ate 1/3 of the carrot in the morning.
"x" at night.
and 2/5 is leftover
so the sum of all those 3 amounts, should give us a whole.
now the LCD of those denominators is 15, 3 is prime, 5 is prime, so the LCD is simply their product.
since the LCD is 15, a "whole" is just 1, namely in this case, a whole is 15/15 = 1.
what we'll do is, multiply both sides by the LCD, to do away with the denominators.
[tex]\bf \stackrel{\textit{morning}}{\cfrac{1}{3}}+\stackrel{\textit{night}}{x}+\stackrel{\textit{leftover}}{\cfrac{2}{5}}=\stackrel{\textit{whole}}{\cfrac{15}{15}}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{15}}{15\left( \cfrac{1}{3}+x+\cfrac{2}{5} \right)=15\left( \cfrac{15}{15} \right)} \\\\\\ (5)1+(15)x+(3)2=(1)15\implies 5+15x+6=15\implies 15x+11=15 \\\\\\ 15x=4\implies x=\cfrac{4}{15}[/tex]
