Here you can learn completely about the concept of dividing fractions with whole numbers. By going through this entire article you will be able to know what is meant by a fraction and what is a whole number, and the procedure to divide fraction numbers and mixed fractions numbers with whole numbers with few solved examples on this concept with clear explanation.
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What is meant by Division of Fractions?
Dividing fractions can be obtained by multiplying the fractions in reverse of one of its two fraction numbers which means by writing the reciprocal of one fraction, reciprocal means if a fraction is given as \(\frac {x}{y} \) then the reciprocal of it will \(\frac {y}{x} \). This means we are simply interchanging the position of numerator and denominator with each other.
Division of fractions requires equivalent fractions to solve them. So first of all we have to make sure that the fractions are equivalent and then we need to follow all the steps in dividing the fractions. So generally when we are dividing fractions in the direct method it requires more effort, but don’t worry we are providing a simple and easy method here.
Dividing Fraction with a Whole Number
Division of Fraction number by a whole number can be done easily by following the below-mentioned step-by-step procedure.
As we already know, a whole number is nothing but the real numbers, including zero and positive and negative integers.
- We have to convert the whole numbers into a fraction, this can be obtained by simply adding 1 as its denominator.
- After converting the given whole number into a fraction number we have to find the reciprocal of the given number.
- Now, we need to multiply the converted fraction with the given fraction number.
- After doing so we need to simplify the equation to get its lowest terms.
Division of Fractions with Whole Numbers Examples
Example 1:
Solve the equation divide a fraction number, \(\frac { 6 }{ 5 } \) with a whole number 10?
Solution:
According to our steps first, we need to covert our given whole number 10 into a fractional number by adding 1 as the denominator. So our whole number becomes \(\frac { 10 }{ 1 } \)
Now after converting take the reciprocal of the obtained fractional number, which gives \(\frac { 1 }{ 10 } \)
Now we need to multiply obtained fraction number and the given fraction number. \(\frac { 6 }{ 5 } * \frac { 1 }{ 10 } \)
To simplify we nedd to muilpty numerators and denominators \(\frac { 6 * 1 }{ 5 * 10 } \)
The result will be \(\frac { 6 }{ 50 } \).
Hence, the result obtained by dividing factional number \(\frac { 6 }{ 5 } \) and the whole number 10 is \(\frac { 6 }{ 50 } \).
This can further simplifed as \(\frac { 3 }{ 25 } \) because both 6 and 50 can be divided by 2.
Answer: \(\frac { 3 }{ 25 } \)
Example 2:
Solve the equation divide a fraction number, \(\frac { 4 }{ 3 } \) with a whole number 8?
Solution:
According to our steps first, we need to covert our given whole number 8 into a fractional number by adding 1 as the denominator. So our whole number becomes \(\frac { 8 }{ 1 } \)
Now after converting take the reciprocal of the obtained fractional number, which gives \(\frac { 1 }{ 8 } \)
Now we need to multiply obtained fraction number and the given fraction number \(\frac { 4 }{ 3 } * \frac { 1 }{ 8 } \)
To simplify we nedd to muilpty numerators and denominators \(\frac { 4 * 1 }{ 3 * 8 } \)
The result will be \(\frac { 4 }{ 24 } \).
Hence, the result obtained by dividing factional number \(\frac { 4 }{ 3 } \) and the whole number 8 is \(\frac { 4 }{ 24 } \).
This can further simplifed as \(\frac { 1 }{ 6 } \) because both 4 and 24 can be divided by 2.
Answer: \(\frac { 1 }{ 6 } \)
Dividing Mixed Fraction with a Whole Number
To divide the given mixed fractions with a whole number initially, we need to convert the given mixed fraction to a normal fraction(improper fraction), by doing this we can solve the given problem with the same method we used for solving division problems on fraction with the whole number.
We need to follow the below-mentioned steps
- First, we need to convert the given mixed fraction number into a fraction number
- We have to convert the whole numbers into a fraction, this can be obtained by simply adding 1 as its denominator.
- After converting the given while number into a fraction number we have to find the reciprocal of the given number.
- Now, we need to multiply the converted fraction with the given fraction number.
- After doing so we need to simplify the equation to get its lowest terms.
Division of Mixed Fractions with Whole Numbers Examples
Example 1:
Solve the equation divide the mixed fraction 3\(\frac { 1 }{ 2 } \) with a whole number 7?
Solution:
First, we need to convert 3\(\frac { 1 }{ 2 } \) to a simple fraction, which gives \(\frac { 7 }{ 2 } \).
Now we need to covert our given whole number 7 into a fractional number by adding 1 as the denominator. So our whole number becomes \(\frac { 7 }{ 1 } \)
Now after converting we need to find the reciprocal of the obtained fractional number, which gives \(\frac { 1 }{ 7 } \)
Now we need to multiply obtained fraction number and the given fraction number \(\frac { 7 }{ 2 } * \frac { 1 }{ 7 } \)
To simplify we nedd to muilpty numerators and denominators \(\frac { 7 * 1 }{ 2 * 7 } \)
The result will be \(\frac { 7 }{ 14 } \).
Hence, the result obtained by dividing mixed factional number 3\(\frac { 1 }{ 2 } \) and the whole number 7 is \(\frac { 7 }{ 14 } \)
This can further simplifed as \(\frac { 1 }{ 2 } \) because both 7 and 14 can be divided by 7.
\(\frac { 1 }{ 2 } \)Example 2:
Solve the equation divide the mixed fraction 2\(\frac { 2 }{ 5 } \) with a whole number 2?
Solution:
First, we need to convert 2\(\frac { 2 }{ 5 } \) to a simple fraction, which gives \(\frac { 12 }{ 5 } \).
Now we need to covert our given whole number 2 into a fractional number by adding 1 as the denominator. So our whole number becomes \(\frac { 2 }{ 1 } \)
Now after converting we need to find the reciprocal of the obtained fractional number, which gives \(\frac { 1 }{ 2 } \)
Now we need to multiply obtained fraction number and the given fraction number \(\frac { 12 }{ 5 } * \frac { 1 }{ 2 } \)
To simplify we nedd to muilpty numerators and denominators \(\frac { 12 * 1 }{ 5 * 2 } \)
The result will be \(\frac { 12 }{ 10 } \).
Hence, the result obtained by dividing mixed factional number 2\(\frac { 2 }{ 5 } \) with a whole number 2 is \(\frac { 12 }{ 10 } \)
This can further simplifed as \(\frac { 6 }{ 5 } \) because both 12 and 10 can be divided by 2.
\(\frac { 6 }{ 5 } \)