What is (4x^2)/(y) * (xy^2)/(12)?

Sep 10, 2016

$\frac{4 {x}^{2}}{y} \cdot \frac{x {y}^{2}}{12} = \frac{{x}^{3} y}{3}$

Explanation:

$\frac{4 {x}^{2}}{y} \cdot \frac{x {y}^{2}}{12}$

= $\frac{2 \times 2 \times x \times x}{y} \cdot \frac{x \times y \times y}{2 \times 2 \times 3}$

= $\frac{\cancel{2} \times \cancel{2} \times x \times x}{\cancel{y}} \cdot \frac{x \times \cancel{y} \times y}{\cancel{2} \times \cancel{2} \times 3}$

= $\frac{x \times x \times x \times y}{3}$

= $\frac{{x}^{3} y}{3}$

Sep 10, 2016

$\frac{{x}^{3} y}{3}$

Explanation:

I always use the following approach in simplifying the multiplication and division of fractions like these in algebra.

Step 1 $\rightarrow$ Determine the final sign of the answer.

Done once, you do not need to look at it again.
An EVEN number of negative signs will give a POSITIVE
An ODD number of negative signs will give a NEGATIVE

Step 2 $\rightarrow$ sort out any negative indices by moving the bases to or from the numerator or denominator.

Step 3 simplify the numbers, cancel first if possible.

Step 4 combine all the variables to give one numerator and one denominator.

Step 5 Simplify the indices of like bases.
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$\frac{4 {x}^{2}}{y} \times \frac{x {y}^{2}}{12} \text{ } \leftarrow$ no negative signs or negative indices.

=$\frac{\cancel{4} {x}^{2}}{y} \times \frac{x {y}^{2}}{\cancel{12}} ^ 3 \text{ } \leftarrow$ cancel numbers

=$\frac{{x}^{3} {y}^{2}}{3 y} \text{ } \leftarrow$ make one numerator and one denominator.

=$\frac{{x}^{3} y}{3} \text{ } \leftarrow$ subtract indices of like bases

Sep 15, 2016

$\frac{{x}^{3} y}{3}$

Explanation:

Using the property called commutative. (can travel$\to$ commute)

Using an example:

$\textcolor{b l u e}{\frac{2}{3} \times \frac{1}{56}} \textcolor{g r e e n}{= \frac{2 \times 1}{3 \times 56}} \textcolor{b r o w n}{= \frac{2 \times 1}{56 \times 3}} \textcolor{m a \ge n t a}{= \frac{2}{56} \times \frac{1}{3}}$

Notice the way the denominators are able to swap round without changing the final value
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Write as:

$\frac{4 {x}^{2}}{12} \times \frac{x {y}^{2}}{y}$

$\frac{4}{12} \times {x}^{2} \times x \times {y}^{2} / y$

$\text{ "1/3xx x^3 xx y" " =" } \frac{{x}^{3} y}{3}$