By what number should \( \frac{-35}{6} \) be divided to get \( \frac{-15}{2} \) ?

To find the number by which \( \frac{-35}{6} \) should be divided to obtain \( \frac{-15}{2} \), you can set up the equation: \[ \frac{-35}{6} \div x = \frac{-15}{2} \] To solve for \( x \), multiply both sides by \( x \): \[ \frac{-35}{6} = \frac{-15}{2} \cdot x \] Now, we can isolate \( x \) by dividing both sides by \( \frac{-15}{2} \): \[ x = \frac{\frac{-35}{6}}{\frac{-15}{2}} \] When dividing fractions, multiply by the reciprocal: \[ x = \frac{-35}{6} \cdot \frac{2}{-15} \] Now, simplify: \[ x = \frac{35 \cdot 2}{6 \cdot 15} \] \[ x = \frac{70}{90} \] Now simplify \( \frac{70}{90} \): \[ x = \frac{7}{9} \] Thus, the number by which \( \frac{-35}{6} \) should be divided to get \( \frac{-15}{2} \) is \( \frac{7}{9} \).