Expressing a percent decrease as a percentage of the original
About this video
The library checked out 28% fewer books this week than last week. Calling last week's books x, this week is x − 0.28x = (1 − 0.28)x = 0.72x. So this week's books are 72% of last week's.
You'll be able to
- write a percent decrease as an expression like x − 0.28x.
- rewrite x − 0.28x as 0.72x by factoring out x.
- state a decreased amount as a percentage of the original, like 72%.
Key words
- percent decrease
- How much an amount goes down, written as a percentage of the original amount.
- original amount
- The starting amount, here the number of books checked out last week.
- percent
- Out of 100; 28% means 28 out of every 100, or 0.28.
Transcript
- [Instructor] We are told this week, the library checked out 28% fewer books than last week. Write the percent decrease as a percentage of the original amount. Or in other words, we have to fill out this blank here. The number of books checked out this week is blank percent of the number checked out last week.
Pause the video, try to do that one. All right, so just to simplify or to imagine what's going on, let's just say that the books last week, we could also consider that the original amount, let's call that x. So last week, x books were checked out. Now, how many books are checked out this week?
Well, it's 28% fewer books. So essentially 28% of x less than x. So another way to think about it is this is going to be minus 28% of x. So this is last week. This is 28% of last week. So if you have 28% of last week subtracted from last week, then this is this week.
This week, now, what's another way to write this? Well, this is the same thing as x minus 0.28x. You could also think of this of course as one x minus 0.28x, which is the same thing as one minus 0.28x. I'm just factoring out an x here. Another way to think about it, if you wanted to go the other way, you could distribute this x and get this expression right over here.
And then what's one minus 0.28? Well, that would be, let's see, that would be zero point... If this was 0.3, it would be 0.7 here. So this is 0.72x. Or another way to think about it, this is 72% of x. Or another way to think about it is this week, the library checked out 72% as many books as it checked out last week.
So this is 72%, and we're done.
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