Question

divide these fractions and simplify the answer.

2x/27 divided by 4x+20/9

Answer 1

To divide the fractions \( \frac{2x}{27} \) by \( \frac{4x+20}{9} \), we will first change the division of fractions into multiplication by the reciprocal.

The expression can be rewritten as:

\[
\frac{2x}{27} \div \frac{4x + 20}{9} = \frac{2x}{27} \times \frac{9}{4x + 20}
\]

Now, we can simplify \( 4x + 20 \):

\[
4x + 20 = 4(x + 5)
\]

Next, substitute this back into the multiplication:

\[
\frac{2x}{27} \times \frac{9}{4(x + 5)}
\]

Now multiply the numerators and the denominators:

\[
\frac{2x \cdot 9}{27 \cdot 4(x + 5)} = \frac{18x}{108(x + 5)}
\]

Now, simplify the fraction \( \frac{18x}{108(x + 5)} \):

Both the numerator and denominator can be divided by 18:

\[
\frac{18x \div 18}{108 \div 18(x + 5)} = \frac{x}{6(x + 5)}
\]

Thus, the simplified answer is:

\[
\frac{x}{6(x + 5)}
\]