Hi,

When talking about percentages you should anways say "percentage OF WHAT". We quite often leave off the "of what" and that can cause confusion. For "percentage difference" I think of a quantity that has some value and then the value changes, and I ask "What is the difference, as a percentage of where you started?"

For your two numbers the difference is 251 - 157 = 94. If you were a storekeeper and bought an item for $157, marked it up $94 and sold it for $251 then I would say that your markup was $94. To express this as a percentage I would find 94 as a percent of 157, that is a percentage of where you started.

 ⁹⁴/₁₅₇ 100 = 59.9 %

and thus 157 increased 59.9% to 251.

If, on the other hand, you were a customer and saw an item in the window for sale that said "marked down from $251 to $157" you might wonder what is the percentage decrease. This time the value went from 251 to 157 and

 ⁹⁴/₂₅₁ 100 = 37.5 %

Thus 257 decreased 37.5% to 157.

94 is 59.9% of 157 and 94 is 37.5% of 251. Which percent you use depends on which way you are going. To be clear I wouldn't say "the difference between 157 and 251 is ??%" but rather "157 increased 59.9% to 251" or "251 decreased 37.5% to 157".

Penny

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