Q2 of 21 Page 28

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

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)


∴


More from this chapter

All 21 →
3

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.

 3

The sum of the square of a number and one, divided by the difference of 1 from the square gives What is the number?

 4

The sum of a number and its square is one and a half times their difference. What is the number?