Divide.
Write your answer in simplest form.
\[ -\dfrac{8}{3} \div \dfrac{1}{4} = {?} \]
wrong. correct answer is -32/3
Apologies for the mistake. You are correct. The correct answer is $\frac{-32}{3}$.
To divide fractions, you need to multiply the first fraction by the reciprocal of the second fraction. To find the reciprocal of a fraction, simply swap the numerator and denominator.
So, for this problem, the reciprocal of the second fraction, doesn't change, it becomes:
Reciprocal of \(\dfrac{1}{4}\) = \(\dfrac{4}{1}\)
To divide \(-\dfrac{8}{3}\) by \(\dfrac{1}{4}\), we multiply:
\(-\dfrac{8}{3} \times \dfrac{4}{1}\)
Next, we multiply the numerators and denominators:
Numerator: \(-8 \times 4 = -32\)
Denominator: \(3 \times 1 = 3\)
Therefore, the result is \(-32/3\).
However, we can simplify this fraction further. To simplify, we need to see if there is a common factor between the numerator and denominator that can be canceled out. In this case, both -32 and 3 have a factor of 1.
When we divide both the numerator and denominator by 1, the fraction doesn't change.
So, the final answer in simplest form is \(-32/3\).
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$, so we have: \begin{align*}
-\dfrac{8}{3} \div \dfrac{1}{4} &= -\dfrac{8}{3} \cdot \dfrac{4}{1}\\
&= -\dfrac{8 \cdot 4}{3 \cdot 1}\\
&= -\dfrac{32}{3}\\
\end{align*} So, $-\dfrac{8}{3} \div \dfrac{1}{4} = -\dfrac{32}{3}$.