide Fractions

Solution:

In the above question, How to Divide Fractions is the dividend and How to Divide Fractions is the divisor.

Step 1: Find the reciprocal of the divisor.

How to Divide Fractions

Step 2: Multiplying dividend by the reciprocal.

How to Divide Fractions

Hence, on dividing How to Divide Fractions by How to Divide Fractions, we get How to Divide Fractions as quotient.

Common Denominator Method

In this method, we make the denominators of both fractions the same. It is the most correct method to divide fractions. Find a common denominator and convert each fraction to its equivalent value.

  • Now denominators are the same, we will divide the numerators only.
  • Simplify the fraction if required.

Note: When converting the fraction to its equivalent value, multiply the same number in numerator and denominator.

How to Divide Fractions

Solution:

In the above question, How to Divide Fractions is the dividend and How to Divide Fractions is divisor.

Step 1: To find the common denominator, we will multiply How to Divide Fractions by 5, and How to Divide Fractions by 4.

How to Divide Fractions

Step 2: Divide the numerator of the fractions.

How to Divide Fractions

Hence, on dividing How to Divide Fractions by How to Divide Fractions, we get How to Divide Fractions as quotient.

How to Divide Fractions

Solution:

In this question, How to Divide Fractions is the dividend and How to Divide Fractions is the divisor having the same denominator. So, we will divide the numerator only, i.e. How to Divide Fractions.

Hence, on dividing How to Divide Fractions by How to Divide Fractions, we get How to Divide Fractions as quotient.

Dividing Fraction and Whole Number

We can also divide a fraction by whole number or vice-versa. While dividing a fraction by the whole number, convert the whole number into a fraction by putting 1 in the denominator. It does not change the value. After that solve the question by using any one method that we have discussed above.

How to Divide Fractions

Solution:

In this question, the divisor is not in the fractional form. First, we will convert the whole number (7) into a fraction, i.e.,How to Divide Fractions. Now we have converted the question into the following:

How to Divide Fractions

Step 1: Find the reciprocal of the divisor.

How to Divide Fractions

Step 2: Multiplying dividend by the reciprocal.

How to Divide Fractions

Hence, on dividing How to Divide Fractions by 7, we get How to Divide Fractions as quotient.

How to Divide Fractions

Solution:

In this question, the dividend is not in the fractional form. First, we will convert the whole number (13) into a fraction, i.e.,How to Divide Fractions. Now we have converted the question into the following:

How to Divide Fractions

Step 1: Find the reciprocal of the divisor.

How to Divide Fractions

Step 2: Multiplying dividend by the reciprocal.

How to Divide Fractions

Hence, on dividing 13 by How to Divide Fractions, we get 104 as quotient.

Dividing Mixed Fraction

When dealing with the mixed fraction, follow the steps given below:

  • Convert the mixed fractions into an improper fractions.
  • Find the reciprocal of the divisor fraction by swapping the numerator and denominator.
  • Multiply the dividend fraction by the reciprocal.
  • Simplify the fraction if required.
How to Divide Fractions

Solution:

Step 1: Convert the mixed fraction into an improper fraction, that is:

How to Divide Fractions

Step 2: Find the reciprocal of the divisor, that is:

How to Divide Fractions

Step 3: On multiplying the dividend fraction by reciprocal, we get:

How to Divide Fractions

Dividing More Than Two Fractions

We use the inverse and multiply method when any number of fractions is given for division. After this simplify the fraction, if required.

How to Divide Fractions

Solution:

Write the first fraction the same, and apply inverse, and multiply method in other fractions. Simplify the fraction, if required.

How to Divide Fractions




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