# How does percentages work? In simple terms. Like discounts, population, food, economics, scores etc…

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Anything that involves percentages.

In: Mathematics It goes back to Latin. “cent” refers to 100. Per cent means how many out of 100.

If you have 100 apples and 20 of them are bad, then 20% are bad. The other 80% are good. Percent means *out of* or *for* one hundred. One hundred *percent* is therefore the maximum value you can have of something (one hundred *out of one hundred* is… 1).

Half of 100 is 50. So if you have a 50% discount on something that costs \$20, you are taking 50% of the cost away (in this case, \$10), and paying only \$10 for the item.

Since 100% is the full amount of something, if you have a town of 1,500 people and there’s a 100% increase in population, then you’ve added 1,500 people to the town (for a new total population of 3,000 people). 200% = twice the full amount of something – if a town of 1,500 people grows by 200%, then 3,000 new people came to the town (double the original amount) and the new total population is 4,500 people. cent = 100. per = rate (kinda)

percentage is just per every hundred. so 20% is 20 per every hundred.

if you are getting a 20% discount on a shirt that is 70 dollars. you are getting 14 dollars off. for every 100 cents you are getting 20 cents off.

so instead of paying 100 cents x 70 = 7000 (70\$) you are paying 80 cents x 70 = 5600 (56\$)

if 35% of the population of Mississippi is obese, that means 35 out of every 100 people are obese. so if theres 1,000,000 ppl in Mississippi that means 35 out of every 100 of those ppl are obese. It helps to know that the root word “cent” means hundred. So percent means “per hundred”. The word is still often written separately as “per cent” in British English.

So 100% is a whole thing. It’s all of something.

50 percent, or 50 per hundred, is the same as 50/100 mathematically. It’s a division problem.

If the percentage is more than 100, such as 300%, that is more than one of something. Say you have 1 apple. If you increase your apples by 300% that means you have more than 1 apple now. 300% is mathematically the same as 300/100, so you have 3 apples. The term “percent” literally means “per 100”. So a value of 20% is 20 per 100, which is the fraction 20/100 (I’m not simplifying fractions because it makes more sense here). Anytime you see a X%, you can replace it with the fraction X/100

Normally you see percentages in relation to a value. If you have a product that costs \$30, but it says it’s 20% off, then you find 20% of \$30. This is just 30 * 20/100, which is 6, so 20% of \$30 is \$6. Since it’s 20% off, we need to subtract the \$6 from the original \$30 to get the new price of \$24.

If something has a 20% increase, then you take the original value, and add an extra amount, where the extra amount is equal to 20% of the original value. For example, a city has a population of 10,000 people, but then after tourists come in, they say there is a 20% increase, then the new population is 10,000 + (20% of 10,000) = 10,000 + 2,000 = 12,000.

A percentage can be greater than 100%, it just doesn’t make sense all the time. If a product had a 150% discount, it would have a negative price. One place you do see percentages over 100% is in loan repayments. For example, if a loan has a 150% interest rate a month, and I borrow \$100, after one month, I’ll owe \$100 + (150% of \$100) = \$100 + \$150 = \$250. Percent is just short for a Latin phrase for “per hundred”. The “cent” in percent is the same cent as the cent that is one hundredth of a dollar or the centimeter that is one hundredth of a meter.

The percent sign comes from a way to write “x/100” very fast very often.

&nbsp;1% is &nbsp;1 out of 100 or 1/100 or 0.01
&nbsp;2% is &nbsp;2 out of 100 or 2/100 or 0.02
&nbsp;3% is &nbsp;3 out of 100 or 3/100 or 0.03
10% is 10 out of 100 or 10/100 or 0.10

50% is half of the whole or 0.5

100% is a whole or simply 1

If you say 1% of a the population you mean one out of a hundred people.

An important thing to keep in mind is that adding and subtracting percentages is not something you can do in any order.

If you normally add and subtract numbers together it doesn’t matter what order you do it in 5 + 3 – 2 is the same as 5 – 2 + 3.

Withe percentages this matters because you always base percentage on current whole.

A Discount of 25% on something that already was 50% of is different than a discount of 50% on something that was 25% off.

Reducing something by 30% and than increasing that by 30% will not get you to where you where you started out.

Also sometimes when you owe money or are investing money you end up in places where cumulative interest is a thing. You may get something like 5% interest every year, but that doesn’t mean that after 5 years you have 25% more than you started with but instead something closer to 27.6% because each year you added 5% of something that was already 5% bigger.

For most things you can just write it out as a decimal number or a fraction and get the same result. a big thing when hearing people talk about percentages is that there can be a MASSIVE difference between “increased *BY* x%” and “increased *TO* x%”. the latter means the chance of something happening is now the new percentage, while the former involves actually calculating what the new value is, and can be tricky or even scary if one doesn’t know about the difference

the most common example I see used is those phrases thrown around that go like ‘having a baby after 45 increases deformities by 80%!’ which at first glance sounds super scary, right? that’s a ton of babies! except that the chance increases BY 80%, not TO 80%. so, say that before mom is 45, chance of those things happening equates to 1% of births (1 in 100, just throwing out a basic number for easy math here). 80% is equivalent to 80/100, or 0.8. you’re adding 80% of the original number to the number to find the new rate, so you would use this:

1 + (0.8 x 1) = 1+0.8 = 1.8

so rather than a big huge number it turns out that for mothers older than 45, a bit less than 2 in 100 babies will have a deformity from the previous 1 in 100.

it can also help to convert to multiplication when figuring out what a percentage means. “per cent” means “of 100” so 100% is equal to multiplying by 1 (100/100), 200% is 2x (200/100), 250% is 2.5x (250/100), 1000% is 10x, etc. basically take the decimal and move it to the left two digits before multiplying the original number by that amount.

“50% more/less” (or other numbers) is common on packaging, but you can equate it to 1.5 and 0.5 respectively (the 1 comes in for the “50% more” because you are adding the original amount to the new amount, you can break this number down to 1x + 0.5x)

tldr, if a Big Bag has 50% more than a Normal Bag, it has the equivalent of 1 1/2 (1.5x) Normal Bags. meanwhile a Mini Bag that has 50% less product is half the amount of a normal bag (0.5x)