Before I begin this chapter, let me make an honest confession. Back in my school days, I had a Mathematics teacher who taught me fractions using the conventional method. The method she used was the LCM method, which I found pretty dull and boring.
In both these fractions, the denominators are different. In the first fraction the denominator is 5 and in the second fraction the denominator is 2. Because the denominators are different, we cannot add them directly. We will first have to find a common multiple of the two denominators. (LCM = Least Common Multiple)
Now we know that 10 is a common multiple of both 5 and 2 and hence we will use 10 as our common denominator. At this stage our answer would look like
We know the denominator is 10 but the numerator is still unknown.To calculate the numerator, we were taught to write a small 10 near each of the fractions.
Next, we had to divide this 10 by the denominator and the quotient so obtained had to be multiplied by the numerator.
So, in the first fraction, 10 divided by the denominator 5 would give a quotient of 2 which had to be multiplied by 3 (the numerator).
Similarly, for the second fraction, if we divide 10 by 2 we get 5 and this 5 multiplied by the numerator 1 gives us an answer of
Could be quite confusing for young children who are introduced to addition and subtraction of fractions for the first time. No wonder many people hate Math in school!
Now let us see an alternative method of adding and subtracting fractions. It is fast and gives the answer directly.
ALTERNATIVE METHOD
This technique has two steps. Here are the steps. Read carefully.
• Cross multiply the numerators and denominators to get the new numerator
• Directly multiply the denominators to get the new denominator.
We first cross multiply (3 × 2) and get 6. Next, we cross multiply (5 × 1) and get 5. Now 6 + 5 is 11 which becomes our final numerator.
Next, we directly multiply the denominators (5 × 2) and get our final numerator as 10.
No need to find the LCM and go through the whole procedure of dividing and multiplying. Easy, isn’t it?
Let us see a few more examples of adding and subtracting fractions using the Vedic Mathematics method
Let us solve one more question.
(Note: Another way to solve this question is to simply multiply the second fraction 3/5 with 3 and write the fraction as 9/15. We are doing this so that both denominators are now 15. Next, we simply add 11/15 and 9/15 to get the answer as 20/15 or 4/3.Both methods are correct.)
SUBTRACTION OF FRACTIONS
The technique for subtraction of fractions is the same. The only difference here is that instead of adding the fractions we will be subtracting them.
So, we can see from the above examples that the LCM method is not the only method to add or subtract fractions. We can also use the cross multiplication method as shown here.
In the exam, you must observe the question and decide which method to use. As I mentioned earlier, in my school, my Mathematics teacher taught me only the LCM method.
The cross multiplication method that I have taught here was something that I learnt many years later.
Generally, when there are two fractions to be added or subtracted, the cross multiplication method is faster.
However,if the number of fractions to be added or subtracted are three or more, then the LCM method may prove better. Always look at the denominators of all the fractions and decide.
In the chapters to follow, we will be adding and subtracting a lot of fractions. So this technique will prove extremely useful.
