Q3 of 21 Page 24

Explain each of the patterns below and write the general principle in algebra.

using identity, a2 - b2 = (a + b)(a-b), in the numerator.






Generally, we can write,


where, n can be any natural number.


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1

Explain each of the patterns below and write the general principle in algebra.

 2

Explain each of the patterns below and write the general principle in algebra.

 1

Look at this method of making a pair of equal fraction from another such pair.


i) Check some more pairs of equal fractions. By interchanging the numerator of one with the denominator of the other, do you get equal fractions?


ii) Write this as a general principle using algebra and explain it.

 2

Look at these calculations:


i) Take some more fractions equal to and form fractions by multiplying the numerators and denominators by 3 and 4 and adding.


Do you get fractions equal to


ii) Take some other pairs of equal fractions and check this


iii) In all these, instead of multiplying numerators and denominators by 3 and 4, multiply by some other numbers and add. Do you still get equal fractions?


iv) Explain why, if the fraction is equal to the fraction then for any pair of natural numbers m and n, the fractions is equal to