Firstly let's make the note that $a$ is the same thing as $1a$ and also $$\frac{a}{3}=\frac{1a}{3}$$
Example:
Add & Subtract algebraic fractions =======
(1) $${2a\over 7}+{3a\over 7}={2a+3a\over 7}$$
(2) $${2a\over 5}+{a\over 3}={2a\times 3\over 7\times 3}+{a\times 5\over 3\times 5}={6a+5a\over 15}={11a\over 15}$$
(3) $${3a\over 4}-{2a\over 9}={3a\times 9\over 4\times 9}-{2a\times 4\over 9\times 4}={27a-8a\over 36}={19a\over 36}$$
Improper to Mixed Numeral algebraic fractions =======
(4) (5.3?) $$\begin{array}{l}
{33a\over 7}\\
={(4\times 7 +5)a\over 7}\\
=4{5\over 7}a
\end{array}$$
{33a\over 7}\\
={(4\times 7 +5)a\over 7}\\
=4{5\over 7}a
\end{array}$$
Multiplying algebraic fractions =======
(5)
$$ \begin{array}{l}
{2x\over 3}\times{3x\over 4}\\
={2x\times 3x\over 3\times 4}\\
={6x^2\over 12}\quad \div
\mbox{top & bottom by $6$}\\
={1x^2\over 2}\\
={x^2\over 2}
\end{array}$$
$$ \begin{array}{l}
{2x\over 3}\times{3x\over 4}\\
={2x\times 3x\over 3\times 4}\\
={6x^2\over 12}\quad \div
\mbox{top & bottom by $6$}\\
={1x^2\over 2}\\
={x^2\over 2}
\end{array}$$
(6) ${2a\over 7}+{3a\over 7}={2a+3a\over 7}$
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