Adding and Subtracting Fractions

A proper fraction has a numerator smaller than its denominator, like $\frac{3}{4}$.

Find the least common denominator (9), rewrite $\frac{2}{3}$ as $\frac{6}{9}$, then add $\frac{6}{9}+\frac{4}{9}=\frac{10}{9}$.

Multiply the whole number by the denominator ($3\times 5=15$) and add the numerator ($15+2=17$), giving $\frac{17}{5}$.

Find the least common denominator (12). Rewrite $\frac{5}{6}$ as $\frac{10}{12}$ and $\frac{3}{4}$ as $\frac{9}{12}$. Add $\frac{10}{12}+\frac{9}{12}=\frac{19}{12}$.

Find the least common denominator (36). Rewrite $\frac{7}{9}$ as $\frac{28}{36}$ and $\frac{11}{12}$ as $\frac{33}{36}$. Subtract $\frac{33}{36}-\frac{28}{36}=\frac{5}{36}$.

Convert both numbers to improper fractions: $2\frac{3}{4}=\frac{11}{4}$ and $6\frac{1}{2}=\frac{13}{2}=\frac{26}{4}$. Subtract $\frac{26}{4}-\frac{11}{4}=\frac{15}{4}$, which simplifies to $3\frac{3}{4}$.