Problem: Which is smaller, 1/3 or 5/9 ? (equivalent fractions)
Problem: Which is smallest, 1/3 or 5/9 ?
Solutions:
This is problem of equivalent fractions !
We are given to fractions,
\[ \frac{1}{3} \] —————–(1)
and
\[ \frac{5}{9} \] ——————-(2)
and we have to tell which one is smallest !
We note that in the second fraction denominator is 9 i-e 5 is being divided by 9
To tell answer we have to make denominator in the first fraction 9 as well !
This can be done by multiplying nominator and denominator by 3
i-e
\[ \frac{1}{3}=\frac{1\times 3}{3\times3}=\frac{3}{9} \] ——————(3)
So, third fraction is equivalent of first fraction – because if we cancel 3 by three in third fraction we again get the first fraction.
Now according to second fraction 5 (bigger thing) is divided by 9 , but in third fraction 3(smaller thing) is divided by 9 , So, obviously the answer of second fraction will be greater and that of thrid fraction will be smaller — so the thrid fraction is smaller !
But third fraction is equivalent of first fraction – hence we can say between first and second fractions – the first one is smaller !