Respuesta :

Answer:

30

Step-by-step explanation:

First Convert Mixed Number to Improper

[tex]6\frac{2}{3} = \frac{2+3*6}{3} = \frac{2+18}{3} = \frac{20}{3}\\\\\frac{20}{3} \div \frac{2}{9}\\[/tex]

Next, we know that when dividing fractions, there is a certain pattern to follow.

It goes like this:
[tex]\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}\\\\[/tex]

A simple way to remember this is to know

KOR.

Keep, Opposite, Reciprocal

Keep:

[tex]\frac{a}{b}[/tex]

Opposite:

[tex]\div \rightarrow \times[/tex]

Reciprocal:

Basically Flip the Numerator and Denominator

[tex]\frac{c}{d}\rightarrow\frac{d}{c}[/tex]

And you can simply solve it then :)

WORK FOR SOLUTION

[tex]\frac{20}{3}\times\frac{9}{2} \\\\\frac{180}{6}\\\\\ =30[/tex]

CloutAnswers

Answer:

Hello! the answer to this question is 30.

Step-by-step explanation:

To solve for the quotient, we have to convert the mixed number to an improper fraction:

[tex]6\frac{2}{3} = \frac{6*3 + 2}{3} = \frac{20}{3}[/tex]

When dividing fractions, we have to flip the divisor to its reciprocal. When doing so, the divisor [tex]\frac{2}{9}[/tex] becomes [tex]\frac{9}{2}[/tex].

Now that we have the reciprocal, the operation will change from division to multiplication. We can take the final steps to solve the problem:

[tex]\frac{20}{3} * \frac{9}{2}[/tex]

This leaves you with a result [tex]\frac{180}{6}[/tex]. This can further be simplified by doing 180 ÷ 6 to get 30.

Therefore, the quotient is 30.

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