How do you divide $\frac{6}{2} \div \frac{10}{9}$ $\frac { 6} { 2} \div \frac { 10} { 9}$ ?

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How do you divide $\frac{6}{2} \div \frac{10}{9}$ $\frac { 6} { 2} \div \frac { 10} { 9}$ ?

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Answer 1 · 2018-01-23T08:06:55

$\frac{27}{10}$ $27/10$

Explanation:

$\frac{6}{2} \div \frac{10}{9}$ $6/2-:10/9$

Well, dividing by a fraction, let's say $\frac{a}{b}$ $a/b$ , is the same as multiplying by its reciprocal, which will be $\frac{b}{a}$ $b/a$ .

So, we can rewrite it as

$\frac{6}{2} \cdot \frac{9}{10}$ $6/2*9/10$

Now, we can just multiply it easily.

$\frac{6 \cdot 9}{2 \cdot 10}$ $(6*9)/(2*10)$

$\frac{54}{20}$ $54/20$

$2 \frac{14}{20}$ $2 14/20$

Furthermore, let's simplify it. We know that the greatest common factor of $14$ $14$ and $20$ $20$ is $2$ $2$ , so we can divide both of them by $2$ $2$ to get:

$2 \frac{7}{10}$ $2 7/10$

Now, let's convert it into an improper fraction, because both fractions in the original problem are improper.

$2 \frac{7}{10} = \frac{27}{10}$ $2 7/10 = 27/10$

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