\[-3\dfrac{1}{2} \div 1\dfrac{1}{4} = \]

Answer 1

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

We first convert the mixed numbers to improper fractions:

$-3\dfrac{1}{2} = -\dfrac{7}{2}$

$1\dfrac{1}{4} = \dfrac{5}{4}$

So, $-3\dfrac{1}{2} \div 1\dfrac{1}{4}$ becomes $-\dfrac{7}{2} \div \dfrac{5}{4}$.

To divide, we multiply by the reciprocal:

$-\dfrac{7}{2} \div \dfrac{5}{4} = -\dfrac{7}{2} \times \dfrac{4}{5}$.

Now, we can simplify:

$-\dfrac{7}{2} \times \dfrac{4}{5} = -\dfrac{7 \times 4}{2 \times 5} = -\dfrac{28}{10}$.

We can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:

$-\dfrac{28}{10} = -\dfrac{14}{5}$.

Therefore, \[-3\dfrac{1}{2} \div 1\dfrac{1}{4} = -\dfrac{14}{5}\].