FDP

Question 1

What are the following Fractions = to in percent value?

1/6
5/6
1/9
1/7
1/11
1/12
1/13
1/14
1/15
1/16
1/17
1/18
1/19
1/20

Answer 1

The following are the correct conversions
1/6 = 16.7%
5/6 = 83.3%
1/9 = 11.1%
1/7 = 14.3%
1/11 = 9.0909%
1/12 = 8.33%
1/13 = 7.69%
1/14 = 7.142%
1/15 = 6.666%
1/17 = 5.88%
1/18 = 5.55%
1/19 = 5.26%
1/20 = 5%

Question 2

Express the following as percents:

80.4, 0.0007

Answer 2

These are the following conversions:

8040%, 0.07%

Question 3

What to do when you have decimals on powers and roots

Answer 3

Always convert to integers to simplify the problem:

Example: o.oooo27^1/3 = (27*10^-6)

27^1/3 * 10^(1/6)1/3=310^-2

Question 4

When you raise a decimal to a power how many decimals do you get

Answer 4

You get the number of original decimals multiplied by the power

example 0.04^3 = .000064 a total of 6 decimals, two decimal places multiplied by 3

Question 5

What happens when you add the same number to both the numerator and denominator

Answer 5

The number moves closer to 1

Question 6

What does of mean?

eg. what is 30% of 80

Answer 6

of means to multiply

30%*80

Question 7

A 500 mL solution is 20% alcohol. If 100mL of water is added, what is the
new concentration of alcohol?

Answer 7

The original ratio 1:5 will become 1:6, so the concentration is 1/6 or 16,67%

Question 8

Two ways to approach an unknown digit problem

Answer 8

1) Look at the answer choices first to limits
(2) use other given constraints to rule out additional possibilities
(3) Focus on the units digit in the product or sum.
(4) Test the remaining choices

Question 9

What do “directly proportional” and “inversely proportional mean, and what is the difference? For the purpose of this discussion, we will relate x to y

Answer 9

If x & y are “directly proportional”, it means that the relationship between x and y can be represented by x=Ky. K is the “coefficient of proportionality” or the “constant of variation”

Now if x&y are “inversely proportional,” it means that the relationship between x & y can be represented by the equation xy=K. K is the “coefficient of proportionality” or the “constant of variation”

Another way to write the “inversely proportional would be x=K(1/y)

Question 10

The variable x is inversely proportional to the square of the variable y. If y is divided by 3a, then x is multiplied by which of the following?

Answer 10

The Set up is Key:

We know the inverse relationship is xy=K or x=K(1/y)

so lets start wit the latter,

x=k*(1/y2)

(y/3a)^2=y^2/(9a^2)

Since this is proportional everything we do to one side we need to do to the other to make sure relationship stays so the equation becomes

(x * ?) * (y^2/(9a^2)=x(y^2)

now rearrange and we get that ? = 9a^2

Question 11

Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.

A. 1250
B. 1563
C. 2250
D. 2560
E. 2752

Answer 11

Look at picture and then know that K * (5/4)^4 = K*625/256=6250 and this equals 2560

Question 12

In an electric circuit, two resistors with resistances x and y are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. What is r in terms of x and y?

(A) xy
(B) x + y
(C) 1/(x + y)
(D) xy/(x + y)
(E) (x + y)/xy

Answer 12

So you get

1/r = 1/x + 1/y

You need a common denominator before we flip, remember this.

so the common denominator is xy, yielding

1/r = Y/xy + x/xy and we flip getting xy/x+Y