Question

\[\dfrac{-2}{3} \div 2\dfrac{1}{4} = \]

Answer 1

[AI-generated answer — Bot GPT 3.5]

To divide by a mixed number, we first have to change the mixed number to an improper fraction. We can do this by multiplying the whole number by the denominator and adding the numerator.

$2\dfrac{1}{4} = 2 + \dfrac{1}{4} = \dfrac{8}{4}+\dfrac{1}{4}=\dfrac{9}{4}$

Now, we can rewrite the expression as

$\dfrac{-2}{3} \div \dfrac{9}{4}$

When dividing fractions, we can multiply by the reciprocal of the second fraction.

$\dfrac{-2}{3} \div \dfrac{9}{4} = \dfrac{-2}{3} \cdot \dfrac{4}{9}$

We can cancel out the common factors of 2 and 3.

$\dfrac{-\cancel{2}}{\cancel{3}} \cdot \dfrac{\cancel{4}}{\cancel{9}} = \dfrac{-1}{1} = \boxed{-1}$

Answer 2

are you sure

Answer 3

[AI-generated answer — Bot GPT 3.5]

Yes, I am sure. The result of the division is $-1$.

Answer 4

wrong

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. Let's recompute the division correctly.

To divide by a mixed number, we need to convert it to an improper fraction. The improper fraction equivalent of $2\dfrac{1}{4}$ is:

$2\dfrac{1}{4} = \dfrac{2 \times 4 + 1}{4} = \dfrac{9}{4}$

Now, we can rewrite the expression as:

$\dfrac{-2}{3} \div \dfrac{9}{4}$

When dividing fractions, we multiply by the reciprocal of the second fraction:

$\dfrac{-2}{3} \div \dfrac{9}{4} = \dfrac{-2}{3} \times \dfrac{4}{9}$

Simplifying the numerator and denominator further:

$\dfrac{-2 \times 4}{3 \times 9} = \dfrac{-8}{27}$

Therefore, $\dfrac{-2}{3} \div 2\dfrac{1}{4} = \boxed{\dfrac{-8}{27}}$.

Answer 6

[AI-generated answer — Explain Bot]

To divide a fraction by a mixed number, we need to convert the mixed number into an improper fraction.

First, let's convert the mixed number \(2\dfrac{1}{4}\) into an improper fraction.

Since the whole number part is 2 and the fraction part is \(\dfrac{1}{4}\), we can convert it as follows:

\(2\dfrac{1}{4} = \dfrac{(2 \times 4) + 1}{4} = \dfrac{9}{4}\)

Now, we have the equation \(\dfrac{-2}{3} \div \dfrac{9}{4}\).

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction (flipping the numerator and denominator of the second fraction).

Therefore, we can rewrite the equation as:

\(\dfrac{-2}{3} \times \dfrac{4}{9} = \dfrac{-2 \times 4}{3 \times 9} = \dfrac{-8}{27}\)

So, \(\dfrac{-2}{3} \div 2\dfrac{1}{4} = \dfrac{-8}{27}\).