# 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 thisiii) 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

i)

We observe that, in these cases also, we obtain

ii)

We observe in these cases also, we obtain equal fraction,

iii) let us now take 2 and 5 instead of 3 and 4 in part(ii).

So, again we get equal fractions.

iv) We know that,

When then, aq = pb ………. (1)

for

(ma + np) × b = a × (mb + nq) this must be satisfied

(ma + np) × b = mab + npb ………… (2)

And a × (mb + nq) = mab + nqa

= mab + npb ………… using (1)

a × (mb + nq) = mab + npb ………….. (3)

Since, (2) is equal to (3)

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