Percentage Flashcards
x%
x/100 (and we reduce the fraction if possible)
5%= 5/100 or 1/20
To convert a decimal or an integer to a percent
multiply the decimal or integer by 100 and attach the percent sign
0.03*100= 3%
To convert a fraction to a percent
multiply the fraction by 100 and attach the percent sign
7/100 -> (7/100)*100= 7%
To convert a percent to a decimal
drop the percent sign and divide by 100 drops the percent sign and divide by 100
5/10= 0.5
When we need to find a percent of an unknown amount, we can either
1) represent the unknown amount by a variable, such as x
2) Assume the unknown amount is 100 items
Percent word problems
1) “Percent of”
2) “What percent”
3) “Percent less than”
4) “Percent greater than”
5) “Percent change”
Percent of represents
multiplication of a given number
i.e: 5 percent ofz= 5/100 (z)= z/20
What percent
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
We may encounter percent problems in which the percents given are variables.
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.
Percent less than Problems
- ## “Percent less than” problems relate to a reduction in the value of something
Percent less than Problems: Reduction
(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.
“Percent greater than” problems
- “Percent greater than” problems relate to the increase in value of something.
“Percent greater than” problems equation
⇒FinalValue *(InitialValue)×(1+PercentGreaterThan/100)
In “Percent Greater Than” problems
x% greater than y is equivalent to (100 + x)% of y
100 percent greater than z
200 percent of z
450 percent greater than z
550 percent of z
Markup by P percent:
$1,000×(1+P/100)
Markdown by P percent:
$1,000(1−P/100)
Successive percent changes
goes through mutiple changes -> up, down,up,up and so on
-> Successive percent changes should be multiplied.Successive percent changes should be multiplied.
an item that initially cost $100 was marked up 20 percent and that the resulting value was then increased 20 percent more.
($100×120/100)×120/100=$144.
What if we took another $100 item, marked it down 20 percent, and then marked the resulting value down 20 percent more?
($100×80/100)×80/100=$64.
“Percent change” problems
- increase or decrease in a value after a change in that value has occurred
$800 is what percent greater than $100?
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.
Percent Change
(FinalValue−Initial Value)/InitialValue)×100
Final Value (Increase)
(InitialValue)×(1+PercentGreaterThan100)
Final Value (decrease)
(InitialValue)×((1−PercentLessThan)/100)
The Value of an Item Decreases Then Returns to Its Original Value.
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:
Profit
Revenue- Cost
%Profit
profit/cost×100
