This page gives detailed information about the concept of division with fraction numbers. We also provide all the important terms, formulae, and the usage of fractions division. You can refer step to step procedure to solve the fraction division problems. This page gives various methods to solve proper, improper, mixed fractions with whole numbers, fractions, etc., and solved examples of division on fractions with an explanation.
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Division of Fractions – Definition
Dividing fractions can be obtained by multiplying the fractions in the reverse order of one of its two fraction numbers which means by writing the multiplicative inverse of one fraction which is also known as reciprocal, reciprocal means if a fraction is given as \(\frac {m}{n} \) then the reciprocal of it will \(\frac {n}{m} \). Here we are simply interchanging the values of the numerator and the denominator with each other.
How to Divide Fractions?
Division of fractions always requires equivalent fractions to solve them. So initially we must make sure that the given fractions are equivalent and then we need to follow the step-by-step procedure to divide the fractions. Generally, dividing fractions in the direct method requires more effort to solve, but don’t worry we are providing a simple and easy method here.
Methods for Dividing Fractions
Any given Fraction number can be divided in three ways, as mentioned below.
- Division of fraction number with a fraction number.
- Division of fraction with the whole number
- Division of fraction with a mixed fraction
Now let us see the way to solve the above-mentioned procedures.
Division of Fraction Number with a Fraction Number
We can divide any given Fractions by following three simple steps. So for dividing any fraction, initially we need to convert it into the multiplication of fractions and then we can obtain the desired result. The procedure is as mentioned below.
- First of all, we need to convert the given second fraction into its reciprocal (multiplicative inverse) and then we need to multiply it with the given first fraction.
- Now we need to multiply the denominators and the numerators of the fractions with each other.
- Finally, we need to simplify the fraction numbers.
Let us consider \(\frac {m}{n} \) is divided with another fraction \(\frac {x}{y} \). Now we can solve the division of these two fraction numbers as:
\(\frac {m}{n} \)÷ \(\frac {x}{y} \)= \(\frac {m}{n} \) * \(\frac {y}{x} \)
\(\frac {m}{n} \)÷ \(\frac {x}{y} \)= \(\frac { m * y }{ n * x } \)
\(\frac {m}{n} \)÷ \(\frac {x}{y} \)=\(\frac { my }{nx } \)
Division of Fraction Number with a Fraction Number
Example 1:
Solve the equation by dividing fraction number \(\frac {2}{3} \) with another fraction number \(\frac {1}{3} \).
Solution:
Initially, we need to convert given into its reciprocal So \(\frac {1}{3} \) becomes \(\frac {3}{1} \).
Now, we have to multiply the given first fraction number with the reciprocal of the second fraction which gives \(\frac {2}{3} \) * \(\frac {1}{3} \)
Multiply both the fractions and simplify \(\frac { 2 * 3 }{ 3 * 1 } \)
Which gives \(\frac {6}{3} \)
Hence, the result obtained by dividing factional number \(\frac { 2 }{ 3 } \) and a fraction number \(\frac { 1 }{ 3 } \) is \(\frac { 6 }{ 3 } \)
This can further simplifed as \(\frac { 2 }{ 1 } \) because both 7 and 14 can be divided by 3.
Answer: 2
How to Divide a Fraction by a Whole Number?
We need to follow the below-mentioned steps to divide a fraction with a whole number.
- We have to convert the given whole numbers into a fraction, this can be obtained by simply adding 1 as its denominator to the given number.
- After converting the given whole number into a fraction, we have to find the reciprocal of the given number.
- Now, we need to multiply the obtained fraction with the given fraction number.
- After doing so we can simplify the equation to its lowest terms.
Dividing Fraction with a Whole Number Examples
Example 1.
Solve the equation divide a fraction number, \(\frac { 4 }{ 5 } \) with a whole number 6?
Solution:
According to our steps first, we need to covert our given whole number 6 into a fractional number by adding 1 as the denominator. So our whole number becomes \(\frac { 6 }{ 1 } \)
Now after converting take the reciprocal of the obtained fractional number, which gives \(\frac {1}{6} \)
Now we need to multiply obtained fraction number and the given fraction number. \(\frac { 4 }{ 5 } * \frac { 1 }{ 6 } \)
To simplify we nedd to muilpty numerators and denominators \(\frac { 4 * 1 }{ 5 * 6 } \)
The result will be \(\frac { 4 }{ 30 } \).
Hence, the result obtained by dividing factional number \(\frac { 4 }{ 5 } \) and the whole number 6 is \(\frac { 4 }{ 30 } \).
This can further simplifed as \(\frac { 2 }{ 15 } \) because both 4 and 30 can be divided by 2.
Answer: \(\frac { 2 }{ 15 } \)
Division of Mixed Fraction with a Whole Number
We need to follow the below-mentioned steps to solve an equation to divide a mixed fraction with a whole number.
- First of all, we need to convert the given mixed fraction number into a fraction number
- We have to convert the given whole numbers into a fraction number, by simply adding 1 as its denominator.
- After this, we have to find the reciprocal of the given number.
- Now, we have to multiply the obtained fraction with the given fraction.
- Finally, we need to solve the equation by simplifying it to its lowest terms.
Division of Mixed Fraction with a Whole Number Examples
Example 1.
Solve the equation by dividing the mixed fraction 4\(\frac { 3 }{ 5 } \) with a whole number 4?
Solution:
First, we need to convert 4\(\frac { 3 }{ 5 } \) to a simple fraction, which gives \(\frac {23}{5} \).
Now we need to covert our given whole number 4 into a fractional number by adding 1 as the denominator. So our whole number becomes \(\frac { 4 }{ 1 } \)
Now after converting we need to find the reciprocal of the obtained fractional number, which gives \(\frac {1}{4} \)
Now we need to multiply both the fraction numbers \(\frac {23}{5} * \frac {1}{4} \)
To simplify we nedd to muilpty numerators and denominators \(\frac { 23 * 1 }{ 5 * 4 } \)
The result will be \(\frac { 23 }{ 20 } \).
Hence, the result obtained by dividing mixed factional number 4\(\frac { 3 }{ 5 } \) and the whole number 4 is \(\frac { 23 }{ 20 } \).