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Understanding fractions and how to solve them


Math is a vast subject, to say that someone can learn all the necessary concepts in a day is utter foolishness. One such aspect in the learning process which is very elementary but equally important is fractions. These are numerical values of the form “a/b”, where a is called numerator and b is known as denominator. For having a clear understanding of the concept of fraction let us understand it with a practical situation. Suppose there are 10 chocolates and 5 children among whom the chocolates are to be distributed equally. Then how do we do it, the natural instinct is to divide 10 by 5 which will give us 2 which means 2 chocolates per child. What we don’t realize here is that while dividing we are unknowingly operating with fraction. That is 10/5 which is the form of a fraction. Likewise if 1 cake is to be distributed among 4 persons equally, then what would be the fraction here? Total number of cakes/ Total number of people= ¼, this is the fraction here.

Just like many other generic operations in fractions such as adding fractions, subtracting them, multiplying them, there is the operation of dividing fractions.

Division of an object means sharing it equally; we are already familiar with concepts such as division of whole numbers, decimal numbers etc. Now we are going to learn about the division of fractions. A fraction as we already know has two parts. The numerator and denominator. The upper part is called numerator while the part at the bottom is known as denominator. Dividing fractions is nothing but multiplying them. For division we multiply the first fraction by the inverse of the second. That gives us the result of division.

Methodology of division:

For the concept of dividing fractions, we can get a clear understanding with the help of example:

(4/3)/(3/5)= 4/3*5/3= 20/6

In the example given above we can see that 4/3 is to be divided by 3/5. So what we do is we multiply 4/3 by the reciprocal of 3/5 which is 5/3. So now the question becomes 4/3*5/3 which is straight multiplication so the answer is 20/6.

So evidently the thumb rule is (a/b)/(c/d)= a/b*d/c= ad/bc. Solely for the purpose of division.

In the process an additional operation which is to be learnt is the addition of fractions. The process of adding fractions is quite simple to learn. Let us try to understand it with the help of an example:

(3/2)+(7/5)= 15+14/10= 29/10

In the above example we see that there are two fractions 3/2 and 7/5 to add both of them, we first need to find the LCM of the denominators of both the fractions, which means we need to find the LCM of 2 & 5 here which is 10. Then we divide the denominator of both the denominators with 10 and multiply the result with numerator, that is 10 divided by 2 equals 5 and 5 times 3 is 15 so the first one being 10, in the second 10 divided by 5 equals 2 and 2 times 7 equals 14, then we add both of them 15 and 14 we get 29 so our result is 29/10.

Below mentioned are some more examples for better understanding:

  • 2/7 + 6/8 = 16 + 42/56 = 58/56

  • 9/4 + 8/6 = 27 + 16/27 = 43/27

  • 2/9 + 5/7 = 14 + 45/63 = 59/63

  • 5/8 + 6/7 = 35 + 48/56 = 83/56

  • 7/2 + 9/5 = 35 + 18/10 = 53/10

Conclusion:

Understanding of the facts and details mentioned above and examining them with precision makes us understand and aware of the importance of sheer usefulness of fractions and its versatile nature. From the very basic concepts of what is a fraction to performing arithmetic operations with it such as adding and dividing fractions. If you need to know more, you can visit Cuemath for professional help.

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