The numerator of a fraction is 3 less than its denominator. If we add

1.	The numerator of a fraction is 3 less than its denominator. If we add 1 to both numerator and denominator, it becomes equal to 5/8. Find the fraction. Please give full explanation and write it on a paper
Answer» EXPLANATION: The numerator of a fraction is 3 less than its denominator. n = d – 3 if we add 1 to both numerator and denominator it becomes equal to 5/8 $\bold{\frac{n + 1}{d + 1} = \frac{5}{8} }$ Cross multiply $\bold{8(n+1) = 5(d+1)}$ $\bold{8n + 8 = 5d + 5}$ $\bold{8n = 5d + 5 - 8}$ $\bold{8n = 5d - 3}$ replace n with (d-3), $\bold{8(d - 3) = 5d - 3}$ $\bold{8d - 24 = 5d - 3}$ $\bold{8d - 5d = - 3 + 24}$ $\bold{3d = 21}$ $\bold{d = \frac{21}{3} }$ $\bold{d = 7}$ Then, $\bold{n = d - 1}$ $\bold{n = 7 - 1}$ $\bold{n = 6}$ THEREFORE, $\bold{ \frac{6}{7} \: is \: the \: fraction}$