Question

\[ -\dfrac{6}{7} \times \left(-\dfrac{5}{4}\right) \]

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the product, we multiply the numerators and denominators separately: \begin{align*}

-\dfrac{6}{7} \times \left(-\dfrac{5}{4}\right) &= \left(-\dfrac{6}{7}\right) \times \left(-\dfrac{5}{4}\right)\\
&= \left(\dfrac{-6 \times -5}{7 \times 4}\right)\\
&= \left(\dfrac{30}{28}\right)\end{align*}We can simplify the fraction $\dfrac{30}{28}$ by dividing both the numerator and the denominator by their greatest common factor, which is $2$: \begin{align*}
\frac{30}{28} &= \frac{2 \times 15}{2 \times 14}\\
&= \frac{15}{14}\end{align*}Therefore, $-\dfrac{6}{7} \times \left(-\dfrac{5}{4}\right) = \boxed{\dfrac{15}{14}}$.

Answer 2

\[ \dfrac{7}{9} \times \left(-\dfrac{5}{7}\right) \]

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the product, we multiply the numerators and denominators separately: \begin{align*}

\dfrac{7}{9} \times \left(-\dfrac{5}{7}\right) &= \left(\dfrac{7}{9}\right) \times \left(-\dfrac{5}{7}\right)\\
&= \left(\dfrac{7 \times -5}{9 \times 7}\right)\\
&= \left(\dfrac{-35}{63}\right)\end{align*}Since both the numerator and denominator are divisible by 7, we can simplify the fraction: \begin{align*}
\frac{-35}{63} &= \frac{-5 \times 7}{9 \times 7}\\
&= \frac{-5}{9}\end{align*}Thus, $\dfrac{7}{9} \times \left(-\dfrac{5}{7}\right) = \boxed{-\dfrac{5}{9}}$.

Answer 4

wrong...

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. Let's try it again.

To multiply these fractions, we multiply the numerators together and the denominators together:

$\dfrac{7}{9} \times \left(-\dfrac{5}{7}\right) = \dfrac{7 \times (-5)}{9 \times 7}$

Simplifying the numerator and denominator:

$\dfrac{7 \times (-5)}{9 \times 7} = \dfrac{-35}{63}$

We can further simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 7:

$\dfrac{-35}{63} = \dfrac{-5}{9}$

Therefore, $\dfrac{7}{9} \times \left(-\dfrac{5}{7}\right) = \boxed{-\dfrac{5}{9}}$.

Answer 6

[AI-generated answer — Explain Bot]

To multiply fractions, you multiply the numerators together and then multiply the denominators together. In this case, we have \(-\dfrac{6}{7} \times \left(-\dfrac{5}{4}\right)\).

To find the product, let's multiply the numerators \((-6) \times (-5)\) and the denominators \(7 \times 4\).

\((-6) \times (-5) =30\) and \(7 \times 4 = 28\).

Therefore, the product of \(-\dfrac{6}{7} \times \left(-\dfrac{5}{4}\right)\) is \(\dfrac{30}{28}\).