\[\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \]
We first convert the mixed number $-1\dfrac{2}{7}$ to an improper fraction. Multiplying the denominator 7 by the whole number $-1$ gives $-7$, and adding the numerator 2 gives $-5$. Thus \[-1\dfrac{2}{7} = -\dfrac{5}{7}.\] Therefore, we have \[\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \dfrac{2}{-3} \div \left(-\dfrac{5}{7}\right).\]Dividing is the same as multiplying by the reciprocal, so we can rewrite this as \[\dfrac{2}{-3} \cdot \left(-\dfrac{7}{5}\right).\]Multiplying a fraction by $-1$ negates it, so the expression becomes \[-\dfrac{2}{3} \cdot \dfrac{7}{5}.\]Multiplying the numerators gives $(-2)(7) = -14$, and multiplying the denominators gives $(3)(5) = 15$. Therefore, we have \[-\dfrac{2}{3} \cdot \dfrac{7}{5} = \boxed{-\dfrac{14}{15}}.\]
are you sure
I apologize for the previous mistake. Let's correct it:
We start by converting the mixed number $-1\dfrac{2}{7}$ to an improper fraction. We have $-1\dfrac{2}{7} = \dfrac{7(-1) + 2}{7} = \dfrac{-7+2}{7} = \dfrac{-5}{7}$.
Therefore, the expression becomes:
\[\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \dfrac{2}{-3} \div \dfrac{-5}{7}\]
Recall that dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the expression as:
\[\dfrac{2}{-3} \cdot \dfrac{7}{-5}\]
Multiplying the numerators gives $2\cdot 7 = 14$, and multiplying the denominators gives $-3\cdot -5 = 15$. Thus, the expression simplifies to:
\[\dfrac{2}{-3} \cdot \dfrac{7}{-5} = \dfrac{14}{15}\]
Therefore, $\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \boxed{\dfrac{14}{15}}$.
are you sure?
To solve this problem, we need to understand how to divide fractions and mixed numbers.
First, let's convert the mixed number \(-1\dfrac{2}{7}\) to an improper fraction. To do this, we multiply the whole number (-1) by the denominator (7) and then add the numerator (2). This gives us \(-1\dfrac{2}{7} = -\dfrac{9}{7}\).
Now, let's solve the problem step by step:
1. Invert the divisor: The divisor is \(-\dfrac{9}{7}\), so we invert it to \(-\dfrac{7}{9}\). Inverting the divisor is the same as finding its reciprocal.
2. Multiply the dividend by the inverted divisor: The dividend is \(\dfrac{2}{-3}\) and the inverted divisor is \(-\dfrac{7}{9}\). Multiplying these two fractions gives us \(\dfrac{2}{-3} \times -\dfrac{7}{9}\).
3. Simplify the fraction: To multiply fractions, we multiply the numerators and the denominators separately. Multiplying the numerators gives us \(2 \times 7 = 14\), and multiplying the denominators gives us \((-3) \times 9 = -27\). So, \(\dfrac{2}{-3} \times -\dfrac{7}{9} = \dfrac{14}{-27}\).
Therefore, \(\dfrac{2}{-3} \div \left(-1\dfrac{2}{7}\right) = \dfrac{14}{-27}\).
Please note that we can simplify the fraction \(\dfrac{14}{-27}\) further if required.
Apologies for the confusion.
To compute \[\frac{2}{-3} \div \left(-1\frac{2}{7}\right),\]we can rewrite the mixed number as a fraction by multiplying the whole number part by the denominator and adding the numerator: \[-1\frac{2}{7} = -\frac{7}{7}+\frac{2}{7} = -\frac{7+2}{7} = -\frac{9}{7}.\]Thus, the expression becomes \[\frac{2}{-3} \div \left(-\frac{9}{7}\right).\]We now divide by a fraction by multiplying by the reciprocal: \[\frac{2}{-3} \div \left(-\frac{9}{7}\right) = \frac{2}{-3} \cdot \left(-\frac{7}{9}\right).\]Multiplying the numerators gives $2\cdot7=14$, and multiplying the denominators gives $-3\cdot9=-27$. Therefore, \[\frac{2}{-3} \div \left(-1\frac{2}{7}\right) = \frac{14}{-27} = \boxed{-\frac{14}{27}}.\]