How Do You Figure Out Ratio/ Proportions/ Markups And Markdowns On A Calculator?

A calculator is just a tool for helping you accomplish the arithmetic. If you don't know how to do those functions, a calculator won't help.

Markup/Markdown
Markup is often expressed as a percentage of a base value. For example, we might want to know the price of a \$50 item marked up by 20%.
(new price) = (original price) + 20% of (original price)

In math, "of" usually means multiply, often represented by "*"
(new price) = (original price) + 20%*(original price)
= (original price)*(1 + 20%)
= (original price)*(1 +20/100)
(new price) = (original price)*(1.20)

On a calculator, you can compute the markup by either of two methods:
1)  compute the markup amount = 20%*\$50 = .20*50 = 10 and add that to the original amount 50 + 10 = 60

2) multiply the original amount by (1+markup) = 1+20/100 = 1.20 like this 50*1.20 = 60  (same answer)

Markdown is the same, except the sign changes to reflect subtraction.
\$50 marked down 20% = 50*(1 - 20/100) = 50*(1 - .20) = 50*(.80) = 40

If you know the final price, and you know it was marked up 20%, and you want to find the original price, you can solve the equation
(final price) = (original price)*(1.20)
(final price)/(1.20) = (original price)    (divide both sides by 1.20)

The same works for finding the price before markdown
(final price) = (original price)*(1-.20) = (original price)*(.80)

(final price)/(.80) = (original price)    (divide both sides by .80)

Ratio/Proportion
A ratio or proportion may be expressed as
x : 40 = 1 : 10,  where the "x" may substitute for a number anywhere in the expression of proportion. Such a proportion can also be written as a ratio
x/40 = 1/10

Since both sides are equal, we can take the inverse of both sides and the result will remain equal. If "x" starts out in the denominator as it is below, this rule can be used to put it in the numerator, as it is above.
40/x = 10/1

Wherever the "x" is in the expression, we generally want to isolate it on one side by performing the same operation on both sides.
x/40 = 1/10
x = 40*(1/10) = 40/10    (multiply both sides by 40)

On the calculator, the math would be 40/10 = 4, or 40*1/10 = 4. Whether you need to do the multiplication depends on the actual numbers in the actual problem.

It is a good idea to get comfortable with expressing "percent" either as a decimal number or as a number with a percent sign:
8.9% = 8.9/100 = .089
20% = 20/100 = .20
143% = 143/100 = 1.43
thanked the writer. 