Question

a strip of wood 78 inches long is to be cut into pieces of 3 and 3/4 inches long how many pieces can be cut

Answer 1

Namely, how many times does 3¾ go into 78?  well, is just their quotient.

let's firstly convert the mixed fraction to "improper", and then divide,

$\bf \stackrel{mixed}{3\frac{3}{4}}\implies \cfrac{3\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{15}{4}}\\\\ -------------------------------\\\\ \cfrac{\quad 78 \quad }{\frac{15}{4}}\implies \cfrac{\quad \frac{78}{1} \quad }{\frac{15}{4}}\implies \cfrac{78}{1}\cdot \cfrac{4}{15}\implies \cfrac{26}{1}\cdot \cfrac{4}{5}\implies \cfrac{104}{5}\implies 20\frac{4}{5}$

so, if we nevermind the 4/5 part, only 20 whole of those then.