what does it mean when something has a 165% increase or like a 98% increase/decrease. I just can’t seem to understand it

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Imagine you own a lemonade stand, and I sell exactly $100 of Lemonade a day. Then, lemons are found to cure cancer (idk), and suddenly you sell $265 in sales. $265 is 165% more than your old $100, and is therefore a 165% increase.

The reason you would use percents over dollar amounts, is because percents are always relative to the “before” number. If your sales went from $100 to $265, OR if your sales went from $5000 to $13250, either way it’s a 165% increase.

*Note: this is (for example) if your sales increased **__*by*__** 165% (or generally if they increased 165%). If they increased **__*to*__** 165%, they would go from $100 to $165. Feel free to ask if you’re confused*

If you have one hundred cookies, increase your cookie count 165%, you now have 265 cookies. One hundred percent increase means double what you have. 98% increase… 98% is 98 out of 100. It would equal 198. Increase over what is already there.

Percentages represent parts of a whole. 100% is one whole. Did you eat 100% of a pie? You ate one whole pie. So, if something increased by 100%, it means you now have one whole more than you had. Did your amount of one pie increase by 100%? You now have two pies. Do you have 150% more pie? That would be one and a half more than the one pie you started with. Yum!

So a percent increase or decrease is a *relative* change – meaning, a change *in relation* to the original/previous value.

If you are increasing by a percentage, you take the original value and raise it by a portion of 100. Remember that % is per 100, always.

Say something is priced at $500. If there is a 1% increase, that $500 increases by 1/100. 1/100 of $500 is $5, right? So, a 1% increase on $500 would be $505.

The math on this is just (1/100) x 500 = 5. Then, 500 + 5 = 505

A 98% increase is like this too. (98/100) x 500 = 490. So you have a $490 increase on your original amount of $500, which brings the price up to $990.

Now, instead of 98%, say there’s a 165% increase. This means that the price has increased by 165/100 of that original amount. What is 165% of $500? You can just take 500 and multiply it by (165/100), like we did before, which gives you $825. So a 165% increase on $500 would be: $500 + $825 = $1325.

It’s like this with the decreasing % too, except instead of adding to the original value, you subtract from it. E.g., a 98% decrease on a list price of $500:

(98/100) x 500 = 490

$500 – $490 = $10

There’s a simple formula for % change (where positive is increase and negative is decrease):

percent change = 100 x (new value – starting value) / old value

So if you started with 83, and now you have 94, the % change is:

percent change = 100 x (94 – 83) / 83 = 13.25 (percent, and it’s an increase since it’s positive)

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If you want to go the other way, you can rearrange that formula to get:

new value = (1 + percent change / 100) * old value

So if you have 173 things, and you decrease by 35%, you have:

new value = (1 + (-35)/100) * 173 = (0.65) * 173 = 112.45.

where the -35 is because it’s a 35% *decrease*.

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Note that one common error is to assume that a decrease of 50%, followed by an increase of 50%, gets you back where you started. It doesn’t. Can you see why? Try calculating it.