Fractions - PSAT Math

Remember that if x has a remainder of 4 when divided by 5, xminus 4 must be divisible by 5. We are therefore looking for a number p such that p - 8 - 4 is divisible by 5. The only answer choice that fits this description is 17.

Dividing by a number (in this case frac {3}{4}) is equivalent to multiplying by its reciprocal (in this case frac {4}{3}). Therefore:

frac {2}{3}div $\frac{3}{4}$ = $\frac{2}{3}$times $\frac{4}{3}$ = $\frac{8}{9}$

First we will evaluate the terms in the parentheses:

Next, we will square the first fraction:

$\frac{100}{169}$div $\frac{3}{4}$

We can evaluate the division as such:

$\frac{100}{169}$times$\frac{4}{3}$=\frac{400}{507}$

Start by rewriting this fraction as a division problem:

When dividing fractions, you multiply by the reciprocal of the second fraction, so you can rewrite your problem like this:

Multiply across the numerators and then across the denominators to get . The x's cancel, and you can reduce the fraction to be .

,

or, equivalently,

, or, equivalently,

,

or, equivalently,

From here we need to find a common denominator.

or, equivalently,

Begin by simplifying any additions that need to be done:

becomes

Now, remember that the numerator can be rewritten :

Now, when you divide fractions, you multiply the numerator by the reciprocal of the denominator:

Cancel the s and you get:

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

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.

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)

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:

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce

66.6/0.6 = 111 ft