Percent word problems
Solving Percent Problems 2 Solving Percent Problems 2
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- 100 is what percent of 80?
- These problems tend to kill people because on some level
- they're kind of simple, they're just 100 and an 80
- there, and they're asking what percent.
- But then people get confused.
- They say, do I divide the 100 by the 80?
- The 80 by 100?
- Or is it something else going on?
- And you really just have to think through what the
- language is saying.
- They're saying that this value right here, this 100, is some
- percentage of 80, and that some percentage is what we
- have to figure out.
- What percent?
- So if we multiply 80 by this what percent, we will get 100.
- So let's view it this way.
- We have 80.
- If we multiply it by something, let's call this
- something x.
- Let me do that in a different color.
- If we multiply 80 by something, we are
- going to get 100.
- And we need to figure out what we need to multiply
- 80 by to get 100.
- And if we just solve this equation as it is, we're going
- to get a value for x.
- And what we need to do is then convert it to a percent.
- Another way you could have viewed this is 100 is what you
- get when you multiply what by 80?
- And then you would have gotten this number, and then you
- could convert it to a percent.
- So this is essentially the equation and now
- we can solve it.
- If we divide both sides of this equation by 80, so you
- divide the left-hand side by 80, the right-hand side
- by 80, you get x.
- x is equal to 100/80.
- They both share a common factor of 20, so 100 divided
- by 20 is 5, and 80 divided by 20 is 4.
- So in simplest form, x is equal to 5/4, but I've only
- expressed it as a fraction.
- But they want to know what percent of 80.
- If they just said 100 is what fraction of
- 80, we would be done.
- We could say 100 is 5/4 of 80, and we would
- be absolutely correct.
- But they want to say what percent?
- So we have to convert this to a percent, and the easiest
- thing to do is to first convert it into a decimal, so
- let's do that.
- 5/4 is literally the same thing as 5 divided by 4, so
- let's figure out what that is.
- Let me do it in magenta.
- So 5 divided by 4.
- You want to have all the decimals there, so let's put
- some zeroes out here.
- 4 goes into 5 one time.
- Let me switch up the colors.
- 1 times 4 is 4.
- You subtract.
- You get 5 minus 4 is 1.
- Bring down the next zero.
- And of course, the decimal is sitting right here, so we want
- to put it right over there.
- So you bring down the next zero.
- 4 goes into 10 two times.
- 2 times 4 is 8.
- You subtract.
- 10 minus 8 is 2.
- Bring down the next zero.
- 4 goes into 20 five times.
- 5 times 4 is 20.
- Subtract.
- No remainder.
- So this is equal to 1.25.
- 5/4 is the same thing as 5 divided by 4,
- which is equal to 1.25.
- So far, we could say, 100 is 1.25 times 80, or 1.25 of 80,
- you could even say, But we still haven't expressed it as
- a percentage.
- This is really just as a number.
- I guess you could call it a decimal, but it's a whole
- number and a decimal.
- It would be a mixed number if we didn't do it as a decimal.
- It's 1 and 1/4, or 1 and 25 hundredths, however you want
- to read it.
- So to write it as a percent, you literally just have to
- multiply this times 100, or shift the decimal over twice.
- So this is going to be equal to, as a percent, if you just
- shift the decimal over twice, this is equal to 125%.
- And that makes complete sense.
- 100 is 125% of 80.
- 80 is 100% of 80.
- 100% percent is more than 80.
- It's actually 1 and 1/4 of 80, and you see that right over
- there, so it makes sense.
- It's 125%.
- It's more than 100%.
- But we are done.
- We've solved the problem.
- It is a 125% of 80.
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