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# Simplify the following fractions: a) $\frac{1}{7}+\frac{3}{7}$ b) $\frac{a}{7}+\frac{b}{7}$ c) $\frac{5}{13}+\frac{6}{13}$ d) $\frac{c}{13}+\frac{d}{13}$ e) $\frac{x}{3}+\frac{y}{3}+\frac{z}{3}$ f) $\frac{p^{2}}{5}+\frac{q^{2}}{5}$

Solution

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$\textbf{a)}$

$\frac{1}{7} + \frac{3}{7}$

Since the denominator is the same, so add the numerator to the numerator:

$= \frac{1 + 3}{7}$

$= \boxed{\color{#c34632}{\dfrac{4}{7}}}$

$\textbf{b)}$

$\frac{a}{7} + \frac{b}{7}$

Since the denominator is the same, so add the numerator to the numerator:

$= \boxed{\color{#c34632}{\dfrac{a + b}{7}}}$

$\textbf{c)}$

$\frac{5}{13} + \frac{6}{13}$

Since the denominator is the same, so add the numerator to the numerator:

$= \frac{5 + 6}{13}$

$= \boxed{\color{#c34632}{\dfrac{11}{13}}}$

$\textbf{d)}$

$\frac{c}{13} + \frac{d}{13}$

Since the denominator is the same, so add the numerator to the numerator:

$= \boxed{\color{#c34632}{\dfrac{c + d}{13}}}$

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