A percentage is a portion of 100, or per 100. So if I am a crazy cat lady and I have 100 cats, 75 of which are black and 25 of which are orange, then 75% of my cats are black.
I don't have to own 100 cats. I really don't, I swear. I only have 3 cats in reality. One is orange, one is gray and one is black. In this case, the total number of cats = 3. So now 33.3% (or
My explanation goes back to fractions a bit, but remember how the denominator of your fraction represents the whole? It's the same thing with percentages, except that your whole represents 100. So my 3 cats represent 100, in which case each cat represents 1 part out of that 3, multiplied by 100.
Whatever number we have, to make it a percentage we need to make it relate to 100.
Let's say I have 5 diamond earrings amongst a collection of 60 earrings total. I want to know what percentage of my earrings are diamond.
So our problem is this:
We want to convert that 60 to 100, which means the 5 is also going to increase proportionally.
First, we need to figure out how many times 60 goes into 100.
1.666
60[100.000
-60
400
-360
400
-360
400
-360
40
__
So 60 goes into 100 1.666 times. For the sake of accuracy and brevity, let's round the last 6, making the number 1.667
Had to do a little rounding there but we were close.
So now we know that 5 is 8.34% of 60. Therefore 8.34% of the earrings are diamond.
What if we are given a percentage but don't know the whole?
Let's say we had a party and 70% of the guests showed. 22 people showed up. How many people did we invite?
We know that 70 out of every 100 people showed up, but only 22 people came so we couldn't have invited 100 people.
This is our problem:
This is going to get a bit into algebra, so keep in mind all we want to do is to isolate ? so that it is the only thing on one side of the equal sign. There are a few steps so please bare with me. First we are going to multiply both side by 1/22 (if we only did that to one side they wouldn't be equal!):
On the right hand side the 22s cancel and we are left with:
Now we need to flip both sides to their reciprocals because we want to make the right side of the equation equal to ?, not ?/1.
Let's multiply the numerator by the numerator and the denominator by the denominator (remember that when multiplying fractions we don't need to find a common denominator):
And our answer is:
Now let's work with what we have and divide 2200 by 70:
31.4285
70[2200.0000
-210
100
-70
300
-280
200
-140
600
-560
400
-350
50
So ? is equal to 31.4285
Divide 22 by 31.4285 and you will get 0.700001590; very close to 70% (not exact because of rounding error)
Of course, we have to round this number because we are talking about people and you can't have a fractional person. So we say 31 people were invited to the party. Maybe 31 adults and 1 child were invited and that accounts for the fractional person. Sometimes you just have to round.
There is another faster, simpler way we could have solved this problem. We had enough information to figure out what 1% of our problem is.
In this case, we can divide 22 by 70 to find what 1% is:
Does the result look familiar? Now, we take the result, 0.3142857, and multiply it by 100 to find out what 100% is (100% = 100 * 1%) . Doing this, we get the same result as before: 31.42857
Another problem we might encounter when using percentages is not knowing the ending percentage.
Let's say we were selling pumpkins at a farmers' market and we were told that 85% of our pumpkins sold. We had brought 312 pumpkins to the market that morning.
How many pumpkins did we sell?
Our problem is now:
312 x 0.85
The difference for our people to the party problem was we were trying to find the total. Now we know the total and we are trying to solve for the parts. Pumpkin parts, that is. It's easier to solve for the parts when we know the total.
312
x 0.85
1560
2496
26520
Now move the decimal place two spaces to the left: 265.20
So now we know that 265.2 is 85% of 312.
It's hard to have 265.2 pumpkins so we'll round again and have 265 pumpkins that we sold. Maybe we sold a really small pumpkin in addition to our 265 normal sized ones. In the real world, sometimes we just don't have remainders. This is when rounding is handy.
These are your two basic problems when dealing with finding percentages. Either you will know the parts or you will know the total. Now you know how to solve both.
I
like this kid's interpretation of remainders. Although in the real
world we would probably round them, they can seem like time wasters lol.
See more funny kid papers.
Conversions
Decimals to Percents
Converting percents to decimals is fairly easy. All you do is move the decimal point of the decimal to the right until the denominator is equal to 100.
Let's convert 0.005 to a percent:
We have found that 0.005 is equal to 0.5% of 100.
Try converting 0.5 to a percent:
0.5 is equal to 50%.
What about 50.0?
50.0 is equal to 5,000%.
Percents to Fractions
Converting percents to fractions is fairly easy. Remember that 100 is the denominator of any percentage and then reduce the fraction to lowest terms if it is not in lowest terms already.
Convert 33% to a fraction:
Convert 200% to a fraction:
We can simplify this fraction further:
Convert 12.5% to a fraction:
Simplify:
Of course, there will become some percentages that you just memorize their conversions, such as 25% =
What if we want to convert those fractions back to percentages? Simply change the denominator back to 100 (make sure to multiply or divide the numerator by the same number so that the fraction stays the same ):
Convert
Our answer is 12.5%
Convert
Our result is 40%
Convert
We have 600%
Convert
The answer is 15%
Aaaand that's about all there is to percentages. On to bigger and better things!
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