Question

Question 7.
Which of the following fraction is the greatest?
(a) $\frac{5}{7}$
(b) $\frac{5}{6}$
(c) $\frac{5}{9}$
(d)$\frac{5}{8}$

Answer 1

(b)

In order to find the greatest fraction among the above given fraction,s we will convert all the fractions to an equivalent fraction with denominator equal to the LCM of their denominators.
$\begin{array}{cc}2& 7,6,9,8\\ 2& 7,3,7,4\\ 2& 7,3,9,2\\ 3& 7,3,9,1\\ 3& 7,1,3,1\\ 7& 7,1,1,1\\ & 1,1,1,1\end{array}$
So, LCM of the denominators i.e. LCM of 7, 6, 9 and 8 = $2\times 2\times 2\times 3\times 3\times 7=504$

The equivalent fractions are:
$\frac{5\times 72}{7\times 72}=\frac{360}{504}$

$\frac{5\times 84}{6\times 84}=\frac{420}{504}$

$\frac{5\times 56}{9\times 56}=\frac{280}{504}$

$\frac{5\times 63}{8\times 63}=\frac{315}{504}$

Clearly,$\frac{420}{504}i.e.\frac{5}{6}$ is greatest.