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.
$\dfrac{-\cancel{2}}{\cancel{3}} \cdot \dfrac{\cancel{4}}{\cancel{9}} = \dfrac{-1}{1} = \boxed{-1}$
\[\dfrac{-2}{3} \div 2\dfrac{1}{4} = \]
5 answers
are you sure
Yes, I am sure. The result of the division is $-1$.
wrong
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, $\dfrac{-2}{3} \div 2\dfrac{1}{4} = \boxed{\dfrac{-8}{27}}$.
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, $\dfrac{-2}{3} \div 2\dfrac{1}{4} = \boxed{\dfrac{-8}{27}}$.
1 answer