Question

Simplify:

(1) $\frac{5}{9}+\frac{8}{9}$
(2) $\frac{13}{8}-\frac{7}{8}$
(3) $\frac{4}{5}+\frac{-7}{10}$
(4) $\frac{-10}{7}-\frac{1}{2}$
(5) $\frac{-13}{4}+\frac{-3}{4}$
(6) $\frac{-13}{4}-\frac{-3}{4}$
(7) $\frac{2}{5}-\frac{7}{9}$
(8) $\frac{-3}{5}+\frac{2}{7}$

Answer 1

(1) $\frac{5}{9}+\frac{8}{9}$

$$\begin{gathered} =\frac{5+8}{9} \\ =\frac{13}{9} \end{gathered}$$

(2) $\frac{13}{8}-\frac{7}{8}$

$$\begin{gathered} =\frac{13-7}{8} \\ =\frac{6}{8} \\ =\frac{3}{4} \end{gathered}$$

(3) $\frac{4}{5}+\frac{-7}{10}$

$$\begin{gathered} =\frac{4\times 2}{5\times 2}+\frac{-7}{10} \\ =\frac{8}{10}+\frac{-7}{10} \\ =\frac{8+\left(-7\right)}{10} \\ =\frac{8-7}{10} \\ =\frac{1}{10} \end{gathered}$$

(4) $\frac{-10}{7}-\frac{1}{2}$

$$\begin{gathered} =\frac{\left(-10\right)\times 2}{7\times 2}-\frac{1\times 7}{2\times 7} \\ =\frac{-20}{14}-\frac{7}{14} \\ =\frac{-20-7}{14} \\ =\frac{-27}{14} \end{gathered}$$

(5) $\frac{-13}{4}+\frac{-3}{4}$

$$\begin{gathered} =\frac{-13+\left(-3\right)}{4} \\ =\frac{-13-3}{4} \\ =\frac{-16}{4} \\ =-4 \end{gathered}$$

(6) $\frac{-13}{4}-\frac{-3}{4}$

$$\begin{gathered} =\frac{-13-\left(-3\right)}{4} \\ =\frac{-13+3}{4} \\ =\frac{-10}{4} \\ =\frac{-5}{2} \end{gathered}$$

(7) $\frac{2}{5}-\frac{7}{9}$

$$\begin{gathered} =\frac{2\times 9}{5\times 9}-\frac{7\times 5}{9\times 5} \\ =\frac{18}{45}-\frac{35}{45} \\ =\frac{18-35}{45} \\ =\frac{-17}{45} \end{gathered}$$

(8) $\frac{-3}{5}+\frac{2}{7}$

$$\begin{gathered} =\frac{-3\times 7}{5\times 7}+\frac{2\times 5}{7\times 5} \\ =\frac{-21}{35}+\frac{10}{35} \\ =\frac{-21+10}{35} \\ =\frac{-11}{35} \end{gathered}$$