Multiply the numerators and the denominators:

\(\displaystyle \frac{1}{6}*\frac{1}{6}=\frac{1}{36}\)

Answer: \(\displaystyle \frac{1}{36}\)

In order to multiply fractions, we can simply multiply straight across:

\(\displaystyle \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}\)

So we can write:

\(\displaystyle \frac{1}{x^3}\times \frac{3x}{2x^2}\times \frac{4x^4}{3}=\frac{1\times 3x\times 4x^4}{x^3\times 2x^2\times 3}\)

\(\displaystyle \frac{12x^5}{6x^5}=\frac{12}{6}=2\)

In order to multiply fractions, we can simply multiply straight across:

\(\displaystyle \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}\)

So we can write:

\(\displaystyle \frac{3}{5}\times \frac{2}{6}\times \frac{3}{7}=\frac{3\times 2\times 3}{5\times 6\times 7}\)

\(\displaystyle =\frac{18}{210}\)

Divide it by the least common factor (i.e. 6) to simplify:

\(\displaystyle \frac{18}{210}=\frac{3}{35}\)

In this problem we need to follow our order of operations; in this case we need to multiply before we subtract fractions. 

To multiply fractions we just need to multiply the numerator by the numerator and the denominator by the denominator. In this case \(\displaystyle 1\times 2\) (the numerators of the fractions being multiplied) and \(\displaystyle 4\times 6\) (the denominators) giving us   

\(\displaystyle \frac{2}{24}\)

We then rewrite our equation.

\(\displaystyle \frac{2}{24}-\frac{1}{8}=?\)

In order to subtract fractions, we must have a common denominator. To do this we need to find a common multiple of 24 and 8. In this case, the 8 nicely goes into 24 three times, so we will only need to multiply one of our fractions to have common denominators.

To do this we must multiply one-eighth three times like this...

\(\displaystyle \frac{3}{3}\left(-\frac{1}{8}\right)=-\frac{3}{24}\)

Remember that if you are multiplying a fraction, you must multiply both the numerator and the denominator in order to obtain a multiple of your original factor. 

Lastly subtract.

\(\displaystyle \frac{2}{24}-\frac{3}{24}=-\frac{1}{24}\)

\(\displaystyle \frac{2}{5}\times \frac{3}{4}=\frac{2\times3}{5\times4}=\frac{6}{20}=\frac{3}{10}\)

To multiply fractions, multiply both numerators on top and both denominators on the bottom.

\(\displaystyle \frac{2}{4}*\frac{5}{7}=\frac{2*5}{4*7}=\frac{10}{28}\)

Then, reduce to simplest form by removing any common factors:

\(\displaystyle \frac{10}{28}=\frac{10\div2}{28\div2}=\frac{5}{14}\)

Answer: \(\displaystyle \frac{5}{14}\)

\(\displaystyle \small \frac{3}{10}\times \frac{16}{15}=\frac{48}{150}=\frac{8}{25}\)

In order to solve for y, cross multiplication must be used. Appyling cross multiplication, we get:

\(\displaystyle \frac{3}{2y}=\frac{6}{x}\)

\(\displaystyle 12y=3x\)

Next, we divide each side by 12. 

This results in \(\displaystyle y=\frac{x}{4}\) 

Given that the sweater's price was reduced by 5 dollars, this is a one third reduction because one third of 15 dollars is 5 dollars. 15 dollars minus 5 dollars is equal to 10 dollars.

Thus, the correct answer is:

 \(\displaystyle \frac{1}{3}\) off

One dollar is equal to 116.76 yen, so multiply $3,000 by this conversion rate to get

\(\displaystyle 3,000 \times 116.76 = 350,280\) yen.