Dividing Fractions: Meaning, Examples, Properties

Dividing a fraction is equal to multiplying the fraction by the reciprocal of the second fraction. A fraction is a part of a whole number. It consists of two parts: a numerator and a denominator. A fraction represents ratios or a part of a whole number. It is not an integer but both the numerator and denominators are integers and the denominator can never be equal to zero. 

Fractions can be divided by other Fractions, whole numbers, and decimals. A fraction includes a denominator and a numerator. 

The steps involved in Dividing Fractions are:

1. Finding the reciprocal
2. Converting division into multiplication
3. Simplification

Also check: Types of Numbers

Key Terms: Dividing Fractions, Division of Fractions, Numerator, Denominator, Properties of Dividing Fractions

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What are Fractions?

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A fraction is a part of a whole number or value. It is denoted by p/q or a/b or m/n etc. The upper part of a fraction is referred to as the numerator and the lower part is referred to as the denominator. Some examples of fractions are ¼, ⅔, ½, ⅗, etc.

All arithmetic functions like addition, multiplication, subtraction, and division can be performed on fractions. Let us learn how to divide a fraction by a whole number, by a fraction, and by a mixed number using examples, in simple steps.

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What are Dividing Fractions?

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Dividing a fraction is nothing but multiplying a fraction by inverting one of the two fractional numbers or writing the reciprocal of one of the fractions. By reciprocal, we mean that if a fraction is a/b, its reciprocal will be b/a. Thus, interchanging the numerator and denominator’s positions.

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How to Divide Fractions?

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The division of fractions can be categorized into three different methods, which are

1. Dividing fractions by a fraction
2. Dividing fractions by the whole number
3. Dividing fractions by a mixed fraction

Steps for Fraction Divided by Fractions

In these simple steps, we can solve the division of fractions by converting it into the multiplication of fractions.

1. Change the second fraction by replacing its numerator with the denominator.
2. Multiply the second fraction by the first fraction by multiplying the numerator and denominator together.
3. If necessary, simplify the fraction.

General Solution

If a/b ÷ c/d then it can be solved as,

Solve: ¾ ÷ ½ 

Solution: Given ¾ ÷ ½

Reciprocal another fraction by replacing its numerator with the denominator.

½ will be 2/1 after reciprocating

Multiplication of both numerator and denominator

3/4 x 2/1 = 6/4

Simplifying the fraction

6/4 = 1 2/4

Steps for Dividing Fractions by Whole Numbers

Converting a whole number to a fraction is the same as dividing the fraction by the fraction.

1. Convert a whole number to a fraction using the denominator 1.
2. Make the number reciprocal by exchanging the denominator with the numerator.
3. Multiply by the fraction.
4. Simplify the result if necessary.

General Solution

When a/b is divided by c, it can be solved as,

Solve: 3/8 ÷ 3

Solution: Given, 3/8 ÷ 3

Convert a whole number to a fraction using 1 as the denominator.

3 =3/1

Change the numerator by exchanging the denominator with the numerator.

The reciprocal of 3/1 will be 1/3.

Multiplying by the fraction.

3/8 X 1/3 = 3/24.

Simplify the result if necessary.

Steps for Dividing Fractions by Decimals

Decimal can be represented as a fraction written in a special form whose denominator is the power of ten and whose numerator is represented by places in the figure, for example, 5/10 can be also written as ½ which can be simplified as 0.5, where the zero is in one place and 5 is in the tenth place.

To divide a decimal with a fraction we have to convert the decimal to a fraction by using 1 as the denominator and then multiplying both the denominator and the numerator by 10 for each number after the decimal.

1. Using 1 as the denominator for the decimal.
2. Multiply both the denominator and numerator by 10 for each number after the decimal
3. Change the numerator by exchanging the denominator with the numerator.
4. Multiplying by the fraction. Simplify the result if necessary.

General Solution

When a/b is divided by c, it can be solved as,

Solve: 3/8 ÷ 0.3

Solution: Given, 3/8 ÷ 0.3

Using 1 as the denominator for the decimal

0.3/1

Multiply both the denominator and numerator by 10 for each number after the decimal

0.3/1 x10/10 = 3/10

Change the numerator by exchanging the denominator with the numerator.

The reciprocal of 3/10 will be 10/3.

Multiplying by the fraction.

3/8 X 10/3 = 30/24.

Simplify the result if necessary.

30/24 = 1 7/24

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Properties of Dividing Fractions

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The properties of division with whole numbers are also true for fractions. 

1. When a fraction is divided by 1, the remainder is the fraction itself. 34/1 = 34
2. When zero is divided by a non-zero fraction, the quotient is always zero. 0/34 = 0
3. When a non-zero fraction is divided by itself, the quotient is 1. 34/34 = 1
4. Division by 0 is not possible and the result is undefined. 34/0 = Not Defined

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Things to Remember

The following points will summarize all the important parts of the article:

• A fraction is a part of a whole number. It consists of two parts numerator and a denominator.
• Dividing a fraction is equal to multiplying the fraction by the reciprocal of the second fraction.
• a/b ÷ c/d= a/b × d/c
• The division of fractions can be categorized into three different methods:
  • Dividing fractions by a fraction
  • Dividing fractions by the whole number
  • Dividing fractions by a mixed fraction
• When zero is divided by a non-zero fraction, the quotient is always zero. When a non-zero fraction is divided by itself, the quotient is 1.
• When a fraction is divided by 1, the remainder is the fraction itself. Division by 0 is not possible and the result is undefined.

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