To add; 3/2+5/3, first we have to calculate the least common divisor which is
2*3 = 6.
then,
3/2+5/3 = (9+10)/6 = 19/6.
Why do we adopt this procedure?
We cannot add apples and oranges. Similarly 3/2 and 5/3 belongs to different categories. 3/2 has 3 times 1/2 and 5/3 has 5 times 1/3. Hence we cannot directly add them. First we should bring them to a common platform . Here LCD 6 comes to our help. 1/6 happens to be the common factor for both the fractions.
9 times 1/6 gives 3/2
9*(1/6) = 3/2
10 times 1/6 gives 5/3
10*(1/6) = 5/3
So instead of adding 3/2 and 5/3; we can easily add 9/6 and 10/6 and get the answer.
9/6 + 10/6 = (9+10)/6 = 19/6
Take a white sheet of unit area and draw the lines as shown in the figure. Each line goes on halving the area(Note: Paper size A series is based on this principle). Now I want to add all the segments' area and get the answer 1. Adding the fractions using our rule,
S = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/64
Note:There are two 1/64 area
=32+16+8+4+2+1+1/64 = 64/64 = 1
Even if the series goes to infinity, the sum will converge at one.
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| EARTH FROM MOON |