Here on this page, you will be able to learn completely about the concept of dividing the whole number with a fraction number. By going through this page, you will know what is meant by a whole number and what is a fraction number, and step by step procedure to solve problems on dividing whole numbers with a fraction. Check out the few solved examples on this concept given with a clear explanation.
Also read,
- Facts about Divison
- Long Divison
- Division of a Fractional Number
- Division of a Fraction by a Whole Number
What does it mean by Division of Fractions?
Dividing fractions can be done by simply multiplying the fractions in reverse order of one of its two fractions this means by writing the multiplicative inverse of one the given fractions, multiplicative inverse which is also known as reciprocal means if a fraction is given as \(\frac {ab}{y} \) then the reciprocal of that fraction will become \(\frac {b}{a} \). In simpler words, this means we are interchanging the position of numerator and denominator with each other.
So whenever we are dividing a fraction it requires always have to an equivalent fraction to solve them. So we always have to make sure that the given fractions are equivalent so that we can produce further after that need to follow all the steps while dividing a whole number with a fraction number.
How to Divide a Whole Number by a Fraction?
So first we need to know a whole number is a real number, which includes zero along with all positive and negative integers.
Now dividing a whole number with a fraction number can be easily done by following few simple steps that are below-mentioned.
- Initially, we need to convert the given whole numbers into a fraction so that we can easily divide both fractions, so to do this we have to simply add 1 as the denominator.
- After doing so we have to find the reciprocal for the obtained fraction number.
- Now, that we have both the factions we need to multiply them with each other.
- Finally, we can simplify the obtained equation to get its lowest terms.
Let us see few examples of this concept following the above-mentioned procedure for better understanding.
Dividing Whole Numbers by Fractions Examples
Example 1:
Solve the equation dividing a whole number 5 with a faction number \(\frac { 2 }{ 4 } \)
Solution:
First, of all, we need to convert our given whole number 5 into a fractional number by simply just adding 1 as its denominator. So our whole number becomes \(\frac { 5 }{ 1 } \)
Now the reciprocal of this faction can be obtained will be \(\frac { 1 }{ 5 } \)
Now we have to multiply both facrtions \(\frac { 1 }{ 5 } * \frac { 2 }{ 4 } \)
As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 2 }{ 5 * 4 } \)
The result will be \(\frac { 2 }{ 20 } \).
Hence, the result of dividing a whole number 5 with a facrtion \(\frac { 2 }{ 4 } \) is \(\frac { 2 }{ 20 } \).
This fraction can further simplifed as \(\frac { 1 }{ 10 } \) because both integers 2 and 20 can be divided by 2.
\(\frac { 1 }{ 10 } \)Example 2:
Solve the equation dividing a whole number 8 with a faction number \(\frac { 3 }{ 7 } \)
Solution:
First, of all, we need to convert our given whole number 8 into a fractional number by simply just adding 1 as its denominator. So our whole number becomes \(\frac { 8 }{ 1 } \)
Now the reciprocal of this faction can be obtained will be \(\frac { 1 }{ 8 } \)
Now we have to multiply both facrtions \(\frac { 1 }{ 8 } * \frac { 3 }{ 7 } \)
As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 3 }{ 8 * 7 } \)
The result will be \(\frac { 3 }{ 57 } \).
Hence, the result of dividing a whole number 8 with a facrtion \(\frac { 3 }{ 7 } \) is \(\frac { 3 }{ 57 } \).
Both these integers 3 and 57 can’t be simplified further so the answer remains the same.
Answer: \(\frac { 3 }{ 57 } \).
Dividing a Whole Number with a Mixed Fraction
We can divide the given Whole number with a mixed faction by initially converting the given mixed fraction to an improper fraction or a simple fraction so that we can solve the given problem with the same method we used for solving dividing a whole number with a fraction. To do so we need to follow the step-by-step procedure as below-mentioned.
- So as already mentioned first we need to convert the given mixed fraction number into a simple faction.
- After doing so we need to convert the given whole number into a simple fraction by simply adding 1 as its denominator.
- Now we have to find the reciprocal of the obtained fraction.
- Finally, we need to multiply both the fractions.
- We need to simplify the fraction to get its lowest terms if it is possible.
Let us see few examples of this concept following the above-mentioned procedure for better understanding.
Dividing Whole Numbers by Mixed Numbers Examples
Example 1:
Solve the equation dividing a whole number 7 with a mixed fraction 3\(\frac { 3 }{ 5 } \)
Solution:
Firstof all, we need to convert 3\(\frac { 3 }{ 5 } \) to a simple fraction, which gives \(\frac { 18 }{ 5 } \).
Now we have to 1 as the denominator to our whole number 7 which give \(\frac { 7 }{ 1 } \)
Let us find the reciprocal of \(\frac { 7 }{ 1 } \) which gives \(\frac { 1 }{ 7 } \)
And now finally we need to multiply these two fractions \(\frac { 1 }{ 7 } * \frac { 18 }{ 5 } \)
Which gives \(\frac { 1 * 18 }{ 7 * 5 } \)
The result will be \(\frac { 18 }{ 35 } \).
So, the result of dividing the whole number 7 with a mixed factional 3\(\frac { 3 }{ 5 } \) and is \(\frac { 18 }{ 35 } \)
This can’t be simplified further so the answer remains the same.
\(\frac { 18 }{ 35 } \)Example 2:
Solve the equation dividing a whole number 2 with a mixed fraction 8\(\frac { 2 }{ 3 } \)
Solution:
Firstof all, we need to convert 8\(\frac { 2 }{ 3 } \) to a simple fraction, which gives \(\frac { 26 }{ 3 } \).
Now we have to 1 as the denominator to our whole number 2 which give \(\frac { 2 }{ 1 } \)
Let us find the reciprocal of \(\frac { 2 }{ 1 } \) which gives \(\frac { 1 }{ 2 } \)
And now finally we need to multiply these two fractions \(\frac { 1 }{ 2 } * \frac { 26 }{ 3 } \)
Which gives \(\frac { 1 * 26 }{ 2 * 3 } \)
The result will be \(\frac { 26 }{ 6 } \).
So, the result of dividing the whole number 2 with a mixed factional 8\(\frac { 2 }{ 3 } \) and is \(\frac { 26 }{ 6 } \)
This fraction can further simplifed as \(\frac { 13 }{ 3 } \) because both integers 26 and 6 can be divided by 3.
\(\frac { 13 }{ 3 } \)