I had always been puzzled about fractions right from my childhood days. Why should we take LCM? Why does the method taught in school yields the correct answer? and questions like that. I happened to meet a class 9 student at a temple. During my conversation i asked him about the math syllabus 8th, 9th etc. He talked about LCM HCF GCD and many more. When i asked him what a LCM actually is, he started showing me the method to calculate LCM. But what is an LCM actually? His teacher had not taught that or like most students he did not care about it. After this i went back and started thinking about fractions. So here is what i got.
question 1) why cant we simply add 1/2 + 1/4 while we can do 1/2 + 1/2 or any other fraction addition with common denominator?
ans: Suppose you ve a cake, then 1/2 means dividing it into 2 "equal" parts and taking 1 part out of it.
Similarly 1/4 means dividing the cake in 4 equal part and taking 1 part out of those 4. So obviously we cant simply(easily) add the two "unequal" parts.
ans) LCM gives us the common denominator that we want. How? well, least common multiple means the smallest number which is multiple of given numbers. Eg. LCM of 2 and 3 is 6 coz the first no. which is common in the tables of 2 and 3 is 6.
now, let us add two fractions. 1/2 + 1/4 = 1/2 * (2/2) + 1/4 * (1/1) = 3/4. [Notice the 2/2 and 1/1, they are masked in the school method which we are taught]. why they are used? we want to take the fractions to a common base keeping the ratio same. So multiply and divide by the number which will take that fraction to the common base form.
Hope this was intuitive!
question 1) why cant we simply add 1/2 + 1/4 while we can do 1/2 + 1/2 or any other fraction addition with common denominator?
ans: Suppose you ve a cake, then 1/2 means dividing it into 2 "equal" parts and taking 1 part out of it.
Similarly 1/4 means dividing the cake in 4 equal part and taking 1 part out of those 4. So obviously we cant simply(easily) add the two "unequal" parts.
ans) LCM gives us the common denominator that we want. How? well, least common multiple means the smallest number which is multiple of given numbers. Eg. LCM of 2 and 3 is 6 coz the first no. which is common in the tables of 2 and 3 is 6.
now, let us add two fractions. 1/2 + 1/4 = 1/2 * (2/2) + 1/4 * (1/1) = 3/4. [Notice the 2/2 and 1/1, they are masked in the school method which we are taught]. why they are used? we want to take the fractions to a common base keeping the ratio same. So multiply and divide by the number which will take that fraction to the common base form.
Hope this was intuitive!
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