Question
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Tutor-Verified Answer
Answer
El resultado es -10.
Solution
Para resolver \( 6 \frac{2}{3} \div -\frac{2}{3} \):
1. **Convierte el número mixto a fracción impropia:**
\[
6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{20}{3}
\]
2. **Realiza la división multiplicando por el recíproco:**
\[
\frac{20}{3} \div -\frac{2}{3} = \frac{20}{3} \times -\frac{3}{2}
\]
3. **Multiplica las fracciones:**
\[
\frac{20 \times -3}{3 \times 2} = \frac{-60}{6} = -10
\]
**Resultado final:**
\[
6 \frac{2}{3} \div -\frac{2}{3} = -10
\]
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Simplify this solution The Deep Dive
To solve \( 6 \frac{2}{3} \div -\frac{2}{3} \), first convert the mixed number into an improper fraction. So, \( 6 \frac{2}{3} = \frac{20}{3} \). Then, divide by \(-\frac{2}{3}\) by multiplying by its reciprocal, giving us \( \frac{20}{3} \times -\frac{3}{2} = -10 \). And voilà! The answer is \( -10 \). When tackling division of fractions, remember that dividing by a fraction is the same as multiplying by its reciprocal. It’s a common mistake to forget this step, leading to confusion! Always flip that second fraction and multiply to keep your calculations on the right track!
