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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Step 1

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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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