55 and 1/2% can be written as a decimal: 0.555. To see what number is about 55.5% of 23, multiply 0.555 by 23. Answer: 12.765 or about 13.

Another route is to say that 55.5% is about half of 23. Half of 23 is 11.5. Since 55.5% is greater than 50%, 13 is the logical choice instead of 11.

We need to find expressions for fifty percent of x and for thirty percent of the positive difference between x and y. Then, we can set these two expressions equal to each other and determine the ratio of x to y.

Fifty percent of x is equal to one-half of x, which is the same as multiplying x by 0.50.

50% of x = 0.5x

Thirty percent of the positive difference between x and y means that we need to multiply the positive difference between x and y by thirty percent. Because x > y, the positive difference between x and y is equal to x – y. We then need to take thirty percent of the quantity x – y. Remember that to convert from a percent to a decimal, we move the decimal two spaces to the left. Therefore, 30% = 0.30. We can now multiply this by (x – y).

30% of x – y = 0.30(x – y)

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

0.5x = 0.30(x – y)

Distribute the right side.

0.5x = 0.3x – 0.3y

The ratio of x to y is represent by x/y. Thus, we want to group the x and y terms on opposite sides of the equations, and then divide both sides by y.

0.5x = 0.3x – 0.3y

Subtract 0.3x from both sides.

0.2x = –0.3y

Divide both sides by 0.2

x = (–0.3/0.2)y

Divide both sides by y to find x/y.

x/y = (–0.3/0.2) = –1.5.

Because the answers are in fractions, we want to rewrite –1.5 as a fraction. We can write –1.5 as –1.5/1 and then mutiply the top and bottom by 2.

(–1.5/1)(2/2) = –3/2

The answer is –3/2

We are told that 50% of x is equal to 25% of y. We need to represent these two pieces of information as algebraic expressions. We can convert 50% and 25% to decimals by moving the decimals two places to the left. Thus, 50% = 0.50, and 25% = 0.25. To find 50% of x, we multiply x by 0.50. In other words, 50% of x = 0.50x. Likewise, 25% of y = 0.25y. We now set 0.50x and 0.25y equal to one another.

0.50x = 0.25y

Let's divide both sides by 0.25 to get rid of decimals.

2x = y

Next, we are told that 40% of y is equal to 60% of z. We will represent 40% and 60% as 0.40 and 0.60, respectively. Thus, we can write the following equation:

0.40y = 0.60z

Ultimately, we are asked to find x as a percentage of z. This means we want to find an equation with x and z, but not y. If we solve for y in the second equation, and then substitute this value into the first, we can eliminate y.

Let's take the equation 0.40y = 0.60z and divide both sides by 0.40.

y = 1.5z

Now, we can take 1.5z and substitute this for y in the first equation.

2x = 1.5z

In order to find x as a percent of z, we must solve for x in terms of z. This means we must divide both sides of the equation by 2.

x = 0.75z

x is 0.75 times z. We can represent 0.75 as 75%, because in order to convert from a decimal to a percent, we need to move the decimal two spaces to the right. Therefore, if x = 0.75z, then x = 75% of z.

The answer is 75.

The correct answer is \(\displaystyle 0.194\). 

This can be obtained by taking the percentage of \(\displaystyle 19.4\%\) and dividing by \(\displaystyle 100\).

This shifts the decimal place over two places to the left, which results in \(\displaystyle 0.194\) as the decimal of \(\displaystyle 19.4\%\).

In order to find the decimal equivalent of a percentage, the number that makes up the percent has to be divided by 100. However, since it is division by a power of 10, we can accomplish the same thing, by moving the decimal point 2 places to the left, thus making the number smaller. For this problem, that looks like this:

\(\displaystyle 26\%\rightarrow0.26\)

In order to find the decimal equivalent of a percentage, the number that makes up the percent has to be divided by 100. However, since it is division by a power of 10, we can accomplish the same thing, by moving the decimal point 2 places to the left, thus making the number smaller. For this problem, that looks like this:

\(\displaystyle 2.53\%\rightarrow0.0253\)

In order to find the decimal equivalent of a percentage, the number that makes up the percent has to be divided by 100. However, since it is division by a power of 10, we can accomplish the same thing, by moving the decimal point 2 places to the left, thus making the number smaller. For this problem, that looks like this:

\(\displaystyle 450\%\rightarrow4.5\)

In order to find the decimal equivalent of a percentage, the number that makes up the percent has to be divided by 100. However, since it is division by a power of 10, we can accomplish the same thing, by moving the decimal point 2 places to the left, thus making the number smaller. For this problem, that looks like this:

\(\displaystyle 0.15\%\rightarrow0.0015\)

In order to find the decimal equivalent of a percentage, the number that makes up the percent has to be divided by 100. However, since it is division by a power of 10, we can accomplish the same thing, by moving the decimal point 2 places to the left, thus making the number smaller. For this problem, that looks like this:

\(\displaystyle 12.7\%\rightarrow0.127\)

In order to find the decimal equivalent of a percentage, the number that makes up the percent has to be divided by 100. However, since it is division by a power of 10, we can accomplish the same thing, by moving the decimal point 2 places to the left, thus making the number smaller. For this problem, that looks like this:

\(\displaystyle 37.1\%\rightarrow0.371\)