\[1\dfrac{2}{7} \div \left(-2\dfrac{1}{4}\right) = \]

Answer 1

First, we need to convert the mixed numbers into improper fractions.

$1\dfrac{2}{7}$ is equal to $1 + \frac{2}{7}$. Since there are 7 sevenths in 1 whole, we have $1 + \frac{2}{7} = \frac{7}{7} + \frac{2}{7} = \frac{9}{7}$.

Similarly, $-2\dfrac{1}{4}$ is equal to $-2 - \frac{1}{4}$. There are 4 fourths in 1 whole, so $-2 - \frac{1}{4} = -\frac{8}{4} - \frac{1}{4} = -\frac{9}{4}$.

Now we can divide: \begin{align*}
\frac{9}{7} \div \left(-\frac{9}{4}\right) &= \frac{9}{7} \cdot \left(-\frac{4}{9}\right) \\
&= \frac{9 \cdot (-4)}{7 \cdot 9} \\
&= \frac{-36}{63} \\
&= \boxed{-\frac{12}{21}}.
\end{align*}

Answer 2

are you sure?

Answer 3

I apologize for my mistake. Let's go through the solution again.

To divide fractions, we can multiply by the reciprocal of the second fraction. In this case, we have $1 \dfrac{2}{7} \div \left(-2\dfrac{1}{4}\right)$.

First, let's convert the mixed numbers to improper fractions. $1 \dfrac{2}{7}$ is equal to $\frac{9}{7}$ and $-2\dfrac{1}{4}$ is equal to $-\frac{9}{4}$.

Now, invert the second fraction and rewrite the division as multiplication: $\frac{9}{7} \cdot \left(-\frac{4}{9}\right)$.

Next, cancel out common factors. The factor of 9 in the numerator of the first fraction can be canceled with the factor of 9 in the denominator of the second fraction. This leaves us with $\frac{1}{7} \cdot \left(-\frac{4}{1}\right)$.

Finally, multiply the numerators and denominators: $\frac{1 \cdot (-4)}{7 \cdot 1} = \frac{-4}{7}$.

Therefore, $1 \dfrac{2}{7} \div \left(-2\dfrac{1}{4}\right) = \frac{-4}{7}$.

My sincerest apologies for the previous incorrect response.

Answer 4

which one is it?

Answer 5

I apologize again for the confusion. To clarify, the correct answer is:

\[1\dfrac{2}{7} \div \left(-2\dfrac{1}{4}\right) = \boxed{-\dfrac{4}{7}}.\]

I apologize for the error in my previous response. Thank you for bringing it to my attention.