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

Question

UpStudy AI · Accepted Answer

To find the number $$ N $$ by which $$ \frac{-35}{6} $$ should be divided to get $$ \frac{-15}{2} $$, we can set up the equation:

$$
\frac{-35}{6} \div N = \frac{-15}{2}
$$

This equation can be rewritten as:

$$
\frac{-35}{6} \times \frac{1}{N} = \frac{-15}{2}
$$

To solve for $$ N $$, multiply both sides by $$ N $$ and then divide both sides by $$ \frac{-15}{2} $$:

$$
\frac{-35}{6} = \frac{-15}{2} \times N
$$

$$
N = \frac{\frac{-35}{6}}{\frac{-15}{2}} = \frac{-35}{6} \times \frac{2}{-15} = \frac{(-35) \times 2}{6 \times (-15)} = \frac{70}{90}
$$

Simplify the fraction:

$$
N = \frac{70 \div 10}{90 \div 10} = \frac{7}{9}
$$

**Answer:** $$\boxed{\dfrac{7}{9}}$$
The number to divide $$ \frac{-35}{6} $$ by to get $$ \frac{-15}{2} $$ is $$ \frac{7}{9} $$.

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