Fractions - PSAT Math

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 0.90_y_ = (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 0.15_x_ = (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.

18_y_ = 3_x_

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.

18_y_ = 3_x_

Divide both sides by 3.

6_y_ = x

Divide both sides by y.

6 = x/y

Thus, the ratio of x to y is 6.

The answer is 6.

To convert a percent into a fraction, simply divide by 100 and reduce. In our case, 62 and 100 have the common factor of 2, so solving and simplification are as follows:

6 students achieved a score of 201-300; 18 achieved a score of 301-400; 30 achieved a score of 401-500. Add these:

The number of students who took the test is the sum of the students who finished in the six ranges:

The question is now to find out what percent 54 is of 120, which can be calculated as follows:

The first hen lays 8 brown eggs: 2/5 * 20 = 8

The second lays 5 brown eggs: 1/4 * 20 = 5

The third lays 6 brown eggs: 3/10 * 20 = 6

Add up the brown eggs and divide by 60, the total number of eggs:

19/60 = 0.31666667 = 31.67%, or 32%.

Convert the improper fraction to the mixed numeral or as the decimal . as a percentage is

First, we will determine the total number of ballots:

Since there are two four year olds, and this question is asking the probability of the chosen child being four, the probability is:

We can right 23% as a fraction and set that equal to over the original price.

From here we cross multiply and divide.

We round this number to $4.28. This is the amount of discoount we need to apply to the original price. To do this we subtract 4.28 from 18.59.

The goal of this problem is to solve for how much Louisa and Caroline have saved, together, towards their goal money for starting a small business. In order to do that, you must add what Louisa has saved to what Caroline has saved, then convert the fraction into a percentage.

Add Louisa and Caroline:

Find the lowest common multiple for the denominator:

Add:

Simplify:

To convert a fraction into a percentage, simply multiply the numerator by 100 and divide by the denominator. There are other methods, but this is the easiest.

Equals

78% is your answer.

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

Divide 16 by 9:

The "7" repeats forever, so

Divide 9 by 16:

We can multiply our numerator and denominator by , which leads to . From here we divide by our denominator, moving the decimal two places to the left.

With this problem the first thing to do is cancel out variables. The x2 can all be divided by each other because they are present in each system. The equation will now look like this:

Now we can see that the equation can all be divided by y, leaving the answer to be:

Another way to represent this question is:

In the one's column, and add to produce a number with a two in the one's place. In the ten's column, we can see that a one must carry in order to get a digit in the hundred's place. Together, we can combine these deductions to see that the sum of and must be twelve (a one in the ten's place and a two in the one's place).

In the one's column:

The one carries to the ten's column.

In the ten's column:

The three goes into the answer and the one carries to the hundred's place. The final answer is 132. From this, we can see that because .

Using this information, we can solve for .

You can check your answer by returning to the original addition and plugging in the values of and .

_x_2 – _y_2 can be also expressed as (x + y)(x – y).

Therefore, the fraction now can be re-written as (x + y)(x – y)/(x + y).

This simplifies to (x – y).

Following this equation, you divide 4 by 8 to get 1/2. When a variable is raised to an exponent, and you are dividing, you subtract the exponents, so 6 – 3 = 3.

125 goes into 2000 evenly 16 times. 1/16 is the fraction in its simplest form.