\[1\dfrac{2}{7} \div \left(-2\dfrac{1}{4}\right) = \]
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.
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*}
are you sure?
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.
which one is it?
To solve this division problem involving mixed numbers, we need to convert the mixed numbers into improper fractions.
Let's start by converting the mixed numbers into improper fractions:
\begin{align*}
1\dfrac{2}{7} &= \dfrac{7}{7} + \dfrac{2}{7} \\
&= \dfrac{9}{7}
\end{align*}
\begin{align*}
-2\dfrac{1}{4} &= -\dfrac{9}{4}
\end{align*}
Now, we can divide the two fractions:
\begin{align*}
\dfrac{9}{7} \div \left(-\dfrac{9}{4}\right) &= \dfrac{9}{7} \cdot \left(-\dfrac{4}{9}\right) \\
&= \dfrac{9 \cdot -4}{7 \cdot 9} \\
&= \dfrac{-36}{63}
\end{align*}
However, it is always good practice to simplify the fraction to its simplest form:
\begin{align*}
\dfrac{-36}{63} &= \dfrac{-36 \div 9}{63 \div 9} \\
&= \dfrac{-4}{7}
\end{align*}
Therefore, \[1\dfrac{2}{7} \div \left(-2\dfrac{1}{4}\right) = -\dfrac{4}{7}\]