Flashcards in Percents & Ratios Deck (15)

Loading flashcards...

1

## How to turn percent questions to mathematical phrase or equation

###

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

2

## Why is the decimal form of a percent called the "multiplier" of that percent?

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

3

## Pointer 1 for gaining number sense with percents:

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

4

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

###
Since: (New) = (multiplier) • (old)

We could say: multiplier = new / old

Then change multiplier to percent

5

## How to find percent increases using percent as multiplier

###
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)

6

## Sequential % changes questions

### Involves % increases and decreases within a single problem

7

## Sequential percent changes, how to solve

###
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%

8

## The basic idea of compound interest is...

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

9

## Big idea #1 of compound interest

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

10

## Big idea #2 of compounding interest

###
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),

11

## When the compounding period is not annual...

###
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)

12

## A ratio is...

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

13

## How to use scale factor in a ratio problem

###
Put letter N beside number in a ratio, eg:

3n / 4n

14

## Do proportioning to relate parts to the whole...

###
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

15