22% = 22/100

Divide everything by 2:

22/100 = 11/50

11 is a prime number, so this is as reduced as this fraction can get.

The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.

If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90y = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.

Similarly, we can write 15% of x as 0.15x = (15/100)x = (3/20)x.

Now, we set these two expressions equal to one another.

(9/10)y = (3/20)x

Multiply both sides by 20 to eliminate fractions.

18y = 3x

The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.

18y = 3x

Divide both sides by 3.

6y = x

Divide both sides by y.

6 = x/y

Thus, the ratio of x to y is 6.

The answer is 6.

First convert the percentage to a decimal:

7.5% = .075

Then turn this into a fraction:

.075 = 75/1000

Simplify by dividing the numerator and denominator by 25:

75/1000 = 3/40

25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

\(\displaystyle 65\%\rightarrow \frac{65}{100}\)

From here, simplify the fraction as necessary:

\(\displaystyle \frac{65}{100}\div \frac{5}{5}=\frac{13}{20}\)

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

\(\displaystyle 46\%\rightarrow \frac{46}{100}\)

From here, simplify the fraction as necessary:

\(\displaystyle \frac{46}{100}\div \frac{2}{2}=\frac{23}{50}\)

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

\(\displaystyle 72\%\rightarrow \frac{72}{100}\)

From here, simplify the fraction as necessary:

\(\displaystyle \frac{72}{100}\div \frac{2}{2}=\frac{36}{50}\div \frac{2}{2}=\frac{18}{25}\)

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

\(\displaystyle 88\%\rightarrow \frac{88}{100}\)

From here, simplify the fraction as necessary:

\(\displaystyle \frac{88}{100}\div \frac{4}{4}=\frac{22}{25}\)

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

\(\displaystyle 44\%\rightarrow \frac{44}{100}\)

From here, simplify the fraction as necessary:

\(\displaystyle \frac{44}{100}\div \frac{4}{4}=\frac{11}{25}\)

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

\(\displaystyle 15\%\rightarrow \frac{15}{100}\)

From here, simplify the fraction as necessary:

\(\displaystyle \frac{15}{100}\div \frac{5}{5}=\frac{3}{20}\)