c. $$ \left(\frac{1}{6}-\frac{4}{6}\right)+\frac{11}{6} \quad $$ d. $$ \frac{6}{7}+\frac{9}{14}-\frac{3}{10} $$ e. $$ \left(\frac{5}{3}+2 \frac{1}{4}\right)-\left(3-\frac{7}{12}\right) $$ f. $$ \left(\frac{3}{4} \cdot \frac{9}{8}\right) $$

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UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\frac{3}{4}\times \frac{9}{8}$$
- step1: Multiply the fractions:
  $$\frac{3\times 9}{4\times 8}$$
- step2: Multiply:
  $$\frac{27}{32}$$
Calculate or simplify the expression $$ 6/7 + 9/14 - 3/10 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{6}{7}+\frac{9}{14}-\frac{3}{10}$$
- step1: Reduce fractions to a common denominator:
  $$\frac{6\times 2\times 5}{7\times 2\times 5}+\frac{9\times 5}{14\times 5}-\frac{3\times 7}{10\times 7}$$
- step2: Multiply the terms:
  $$\frac{6\times 2\times 5}{70}+\frac{9\times 5}{14\times 5}-\frac{3\times 7}{10\times 7}$$
- step3: Multiply the numbers:
  $$\frac{6\times 2\times 5}{70}+\frac{9\times 5}{70}-\frac{3\times 7}{10\times 7}$$
- step4: Multiply the numbers:
  $$\frac{6\times 2\times 5}{70}+\frac{9\times 5}{70}-\frac{3\times 7}{70}$$
- step5: Transform the expression:
  $$\frac{6\times 2\times 5+9\times 5-3\times 7}{70}$$
- step6: Multiply the terms:
  $$\frac{60+9\times 5-3\times 7}{70}$$
- step7: Multiply the numbers:
  $$\frac{60+45-3\times 7}{70}$$
- step8: Multiply the numbers:
  $$\frac{60+45-21}{70}$$
- step9: Calculate:
  $$\frac{84}{70}$$
- step10: Reduce the fraction:
  $$\frac{6}{5}$$
Calculate or simplify the expression $$ (5/3 + 2 + 1/4) - (3 - 7/12) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{5}{3}+2+\frac{1}{4}\right)-\left(3-\frac{7}{12}\right)$$
- step1: Add the numbers:
  $$\frac{47}{12}-\left(3-\frac{7}{12}\right)$$
- step2: Subtract the numbers:
  $$\frac{47}{12}-\frac{29}{12}$$
- step3: Transform the expression:
  $$\frac{47-29}{12}$$
- step4: Subtract the numbers:
  $$\frac{18}{12}$$
- step5: Reduce the fraction:
  $$\frac{3}{2}$$
Calculate or simplify the expression $$ (1/6 - 4/6) + 11/6 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{1}{6}-\frac{4}{6}\right)+\frac{11}{6}$$
- step1: Reduce the fraction:
  $$\left(\frac{1}{6}-\frac{2}{3}\right)+\frac{11}{6}$$
- step2: Subtract the numbers:
  $$\left(-\frac{1}{2}\right)+\frac{11}{6}$$
- step3: Remove the parentheses:
  $$-\frac{1}{2}+\frac{11}{6}$$
- step4: Reduce fractions to a common denominator:
  $$-\frac{3}{2\times 3}+\frac{11}{6}$$
- step5: Multiply the numbers:
  $$-\frac{3}{6}+\frac{11}{6}$$
- step6: Transform the expression:
  $$\frac{-3+11}{6}$$
- step7: Add the numbers:
  $$\frac{8}{6}$$
- step8: Reduce the fraction:
  $$\frac{4}{3}$$
Aquí están las soluciones a los problemas que proporcionaste:

c. $$ \left(\frac{1}{6}-\frac{4}{6}\right)+\frac{11}{6} $$

Primero, resolvemos la resta dentro del paréntesis:
$$
\frac{1}{6} - \frac{4}{6} = -\frac{3}{6} = -\frac{1}{2}
$$
Luego, sumamos $$ \frac{11}{6} $$:
$$
-\frac{1}{2} + \frac{11}{6} = -\frac{3}{6} + \frac{11}{6} = \frac{8}{6} = \frac{4}{3}
$$

**Resultado:** $$ \frac{4}{3} $$ o $$ 1\frac{1}{3} $$ o $$ 1.3\overline{3} $$

---

d. $$ \frac{6}{7}+\frac{9}{14}-\frac{3}{10} $$

Primero, encontramos un común denominador para $$ \frac{6}{7} $$, $$ \frac{9}{14} $$ y $$ \frac{3}{10} $$. El mínimo común múltiplo de 7, 14 y 10 es 70.

Convertimos cada fracción:
$$
\frac{6}{7} = \frac{60}{70}, \quad \frac{9}{14} = \frac{45}{70}, \quad \frac{3}{10} = \frac{21}{70}
$$
Ahora sumamos y restamos:
$$
\frac{60}{70} + \frac{45}{70} - \frac{21}{70} = \frac{60 + 45 - 21}{70} = \frac{84}{70} = \frac{6}{5}
$$

**Resultado:** $$ \frac{6}{5} $$ o $$ 1\frac{1}{5} $$ o $$ 1.2 $$

---

e. $$ \left(\frac{5}{3}+2 \frac{1}{4}\right)-\left(3-\frac{7}{12}\right) $$

Primero, convertimos $$ 2 \frac{1}{4} $$ a una fracción impropia:
$$
2 \frac{1}{4} = \frac{9}{4}
$$
Ahora sumamos $$ \frac{5}{3} + \frac{9}{4} $$. El mínimo común múltiplo de 3 y 4 es 12:
$$
\frac{5}{3} = \frac{20}{12}, \quad \frac{9}{4} = \frac{27}{12}
$$
Sumamos:
$$
\frac{20}{12} + \frac{27}{12} = \frac{47}{12}
$$

Ahora resolvemos $$ 3 - \frac{7}{12} $$:
$$
3 = \frac{36}{12} \quad \Rightarrow \quad \frac{36}{12} - \frac{7}{12} = \frac{29}{12}
$$

Finalmente, restamos:
$$
\frac{47}{12} - \frac{29}{12} = \frac{18}{12} = \frac{3}{2}
$$

**Resultado:** $$ \frac{3}{2} $$ o $$ 1\frac{1}{2} $$ o $$ 1.5 $$

---

f. $$ \left(\frac{3}{4} \cdot \frac{9}{8}\right) $$

Multiplicamos las fracciones:
$$
\frac{3 \cdot 9}{4 \cdot 8} = \frac{27}{32}
$$

**Resultado:** $$ \frac{27}{32} $$ o $$ 0.84375 $$

---

Si necesitas más ayuda o aclaraciones, ¡hazmelo saber!
c. $$ \frac{4}{3} $$ o $$ 1\frac{1}{3} $$ o $$ 1.3\overline{3} $$ d. $$ \frac{6}{5} $$ o $$ 1\frac{1}{5} $$ o $$ 1.2 $$ e. $$ \frac{3}{2} $$ o $$ 1\frac{1}{2} $$ o $$ 1.5 $$ f. $$ \frac{27}{32} $$ o $$ 0.84375 $$

c. \( \left(\frac{1}{6}-\frac{4}{6}\right)+\frac{11}{6} \quad \) d. \( \frac{6}{7}+\frac{9}{14}-\frac{3}{10} \) e. \( \left(\frac{5}{3}+2 \frac{1}{4}\right)-\left(3-\frac{7}{12}\right) \) f. \( \left(\frac{3}{4} \cdot \frac{9}{8}\right) \)

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