Percentage

Question 1

x%

Answer 1

x/100 (and we reduce the fraction if possible)

5%= 5/100 or 1/20

Question 2

To convert a decimal or an integer to a percent

Answer 2

multiply the decimal or integer by 100 and attach the percent sign

0.03*100= 3%

Question 3

To convert a fraction to a percent

Answer 3

multiply the fraction by 100 and attach the percent sign

7/100 -> (7/100)*100= 7%

Question 4

To convert a percent to a decimal

Answer 4

drop the percent sign and divide by 100 drops the percent sign and divide by 100

5/10= 0.5

Question 5

When we need to find a percent of an unknown amount, we can either

Answer 5

1) represent the unknown amount by a variable, such as x

2) Assume the unknown amount is 100 items

Question 6

Percent word problems

Answer 6

1) “Percent of”
2) “What percent”
3) “Percent less than”
4) “Percent greater than”
5) “Percent change”

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Question 7

Percent of represents

Answer 7

multiplication of a given number

i.e: 5 percent ofz= 5/100 (z)= z/20

Question 8

What percent

Answer 8

we can translate “what percent” into x/100, and then set up an equation to solve for “x.”

• > 20 is what percent of 80 can be solved using the (a/b)100 = (20/80)100
• > this method will either yield a decimal or integer unless we multiply the quotient

Question 9

We may encounter percent problems in which the percents given are variables.

Answer 9

For example, “p percent of q is equal to r.” We can translate this to p100×q=r, or “a percent of b is equal to c.” We can translate this to a100×b=c.

Question 10

Percent less than Problems

Answer 10

• ## “Percent less than” problems relate to a reduction in the value of something

Question 11

Percent less than Problems: Reduction

Answer 11

(InitialValue)×(1−”PercentLessThan”/100).

-The initial value is the value of an item before its value is reduced, and the final value of an item is the value after the reduction has occurred.

Question 12

“Percent greater than” problems

Answer 12

• “Percent greater than” problems relate to the increase in value of something.

Question 13

“Percent greater than” problems equation

Answer 13

⇒FinalValue *(InitialValue)×(1+PercentGreaterThan/100)

Question 14

In “Percent Greater Than” problems

Answer 14

x% greater than y is equivalent to (100 + x)% of y

Question 15

100 percent greater than z

Answer 15

200 percent of z

Question 16

450 percent greater than z

Answer 16

550 percent of z

Question 17

Markup by P percent:

Answer 17

$1,000×(1+P/100)

Question 18

Markdown by P percent:

Answer 18

$1,000(1−P/100)

Question 19

Successive percent changes

Answer 19

goes through mutiple changes -> up, down,up,up and so on

-> Successive percent changes should be multiplied.Successive percent changes should be multiplied.

Question 20

an item that initially cost $100 was marked up 20 percent and that the resulting value was then increased 20 percent more.

Answer 20

($100×120/100)×120/100=$144.

Question 21

What if we took another $100 item, marked it down 20 percent, and then marked the resulting value down 20 percent more?

Answer 21

($100×80/100)×80/100=$64.

Question 22

“Percent change” problems

Answer 22

• increase or decrease in a value after a change in that value has occurred

Question 23

$800 is what percent greater than $100?

Answer 23

The final price may be 8 times the starting price, but the stock’s final value is only 700 percent greater than its initial value.

Question 24

Percent Change

Answer 24

(FinalValue−Initial Value)/InitialValue)×100

Question 25

Final Value (Increase)

Answer 25

(InitialValue)×(1+PercentGreaterThan100)

Question 26

Final Value (decrease)

Answer 26

(InitialValue)×((1−PercentLessThan)/100)

Question 27

The Value of an Item Decreases Then Returns to Its Original Value.

Answer 27

To return a discounted value back to the original value, we must increase the discounted value by some percent greater than the percent by which it was discounted.
-> To determine the percent by which we must increase a discounted value to return it back to its original value, we can use the percent change formula:

Question 28

Profit

Answer 28

Revenue- Cost

Question 29

%Profit

Answer 29

profit/cost×100