Estimating large sums and differences word problems
About this video
The video solves two word problems that ask 'about how many', so the answer only needs an estimate. Both numbers are rounded to the nearest thousand, then added or subtracted in your head. It also shows how to use common sense to rule out answers that cannot be right.
You'll be able to
- spot words like 'about' that tell me to estimate instead of finding an exact answer.
- round large numbers to the nearest thousand to estimate a sum or difference.
- check if an estimate makes sense, like a subtraction answer being smaller than the starting number.
Key words
- estimate
- A close answer that is good enough, found by using rounder, easier numbers.
- round
- To change a number to the nearest ten, hundred, thousand and so on, so it is easier to work with.
- nearest thousand
- The multiple of 1,000 that a number is closest to, like 13,246 being closest to 13,000.
- approximately equal to
- Close to but not exactly equal, shown with a squiggly equals sign.
Transcript
- [Instructor] We're told a library received 13,246 books from a book company. Later that month, they received another 3,899 books from a book donation program. About how many books did the library receive in total? So pause this video, have a go at this and recognize it's saying about, so you just have to estimate.
You don't have to get the exact number. Alright, now let's do this together. So this first video, sorry, this first number, I should say, 13,000. We could round it if we wanna estimate to the nearest 10,000. But the second number is just in the thousand. So actually I wanna round both of these to the nearest thousand.
So this first number, I'm gonna say this is all going to be roughly equal to, little squiggly equal signs. So if I round 13,246 to the nearest thousand, it's closer to 13,000 than it is to 14,000. So it's gonna be 13,000 plus, if I round the second number to the nearest thousand, it's closer to 4,000 than it is to 3,000.
So I'll say plus 4,000, and we can do this in our head. 13 plus four is 17. So we're talking about 17,000, which is this choice right over here. And once again, there are multiple ways that you could have approached this and you just have to get whichever is closest to your answer.
Let's do another example. So here we're told a farmer picked 35,250 apples this season. She sold 4,339 apples at the market. About how many apples does the farmer have left? So pause the video again and see if you can tackle this. All right, so once again, it's about, so we can estimate, which is always fun to do and not have to do a bunch of hairy math.
And this number right here is in the thousands. This number over here is in the tens of thousands, but I like to round to the similar place. So let's round both to the nearest thousand. So this is going to be roughly equal to 35,250 is closer to 35,000 than it is to 36,000 and 4,339 is closer to 4,000 than it is to 5,000.
And I want to subtract, 'cause she's selling these, these roughly 4,000 apples. And so if 35,000 minus 4,000, that is going to be 31,000 right over here. And an interesting thing to just be aware of is if, even if you look at these other choices, if you start with roughly 35,000 apples, if you're selling some, there's no way that your apples should increase.
So if you do some type of estimation, and there are ways, if you rounded in a certain way, if you rounded to the nearest 10,000, that you actually could end up increasing. But if you're subtracting, you should never estimate with a number that is larger after the subtraction than the number that you started off with.
So that one doesn't make sense. And even if you look at choice B right over here, while the difference between 35,250 and 34,400 is less than a thousand, we're selling way more apples than that.
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