$\begin{align} \frac{3}{4}+\frac{1}{16} &\cssId{Step1}{= \frac{3}{4}\left(\frac{4}{4}\right)+\frac{1}{16}\left(\frac{1}{1}\right)}\\ &\cssId{Step2}{= \frac{12}{16}+\frac{1}{16}}\\ &\cssId{Step3}{= \frac{12+1}{16}}\\ &\cssId{Step4}{= \frac{13}{16}} \end{align}$
$\text{Multiples of 4 are 4, 8, 12, 16, 20, ...}$
$\text{Multiples of 16 are 16, 32, 48, 64, 80, ...}$
$\text{Since 16 is the first multiple of each that matches, LCD = 16.}$
$\text{Also, fractions}$ $\frac{3}{4}=\frac{12}{16}$ $\text{and}$ $\frac{1}{16}=\frac{1}{16}$.
$\begin{align} \frac{1}{6}+\frac{7}{15} &\cssId{Step5}{= \frac{1}{6}\left(\frac{5}{5}\right)+\frac{7}{15}\left(\frac{2}{2}\right)}\\ &\cssId{Step6}{= \frac{5}{30}+\frac{14}{30}}\\ &\cssId{Step7}{= \frac{5+14}{30}}\\ &\cssId{Step8}{= \frac{19}{30}} \end{align}$
$\text{Multiples of 6 are 6, 12, 18, 24, 30, ...}$
$\text{Multiples of 15 are 15, 30, 45, 60, 75, ...}$
$\text{Since 30 is the first multiple of each that matches, LCD = 30.}$
$\text{Also, fractions}$ $\frac{1}{6}=\frac{5}{30}$ $\text{and}$ $\frac{7}{15}=\frac{14}{30}$.
$\begin{align} \frac{5}{12}-\frac{3}{8} &\cssId{Step9}{= \frac{5}{12}\left(\frac{2}{2}\right)-\frac{3}{8}\left(\frac{3}{3}\right)}\\ &\cssId{Step10}{= \frac{10}{24}-\frac{9}{24}}\\ &\cssId{Step11}{= \frac{10-9}{24}}\\ &\cssId{Step12}{= \frac{1}{24}} \end{align}$
$\text{Multiples of 12 are 12, 24, 36, 48, 60, ...}$
$\text{Multiples of 8 are 8, 16, 24, 32, 40, ...}$
$\text{Since 24 is the first multiple of each that matches, LCD = 24.}$
$\text{Also, fractions}$ $\frac{5}{12}=\frac{10}{24}$ $\text{and}$ $\frac{3}{8}=\frac{9}{24}$.
New problem.
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$\begin{align} &\cssId{Step10}{= \frac{10}{24}-\frac{9}{24}}\\ &\cssId{Step11}{= \frac{10-9}{24}}\\ &\cssId{Step12}{= \frac{1}{24}} \end{align}$
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