Mills Lane
07/29/2023 · High School
4. Resuelva las siguientes operaciones con número racionales. \( \left(-\frac{3}{5}\right)\left(\frac{4}{7}\right)\left(-\frac{1}{6}\right) \) \( \left(-\frac{11}{7}\right)\left(-\frac{5}{9}\right)\left(-\frac{15}{6}\right) \) \( \left(-\frac{2}{5}\right)\left(-\frac{45}{2}\right) \) - \( (-7)\left(-\frac{5}{8}\right)\left(-\frac{9}{7}\right) \) - \( \left(-\frac{4}{5} \div-\frac{3}{4}\right. \) \( \frac{9}{8} \div \frac{7}{5} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Vamos a resolver cada una de las operaciones con números racionales paso a paso.
1. **Operación:**
\[
\left(-\frac{3}{5}\right)\left(\frac{4}{7}\right)\left(-\frac{1}{6}\right)
\]
Primero, multiplicamos los numeradores y los denominadores:
\[
= \frac{(-3) \cdot 4 \cdot (-1)}{5 \cdot 7 \cdot 6} = \frac{12}{210}
\]
Simplificamos:
\[
= \frac{2}{35}
\]
2. **Operación:**
\[
\left(-\frac{11}{7}\right)\left(-\frac{5}{9}\right)\left(-\frac{15}{6}\right)
\]
Multiplicamos los numeradores y los denominadores:
\[
= \frac{(-11) \cdot (-5) \cdot (-15)}{7 \cdot 9 \cdot 6} = \frac{-825}{378}
\]
Simplificamos:
\[
= -\frac{275}{126}
\]
3. **Operación:**
\[
\left(-\frac{2}{5}\right)\left(-\frac{45}{2}\right)
\]
Multiplicamos los numeradores y los denominadores:
\[
= \frac{(-2) \cdot (-45)}{5 \cdot 2} = \frac{90}{10} = 9
\]
4. **Operación:**
\[
(-7)\left(-\frac{5}{8}\right)\left(-\frac{9}{7}\right)
\]
Multiplicamos los numeradores y los denominadores:
\[
= \frac{(-7) \cdot (-5) \cdot (-9)}{1 \cdot 8 \cdot 7} = \frac{-315}{56}
\]
Simplificamos:
\[
= -\frac{315}{56} \quad \text{(no se puede simplificar más)}
\]
5. **Operación:**
\[
\left(-\frac{4}{5} \div -\frac{3}{4}\right)
\]
Dividir por un número racional es lo mismo que multiplicar por su inverso:
\[
= \left(-\frac{4}{5}\right) \cdot \left(-\frac{4}{3}\right) = \frac{16}{15}
\]
6. **Operación:**
\[
\frac{9}{8} \div \frac{7}{5}
\]
Al igual que antes, multiplicamos por el inverso:
\[
= \frac{9}{8} \cdot \frac{5}{7} = \frac{45}{56}
\]
### Resumen de resultados:
1. \( \frac{2}{35} \)
2. \( -\frac{275}{126} \)
3. \( 9 \)
4. \( -\frac{315}{56} \)
5. \( \frac{16}{15} \)
6. \( \frac{45}{56} \)
Quick Answer
1. \( \frac{2}{35} \)
2. \( -\frac{275}{126} \)
3. \( 9 \)
4. \( -\frac{315}{56} \)
5. \( \frac{16}{15} \)
6. \( \frac{45}{56} \)
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