$$ \begin{array}{ll} ext { ea. } \frac{3}{4}-\frac{1}{4} \cdot\left(\frac{3}{5}-\frac{1}{10} ight) & \frac{3}{8}-\frac{1}{4}:\left(\frac{2}{3} \cdot \frac{3}{4} ight) \ ext { l. } 5+\frac{7}{3}:\left(\frac{4}{3}+2 ight) & ext { d. } \frac{8}{3}-\left(\frac{1}{3}+\frac{1}{2} ight): \frac{5}{4}\end{array} $$

Question

$$ \begin{array}{ll}	ext { ea. } \frac{3}{4}-\frac{1}{4} \cdot\left(\frac{3}{5}-\frac{1}{10}ight) & \frac{3}{8}-\frac{1}{4}:\left(\frac{2}{3} \cdot \frac{3}{4}ight) \ 	ext { l. } 5+\frac{7}{3}:\left(\frac{4}{3}+2ight) & 	ext { d. } \frac{8}{3}-\left(\frac{1}{3}+\frac{1}{2}ight): \frac{5}{4}\end{array} $$

UpStudy AI · Accepted Answer

Claro, a continuación se resuelven las expresiones proporcionadas:

### ea. $$ \frac{3}{4} - \frac{1}{4} \cdot \left( \frac{3}{5} - \frac{1}{10} \right) $$

**Solución:**
$$
\begin{align*}
\frac{3}{4} - \frac{1}{4} \cdot \left( \frac{3}{5} - \frac{1}{10} \right) &= \frac{3}{4} - \frac{1}{4} \cdot \left( \frac{6}{10} - \frac{1}{10} \right) \
&= \frac{3}{4} - \frac{1}{4} \cdot \frac{5}{10} \
&= \frac{3}{4} - \frac{1}{8} \
&= \frac{6}{8} - \frac{1}{8} \
&= \frac{5}{8}
\end{align*}
$$

**Resultado:** $$ \frac{5}{8} $$

---

### $$ \frac{3}{8} - \frac{1}{4} : \left( \frac{2}{3} \cdot \frac{3}{4} \right) $$

**Solución:**
$$
\begin{align*}
\frac{3}{8} - \frac{1}{4} : \left( \frac{2}{3} \cdot \frac{3}{4} \right) &= \frac{3}{8} - \frac{1}{4} \div \left( \frac{6}{12} \right) \
&= \frac{3}{8} - \frac{1}{4} \div \frac{1}{2} \
&= \frac{3}{8} - \left( \frac{1}{4} \times 2 \right) \
&= \frac{3}{8} - \frac{2}{4} \
&= \frac{3}{8} - \frac{1}{2} \
&= \frac{3}{8} - \frac{4}{8} \
&= -\frac{1}{8}
\end{align*}
$$

**Resultado:** $$ -\frac{1}{8} $$

---

### l. $$ 5 + \frac{7}{3} : \left( \frac{4}{3} + 2 \right) $$

**Solución:**
$$
\begin{align*}
5 + \frac{7}{3} : \left( \frac{4}{3} + 2 \right) &= 5 + \frac{7}{3} \div \left( \frac{4}{3} + \frac{6}{3} \right) \
&= 5 + \frac{7}{3} \div \frac{10}{3} \
&= 5 + \left( \frac{7}{3} \times \frac{3}{10} \right) \
&= 5 + \frac{21}{30} \
&= 5 + \frac{7}{10} \
&= 5.7 \
&= \frac{57}{10}
\end{align*}
$$

**Resultado:** $$ \frac{57}{10} $$ o $$ 5.7 $$

---

### d. $$ \frac{8}{3} - \left( \frac{1}{3} + \frac{1}{2} \right) : \frac{5}{4} $$

**Solución:**
$$
\begin{align*}
\frac{8}{3} - \left( \frac{1}{3} + \frac{1}{2} \right) : \frac{5}{4} &= \frac{8}{3} - \left( \frac{2}{6} + \frac{3}{6} \right) \div \frac{5}{4} \
&= \frac{8}{3} - \frac{5}{6} \div \frac{5}{4} \
&= \frac{8}{3} - \left( \frac{5}{6} \times \frac{4}{5} \right) \
&= \frac{8}{3} - \frac{20}{30} \
&= \frac{8}{3} - \frac{2}{3} \
&= \frac{6}{3} \
&= 2
\end{align*}
$$

**Resultado:** $$ 2 $$

---

**Resumen de Resultados:**
- **ea.** $$ \frac{5}{8} $$
- **Sin etiqueta.** $$ -\frac{1}{8} $$
- **l.** $$ \frac{57}{10} $$ o $$ 5.7 $$
- **d.** $$ 2 $$
**Resultados:** - **ea.** $$ \frac{5}{8} $$ - **Sin etiqueta.** $$ -\frac{1}{8} $$ - **l.** $$ \frac{57}{10} $$ o $$ 5.7 $$ - **d.** $$ 2 $$

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