4. Percents

Question 1

Represent percents as fractions or decimals

Answer 1

To express a percent as a fraction, simply divide it by 100

Should that percent contain a decimal, nothing changes! Simply divide the decimal by a 100 and get rid of the decimal point by shifting it an equal number of times in the numerator and the denominator

If that percent contains a fraction, divide the fraction by a 100 and simplify the resulting fraction within a fraction
(⅝)% = ⅝ / 100
= ⅝ * 1/100
= 1 / 160

Question 2

Express a percent as a decimal

Answer 2

shift the decimal point two spaces to the left

20% = 0.20 = 0.2

Question 3

Convert fractions and decimals into percents by reversing these steps

Answer 3

1) Convert a decimal into a percent

2) Shift the decimal point two spaces to the right

Question 4

Convert a fraction into a percent

Answer 4

Multiply by 100

Question 5

Taking a “percent of” a number

Answer 5

the easiest way to determine a “percent of a number” is to convert the percent into a fraction and translate the word “of” as “multiply”

1) cancel out any zeroes that are in common to the num and the den

Question 6

Shortcuts to determine various percents (2)

Answer 6

Think of percents as a combination of 100 percents, 10 percents, and 1 percents

1) First get to 10%
» shifts the decimal spot one space to the left

2) First get to 1%
» shift its decimal spot two spaces to the left

Question 7

Shortcuts to determine various percents (2)

Answer 7

Think of percents as a combination of 100 percents, 10 percents, and 1 percents

1) First get to 10%
» shifts the decimal spot one space to the left

2) First get to 1%
» shift its decimal spot two spaces to the left

Question 8

Formula percent change

Answer 8

Percent change = difference / original

(original - new)/original = +-%

If the new value of the item is GREATER than the original value of the item, the percent change formula will measure the INCREASE in the value of the item.

If the new value of the item is LESS than the original value of the item, the percent change formula will measure the DECREASE in the value of the item.

Question 9

If the new value of the item is GREATER than the original value of the item, the percent change formula will measure the ________ in the value of the item.

Answer 9

INCREASE

If the new value of the item is GREATER than the original value of the item, the percent change formula will measure the INCREASE in the value of the item.

Question 10

If the new value of the item is LESS than the original value of the item, the percent change formula will measure the ________ in the value of the item.

Answer 10

DECREASE

If the new value of the item is LESS than the original value of the item, the percent change formula will measure the DECREASE in the value of the item.

Question 11

Problems that involve percent changes greater than 100% are easy to misconstrue.

Answer 11

Be sure to treat such problems as you would any other problem that involved percent change!

Question 12

When the value of an object increases or decreases, the relationship between its original value and its new value is can be stated as:

Answer 12

Original * (1 +- change) = new

Question 13

If the percent change is an INCREASE, the value of that increase should be _______ from 1

Answer 13

If the percent change is an increase, the value of that increase should be added to 1

Question 14

If the percent change is a DECREASE, the value of that decrease should be _______ from 1

Answer 14

If the percent change is a decrease, the value of that decrease should be subtracted from 1

Question 15

Two types of interest:

Answer 15

Simple

Compound

Question 16

Simple interest (I)

Answer 16

I = PRT

P: Principal
R: Rate
T: Time

Only the original principal generates interest

Question 17

Compound Interest

Answer 17

Total value = P (1+ R/T)^TY

P: Principal
R: Rate
T: Times per year
Y: Years

Cf. consecutive percent problems

!!

1) CI generates more interest than simple interest
2) the more frequent the compounding, the more interest

Question 18

Percents with Unspecified Quantities (PUQ) : Pick 100!

Answer 18

If not specified, pick numbers and let the original value equal 100

Question 19

p percent of q is decreased by p percent

Answer 19

(p/100) * q * (1 – (p/100))