Percents & Ratios

Question 1

How to turn percent questions to mathematical phrase or equation

Answer 1

1. Treat “is” as an equal sign
2. Treat “of” as a multiplication sign
3. Convert from % to decimal form
4. Assign letter variables for unknowns

Question 2

Why is the decimal form of a percent called the “multiplier” of that percent?

Answer 2

Because we multiply by the decimal form to get the percent form of a number

Question 3

Pointer 1 for gaining number sense with percents:

Answer 3

Think 10% of the whole, and sometimes 1%, and work from there

Question 4

How to find the percent increase/decrease when starting and ending values are given

Answer 4

Since: (New) = (multiplier) • (old)

We could say: multiplier = new / old

Then change multiplier to percent

Question 5

How to find percent increases using percent as multiplier

Answer 5

See percent increase as:

Y increased by n%, or X is n% greater than Y

Thus

(Multiplier for P% increase) = 1 + (P% as a decimal)

Question 6

Sequential % changes questions

Answer 6

Involves % increases and decreases within a single problem

Question 7

Sequential percent changes, how to solve

Answer 7

Whenever two or more percent changes are in a row, NEVER add or subtract the percents. Instead, use multipliers:

At beg of year, price of item increased by 30%. After increase, an employee bought it at 40% discount. What % below original did employee pay?

30% increase is 1 + 0.3 of multiplier = 1.3

40% decrease is 1 - 0.4 of multiplier = 0.6

Then multiply the two multipliers (1.3) (0.6) = 0.78

1 - 0.78 = 0.22 = 22%

Question 8

The basic idea of compound interest is…

Answer 8

Interest on interest, i.e., interest paid on total amount that has already accrued, principal + all previous interests and payments.

Question 9

Big idea #1 of compound interest

Answer 9

Compound interest always outperforms simple interest, as long as there is more than one year (one compounding period)

Question 10

Big idea #2 of compounding interest

Answer 10

In Y years, the principal is multiplied by % increase multiplier Y times. If P is the principal and R the multiplier, the total amount of account after Y years is…

A = P (R ^ Y).

with R = (1 + i / 100),

Question 11

When the compounding period is not annual…

Answer 11

Assign N as the number of times that compounding period occurs on a year…

Quarterly: N = 4

Monthly: N = 12

Daily: N = 365

N is then used to divide the annual percent of interest so that

R = (1 + i / 100N) and A = P (R ^NY)

Question 12

A ratio is…

Answer 12

A fraction that may compare part-to-whole or part-to-part

Question 13

How to use scale factor in a ratio problem

Answer 13

Put letter N beside number in a ratio, eg:

3n / 4n

Question 14

Do proportioning to relate parts to the whole…

Answer 14

If boy-girl ratio is 3:5

Boys are 3 parts of class, and girls 5 parts

Which adds up to 8 parts

Therefore, boys constitute ⅜ of class, and girls ⅝

Question 15

Percent means…

Answer 15

divided by 100