Dividing Fractions

A fraction is a part of whole number it consist of two parts numerator and a denominator .A fraction is a representation of ratios or a part of a whole number .It is not an integer but both the numerator and denominators are integers and denominator can never be equal to zero. Fraction can be divided by other Fractions, whole numbers and decimals .In this article we will go through what is dividing fractions, how to divide fraction?Dividing fractions by whole number, how to divide decimal fraction ,how to divide a fraction over a fraction and solve some word problem and examples as we go through the topic.

Dividing Fractions is division of fraction or as same as multiplying the fraction by the reciprocal which is inverse of the other fraction. We can get reciprocal of a fraction by interchanging its numerator with its denominator. This method of dividing the fraction by multiplying with the reciprocal was introduced later as division of fraction by direct method required more effort. Here, we will learn different methods on dividing fractions with some examples.

(Image to be added soon)


How To Divide Fractions?

Fraction can be divided with other fractions, whole numbers and decimals.  For dividing the whole number and decimal with fraction it needs to be converted into fractional form. Dividing fractions with fractions just requires a few steps just by reciprocating the other fraction and then multiplying it with the first one.

(Image to be added soon)


Steps For Fraction Divided By Fractions

In these simple steps we can solve division of fraction by converting it into multiplication if fraction.

  1. Reciprocate the second fraction by interchanging its numerator with the denominator.

  2. Multiply the second fraction with the first one by multiplying the numerators and denominators with each other.

  3. Simplify the fraction, if needed.


General Solution:

If a/b is divide by c/d then we can solve it as,

  • a/b ÷ c/d = a/b × d/c

  • a/b ÷ c/d = a×d / b×c

  • a/b ÷ c/d = ad/bc

(Image to be added soon)


Examples -

  ¾ ÷ ½ 

Solution:  Given ¾ ÷ ½ 

Reciprocating the second fraction by interchanging its numerator with denominator.

½ after reciprocating will be 2/1 

Multiplying both numerator and denominator

 3/4 x 2/1 = 6/4

Simplify the fraction

6/4 = 1 2/4


Steps For Dividing Fractions By Whole Numbers 

Dividing the whole number is the same as dividing fraction with fraction just by changing the whole number into fractions.

  1. Convert the whole number into fraction by using denominator as 1. 

  2. Reciprocate the number by interchanging the denominator with the numerator. 

  3. Multiply by the fraction. 

  4. Simplify the result, if needed. 


General Solution:

If a/b is divide by c then we can solve it as,

  • a/b ÷ c/1 = a/b × 1/c

  • a/b ÷ c/1 = a×1 / b×c

  • a/b ÷ c/1 = a/bc

3/8 ÷ 3

Solution: Given, 3/8 ÷ 3

Convert the whole number into fraction by using denominator as 1.

3 =3/1

Reciprocate the number by interchanging the denominator with the numerator. 

Reciprocal of 3/1 will be 1/3.

Multiply by the fraction. 

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

Simplify the result, if needed. 


Steps For Dividing Fractions By Decimals

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

To divide a decimal with a fraction we need to change the decimal into fraction by writing the denominator as 1 and then multiplying both numerator and denominator by 10 for every number after the decimal.

  1. Writing the denominator as 1 for the decimal

  2. Multiplying both numerator and denominator by 10 for every number after the decimal.

  3. Reciprocate the number by interchanging the denominator with the numerator. 

  4. Multiply by the fraction. 

Simplify the result, if needed


General Solution:

If a/b is divide by c then we can solve it as,

  • a/b ÷ 0.c= a/b ÷( 0.c/1)

  • a/b ÷ 0.c= a/b ÷( 0.c/1 x 10/10)

  • a/b ÷ 0.c= a/b ÷c/10

  • a/b ÷ 0.c = a/b × 10/c

  • a/b ÷ 0.c = a×10 / b×c

  • a/b ÷ 0.c = 10a/bc


Examples

3/8 ÷0.3

Solution: Given, 3/8 ÷ 0.3

Writing the denominator as 1 for the decimal

0.3/1

Multiplying both numerator and denominator by 10 for every number after the decimal.

0.3/1 x10/10 = 3/10

Reciprocate the number by interchanging the denominator with the numerator. 

Reciprocal of 3/10 will be 10/3.

Multiply by the fraction. 

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

Simplify the result, if needed. 

30/24 = 1 7/24


Questions To Be Solved:

  1. 7/8÷3/9

  2. 3/4÷5/8

  3. 4/8÷ 9

  4. 6/7 ÷18

  5. 3/4÷0.5

  6. 4/8÷ 0.8


Solved Example:-

Question 1:    ¾ ÷ ½ 

Solution:  Given ¾ ÷ ½ 

Reciprocating the second fraction by interchanging its numerator with denominator.

½ after reciprocating will be 2/1 

Multiplying both numerator and denominator

3/4 x 2/1 = 6/4

Simplifying the fraction,

6/4 = 3/2


Interesting Facts-

  • Every fraction has two parts numerator and denominator the numerator of the fraction sums up the equal number of parts we have and the denominator part of the fraction sums up the total number of parts as a whole.

  • The denominator of a fraction can never be less than or equal to zero.

  • Multiplication and division of fraction do not require a common denominator.

FAQ (Frequently Asked Questions)

1. How To Reciprocate A Fraction And Why Its Sign Changes?

We can reciprocate a fraction by simply switching the denominator with the numerator. Reciprocating the fraction changes the sign because the inverse of multiplication is division .Dividing Fractions is division of fraction or as same as multiplying the fraction by the reciprocal which is the inverse of the other fraction. We can get reciprocal of a fraction by interchanging its numerator with its denominator. This method of dividing the fraction by multiplying with the reciprocal .The reciprocal of the sign of multiplication is division.That is the reason why the sign of multiplication changes to division.

2. How To Convert Decimal Into Fraction And How To Divide?

Division of fraction or as same as multiplying the fraction by the reciprocal which is inverse of the other fraction. We can get reciprocal of a fraction by interchanging its numerator with its denominator.We can change the decimal into fraction by writing the denominator as 1 and then multiplying both numerator and denominator by 10 for every number after the decimal.

To divide a decimal with a fraction we need to change the decimal into fraction by writing the denominator as 1 and then multiplying both numerator and denominator by 10 for every number after the decimal.

  1. Writing the denominator as 1 for the decimal

  2. Multiplying both numerator and denominator by 10 for every number after the decimal.

  3. Reciprocate the number by interchanging the denominator with the numerator. 

  4. Multiply by the fraction. 

  5. Simplify the result, if needed.