Question

Which of the following is a reducible fraction?

$\left(a\right)\frac{105}{112}$

$\left(b\right)\frac{104}{121}$

$\left(c\right)\frac{77}{72}$

$\left(d\right)\frac{46}{63}$

Answer 1

A fraction that is reducible, have a common factor of numerator and denominator.

Now, Lets check the options,

$\left(a\right)\frac{105}{112}$

The common factor of $105,112=7$

$\frac{105}{112}=\frac{105÷7}{112÷7}=\frac{15}{16}$

[On Dividing both the numerator and the denominator by $7$]
Thus,$\frac{105}{112}$ is a reducible fraction.

$\left(b\right)\frac{104}{121}$

Since, $104,121$ have no common factors. So $\frac{104}{121}$ is not a reducible fraction.

$\left(c\right)\frac{77}{72}$

Since, $77,72$ have no common factors. So $\frac{77}{72}$ is not a reducible fraction.

$\left(d\right)\frac{46}{63}$

Since, $46,63$ have no common factors. So $\frac{46}{63}$ is not a reducible fraction.

Hence, Option $\left(a\right)$ is correct.