Adding and subtracting decimals
Subtracting decimals (old) Subtracting decimal numbers
⇐ Use this menu to view and help create subtitles for this video in many different languages.
You'll probably want to hide YouTube's captions if using these subtitles.
- Welcome to the presentation on subtracting decimal numbers.
- Let's get started with some problems.
- The first problem I have here says five point seven three
- minus point zero eight two one equals who knows?
- So the first thing you always want to do with a decimal like this,
- and I actually kind of inadvertently did this,
- is that you want to line up the decimals.
- So you actually want this decimal to be right above this decimal.
- I almost did that when I did it,
- it must have been my subconscious doing it.
- But let me just do it a little bit neater.
- So it's five point seven three, and I'll put the decimal here.
- Decimal zero eight two one.
- And some people say it's good to always put a zero in front of the decimal.
- My wife's a doctor and she says it's critical
- otherwise you might give someone the wrong amount of medicine.
- So, we've lined up the decimals
- and now we're ready to subtract.
- So one thing that you have to think about when you do decimals
- is we're going to have to subtract this twenty-one ten thousandths
- or this two and this one from something.
- We can't just subtract it from this blank space.
- So we have to add two zeros here.
- And as you know, with the decimal when you add zeros to the end of it,
- it really doesn't change the value of the decimal.
- So at this point,
- we just view this like a level four subtraction problem.
- So the first thing we do in any subtraction problem
- is see if any of the numbers on top
- are smaller than any of the numbers on the bottom.
- Well in this case there are a lot of them.
- So this zero is less than this one, this zero is less than this two,
- this three is less than this eight.
- So we're going to have to borrow.
- Some people will like to do their borrowing and subtracting,
- they kind of alternate between the two.
- I like to do all of my borrowing ahead of time.
- So what I do is I start in the top right and I say
- okay, zero is less than one.
- So that zero becomes a ten.
- But in order to become a ten,
- I would have had to borrow one from some place.
- I look to the left of that zero
- and I say well, can I borrow the one from zero?
- Well, no.
- This is just the way I do it.
- There are people who would actually let you borrow the one from the zero,
- but I say no, instead of borrowing the one from the zero,
- I borrow the one from this entire thirty.
- So this thirty -- see right there, this is three zero
- so I'm going to borrow one from it and it becomes twenty-nine.
- So we borrowed one from this thirty to get a ten here,
- and now let's check again to see if all of our numbers on top
- are larger than all the numbers on the bottom.
- Well ten is larger than one, nine is larger than two,
- two is not larger than eight.
- So we have to borrow again.
- So if we're going to borrow,
- the two becomes a twelve, and the seven--
- we borrowed one from that -- becomes a six.
- So let's check again.
- Ten is larger than one, nine is larger than two, twelve is larger than eight,
- six is larger than zero, and five is larger than zero.
- So now we've done all of our borrowing and we're ready to do some subtraction,
- and this is the easy part.
- Ten minus one is nine.
- Nine minus two is seven.
- Twelve minus eight is four.
- Six minus zero is six.
- Five minus zero is five.
- And we just bring down the decimal point.
- So there's our answer.
- Five point seven three minus zero point zero eight two one is equal to five point six four seven nine.
- There you go.
- I probably confused you, so let's do some more problems.
- Here's another one.
- Eight -- let me leave some space on top to do the borrowing.
- Eight point two five minus zero point zero one zero five.
- So what was that first step that I always have to do?
- Right.
- To line up the decimals.
- So let me do that.
- So it's eight point two five and zero point zero one zero five.
- Notice I lined up this decimal right below this decimal.
- Now I add the zeros,
- just because this zero and this five need to be subtracted from something.
- Now let me do my borrowing.
- So once again, all I do is check to see
- whether the top number is larger than the number below it.
- Well, this zero is smaller than five, so I'm going to have to borrow.
- So I'm going to borrow.
- I can't borrow from this zero,
- I have to borrow from this entire fifty.
- So this fifty, if I borrow one from fifty I get forty-nine.
- And this zero will then become a ten, right?
- I borrowed one from fifty to get a ten.
- Now, am I done?
- Ten is larger than five.
- Nine is larger than zero.
- Four is larger than one.
- Two is larger than zero.
- Eight is larger than zero.
- So I think I'm ready to subtract.
- Ten minus five, well that's five.
- Nine minus zero is nine.
- Four minus one is three.
- Two minus zero is two.
- Eight minus zero is eight.
- And I bring down the decimal point.
- So if you mastered level four subtraction,
- the decimal problems really are just about lining up the decimal point,
- adding the zeros and then just doing a normal subtraction problem.
- In general with subtraction,
- I think most people have the most trouble with the borrowing.
- The way I do it I think is a little bit different than is taught in a lot of schools.
- A lot of schools they'll do the subtraction,
- and they'll borrow alternatively.
- But I find this easier when I just borrow ahead of time,
- and I also, like for example in this problem, when I had to make this zero into a ten,
- instead of borrowing from the zero, which is not intuitive
- because I can't really borrow from the zero,
- I borrowed from this entire fifty, and I made that into a forty-nine.
- Let's do one more problem.
- If I have two point six four minus zero point zero four eight six.
- So once again, let's line up the decimal points.
- Two point six four and it's point zero four eight six.
- Lined up the decimal points, include the zeros on top.
- You're going to have a zero here, so I have to borrow.
- Becomes a ten.
- Can't borrow from the zero,
- so I have to borrow from this entire forty.
- So this forty becomes a thirty-nine.
- I think I'm running out of space.
- So ten is larger than six.
- Nine is larger than eight.
- Three is not larger than four.
- So this three I'm going to have to borrow.
- So three becomes a thirteen.
- And this six becomes a five.
- This is really bad, I shouldn't do it so messy.
- But now we say the ten is larger than six, the nine is larger than the eight,
- this thirteen should be on top of that three.
- The thirteen is larger than four, and five is larger than zero.
- So we're ready to subtract.
- Ten minus six is four.
- Nine minus eight is one.
- Thirteen minus four is nine.
- Five minus zero is five.
- Two minus nothing is two.
- Bring down the decimal point.
- So two point six four minus point zero four eight six is equal to two point five nine one four.
- Hope I didn't confuse you too much.
- But I think you're ready now to try the subtraction of decimals.
- Have fun!
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
|
Have something that's not a question about this content? |
This discussion area is not meant for answering homework questions.
Discuss the site
For general discussions about Khan Academy, visit our Reddit discussion page.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
abuse
- disrespectful or offensive
- an advertisement
not helpful
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
wrong category
- a tip or feedback in Questions
- a question in Tips & Feedback
- an answer that should be its own question
about the site
Share a tip
Suggest a fix
Have something that's not a tip or feedback about this content?
This discussion area is not meant for answering homework questions.