Multiply and simplify

Explanation

• Since the answer is positive, drop both - signs and continue
  • \(\frac23 \left(-\frac{9}{14} \right) \left( -\frac{7}{10}\right)\) = \(\frac23 \left(\frac{9}{14} \right) \left( \frac{7}{10}\right)\)
• Multiply the numerators.  Multiply the denominators
  • = \(\frac{2 \cdot 9 \cdot 7}{3 \cdot 14 \cdot 10}\)
• To prepare to simplify, write 9, 14, and 10 in prime factored form
  • = \(\frac{2 \cdot 3 \cdot 3 \cdot 7}{3 \cdot 2 \cdot 7 \cdot 2 \cdot 5}\)
• To simplify, remove the common factors of 2, 3, and 7 from the numerator and denominator
  • = \(\require{cancel} \frac{\cancel{2}^1 \cdot \cancel{3}^1 \cdot 3 \cdot \cancel{7}^1}{\cancel{3}_1 \cdot 2 \cdot \cancel{7}_1 \cdot \cancel{2}_1 \cdot 5}\)
• Multiply the remaining factors in the numerators.  Multiply the remaining factors in the denominator
  • \(\frac{3}{10}\)