In the earlier grades, you must have learned about the division of natural numbers and whole numbers. Fractions are expressed in ratios where numerator and denominator are integers and not equal to zero. Here, we have mentioned the Division of Fractions by using different methods along with examples. Fractions Division is a bit difficult so we have provided an easy and alternative method to perform Division of Fractions. Rather than doing division, you can perform multiplication as it is quite simple in comparison.
Refer to the procedures on how to divide fractions using different methods. For better understanding, we even provided solved examples for a better understanding of the concept.
What is meant by Dividing Fractions?
Dividing Fractions is simply a multiplication of fractions by reversing one of the two fractions or by writing the reciprocal of one of the fractions. If a fraction is given as a/b, then the reciprocal is b/a and is obtained by interchanging the numerator and denominator with each other.
How to Divide Fractions?
Division of Fractions are classified into three different ways and they are as such
- Dividing fractions by a fraction
- Dividing fractions by whole number
- Dividing fractions by mixed fraction
Continue reading the further modules to learn about all three procedures in a detailed way.
Dividing Fraction by a Fraction
Refer to the Procedure of dividing fractions by converting them into a multiplication of fractions. The procedure is as follows
- Write the Reciprocal of Second Fraction and then multiply with the first fraction number.
- Multiply the Numerators and Denominators of both the fractions.
- Simplify the fraction if possible.
If \(\frac { a }{ b } \), \(\frac { c }{ d } \) are two fractions then
\(\frac { a }{ b } \) ÷ \(\frac { c }{ d } \) = \(\frac { a }{ b } \)*\(\frac { d }{ c } \)
= \(\frac { (a×d) }{ (b×c) } \)
= \(\frac { (ad) }{ (bc) } \)
From the above expressions it is clear that we divided \(\frac { a }{ b } \) with \(\frac { c }{ d } \) and then rewrote the same as multiplication of reciprocal of second term i.e. \(\frac { c }{ d } \). Later multiply both the numerators a,d and denominators b,c.
Dividing Fraction by a Whole Number
Division of Fractions with the Whole Number is quite simple. Go through the procedure below to learn how to divide fractions with a whole number. They are along the lines
Step 1: In the first step, change the whole number to a fraction by placing the denominator value 1.
Step 2: Take the Reciprocal of a Number
Step 3: Multiply the fractional value with the given fraction.
Step 4: Simplify the obtained result if possible.
Example:
Divide 3/10 with 5?
Solution:
Given Whole Number is 5
Convert it to a fraction by placing the numerator value as it is and the denominator as 1 i.e. \(\frac { 5 }{ 1 } \)
Take the reciprocal of it i.e. \(\frac { 1 }{ 5 } \)
Multiply \(\frac { 3 }{ 10 } \) and \(\frac { 1 }{ 5 } \) i.e. \(\frac { 3 }{ 10 } \) *\(\frac { 1 }{ 5 } \)
= \(\frac { 3 }{ 50 } \)
Dividing Fractions by a Mixed Fraction
Process of Dividing fractions by a mixed fraction is similar to dividing fraction by fraction. The Procedure to follow for fractions by a mixed fraction are given in the below modules. They are as such
Step 1: In the initial stage convert the given mixed fraction to improper fraction
Step 2: After that, take the reciprocal of the given improper fraction
Step 3: Multiply the obtained fraction with the given fraction
Step 4: Simplify the resultant fraction to possible extent.
Example:
Divide \(\frac { 3 }{ 4 } \) and 5 \(\frac { 1 }{ 2 } \)?
Solution:
Given Mixed Fraction is 5 \(\frac { 1 }{ 2 } \)
Convert it to Improper Fraction i.e. \(\frac { 11 }{ 2 } \)
Take the reciprocal of improper fraction \(\frac { 11 }{ 2 } \) i.e. \(\frac { 2 }{ 11 } \)
Multipy \(\frac { 3 }{ 4 } \) and \(\frac { 2 }{ 11 } \) i.e. \(\frac { (3*2) }{ (4*11) } \)
= \(\frac { 6 }{ 44 } \)
Simplifying it further we get \(\frac { 3 }{ 22 } \)
FAQs on Dividing Fractions
1. What are the basic arithmetic operations performed on Fractions?
The Basic Arithmetic Operations performed on Fractions are
- Addition
- Subtraction
- Multiplication
- Division
2. What is meant by dividing fractions?
Dividing a fraction by another fraction is the same as multiplying the fraction by the reciprocal (inverse) of the other.
3. What are the 3 Rules for Dividing Fractions?
The rules to keep in mind while dividing fractions are as follows
- Flip the divisor into a reciprocal.
- Change the division sign into a multiplication sign and multiply.
- Simplify if possible.
4. What are the different methods in Dividing Fractions?
Dividing Fractions are classified into three different methods and they are as follows
- Dividing fractions by a fraction
- Dividing fractions by whole number
- Dividing fractions by mixed fraction