
Portinkam 
Before we jump into the
division of fraction by fraction, let's look at or understand some few basic terms, which are very important for understanding the mathematical concept of fraction:
Fraction
Fraction is a part of a whole or ratio of two numbers, the numerator, and denominator, with the numerator written above the denominator.
Numerator
The numerator infraction is the number written above the division line in a fraction as seen in the above picture.
Denominator
While denominator infraction is a number written below the division line in a fraction.
Reciprocal Number
Reciprocal simply means the opposite version of something such as come and go, sleep and wake up and so on.
In mathematics:
Reciprocal number infraction is an arithmetic expression where the denominator is taken to the top of the division line and the numerator to the bottom of the division line.
In general, reciprocal of a number is the number obtained by dividing the number with one.
Example 1: what is the reciprocal number of 2?
Answer: the reciprocal number of 2 is 1/2.
As you can see from the above example, the reciprocal number is obtained by dividing the whole number with 1.
But, this is a whole number. What if you are asked to find the reciprocal number of a fraction?
That is what we are going to be discussing now:
Reciprocal Fraction
Reciprocal fraction is obtained by exchanging or flipping the numerator to the bottom of the fraction, and the denominator to the top of the fraction. In other words, taking numerator from above the fraction to the bottom of the fraction, and taking denominator from bottom of the fraction to the top of the fraction.
Example 2
What is the reciprocal fraction of 2/5?
Answer
The reciprocal fraction of 2/5 is 5/2.
Example 3
What is the reciprocal fraction of 42/3?
Answer
This type of fraction is called mixed fractions. Because the fraction contains a whole number and fraction combined together.
42/3
Therefore, we need to simplify the mixed fraction to fraction.
42/3 = 14/3
The above result is obtained by multiplying 4 and 3 and then adding the result with 2.
In practice,
4× 3 = 12 + 2 = 14
Then, divide the final result with the denominator of the mixed fraction.
That is, 14/3
Now, with this solid background about fraction, let's talk about the division of fraction by fraction:
Division Of Fraction By Fraction
To
divide a fraction by fraction, it simply means to find out how many times a given denominator of fraction can be found in a given numerator of fraction.
Example 4
If someone gave you 5 oranges to share between you and your sister. And the person who gave you the oranges told you to take 3 oranges and give the remaining 2 oranges to your sister.
In mathematics, this statement can be summarised as follows:
Total number of the oranges = 5
Your share in 5 oranges = 3
Your sister's share in 5 oranges = 2
Infraction,
You will have 3 out of 5 oranges
3/5
And your sister will be having 2 out of 5 oranges,
2/5
Now, how many 3/5 can be found in 2/5
This means 2/5 of your sister's share divided by your own share.
That is, 2/5 ÷ 3/5
Now, to divide 2/5 3/5, we need to first change the division sign to multiplication sign.
To do this, we need to take the reciprocal of ÷ 3/5
If you could remember, the reciprocal fraction is obtained by taking denominator of fraction to the top, and numerator of fraction to the bottom.
Therefore,
3/5 = 5/3
And also, the division sign will also change to a multiplication sign, when you take the reciprocal fraction.
Therefore,
÷3/5 = ×5/3
When you replace ÷ 3/5 with ×5/3 in the above fraction,
The expression 2/5 ÷ 3/5 will completely change to:
2/5 × 5/3
Then, the next thing multiply the numerators of both fractions and also multiply the denominators of both fractions.
In practice,
2/5 × 5/3
Numerators = 2× 5 = 10
Denominator = 5×3 = 15
The new fraction will look this:
New fraction = 10/ 15
But, the above expression can be simplified further. 5 can go into 10 and 15.
Therefore,
10/25 = 2/3
5 divides 10 2 times, and divides 15 3 times.
This shows that we can find 2/3 of 3/5 is 2/5.
Worked Example 1
Divide 4/7 by 3/4
Answer
4/7 ÷ 3/4
Take the reciprocal fraction of ÷3/4
÷ 3/4 = × 4/3
Multiply the reciprocal fraction with the given expression
That is,
4/7 × 4/3 = 16/21
Worked Example 2
Divide 31/2 by 2/3
Answer
One of the fractions is from the given expression is mixed fraction.
So, we need to change the mixed fraction to improper or proper fractions.
Therefore,
31/2 ÷ 2/3 = 7/2 ÷ 2/3
Take the reciprocal fraction of ÷ 2/3.
÷ 2/3 = × 3/2
Multiply the reciprocal fraction with the given expression.
That is,
7/2 × 3/2 = 21/4
Related: Division of fraction by fraction
Conclusion
I hope this guide helps you in understanding fraction, terms commonly use infraction and how to divide fraction by fraction.
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