Dividing decimals
Dividing Decimals Dividing Decimals
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- We need to divide 0.25 into 1.03075.
- Now the first thing you want to do when your divisor, the
- number that you're dividing into the other number, is a
- decimal, is to multiply it by 10 enough times so that it
- becomes a whole number so you can shift the
- decimal to the right.
- So every time you multiply something by 10, you're
- shifting the decimal over to the right once.
- So in this case, we want to switch it over the
- right once and twice.
- So 0.25 times 10 twice is the same thing as 0.25 times 100,
- and we'll turn the 0.25 into 25.
- Now if you do that with the divisor, you also have to do
- that with the dividend, the number that
- you're dividing into.
- So we also have to multiply this by 10 twice, or another
- way of doing it is shift the decimal over
- to the right twice.
- So we shift it over once, twice.
- It will sit right over here.
- And to see why that makes sense, you just have to
- realize that this expression right here, this division
- problem, is the exact same thing as having 1.03075
- divided by 0.25.
- And so we're multiplying the 0.25 by 10 twice.
- We're essentially multiplying it by 100.
- Let me do that in a different color.
- We're multiplying it by 100 in the denominator.
- This is the divisor.
- We're multiplying it by 100, so we also have to do the same
- thing to the numerator, if we don't want to change this
- expression, if we don't want to change the number.
- So we also have to multiply that by 100.
- And when you do that, this becomes 25, and
- this becomes 103.075.
- Now let me just rewrite this.
- Sometimes if you're doing this in a workbook or something,
- you don't have to rewrite it as long as you remember where
- the decimal is.
- But I'm going to rewrite it, just so it's
- a little bit neater.
- So we multiplied both the divisor and
- the dividend by 100.
- This problem becomes 25 divided into 103.075.
- These are going to result in the exact same quotient.
- They're the exact same fraction, if you want to view
- it that way.
- We've just multiplied both the numerator and the denominator
- by 100 to shift the decimal over to the right twice.
- Now that we've done that, we're ready to divide.
- So the first thing, we have 25 here, and there's always a
- little bit of an art to dividing something by a
- multiple-digit number, so we'll see how well we can do.
- So 25 does not go into 1.
- 25 does not go into 10.
- 25 does go into 103.
- We know that 4 times 25 is 100, so 25 goes
- into 100 four times.
- 4 times 5 is 20.
- 4 times 2 is 8, plus 2 is 100.
- We knew that.
- Four quarters is $1.00.
- It's 100 cents.
- And now we subtract.
- 103 minus 100 is going to be 3, and now we can
- bring down this 0.
- So we bring down that 0 there.
- 25 goes into 30 one time.
- And if we want, we could immediately put
- this decimal here.
- We don't have to wait until the end of the problem.
- This decimal sits right in that place, so we could always
- have that decimal sitting right there in our quotient or
- in our answer.
- So we were at 25 goes into 30 one time.
- 1 times 25 is 25, and then we can subtract.
- 30 minus 25, well, that's just 5.
- I mean, we can do all this borrowing business, or
- regrouping.
- This can become a 10.
- This becomes a 2.
- 10 minus 5 is 5.
- 2 minus 2 is nothing.
- But anyway, 30 minus 25 is 5.
- Now we can bring down this 7.
- 25 goes into 57 two times, right?
- 25 times 2 is 50.
- 25 goes into 57 two times.
- 2 times 25 is 50.
- And now we subtract again.
- 57 minus 50 is 7.
- And now we're almost done.
- We bring down that 5 right over there.
- 25 goes into 75 three times.
- 3 times 25 is 75.
- 3 times 5 is 15.
- Regroup the 1.
- We can ignore that.
- That was from before.
- 3 times 2 is 6, plus 1 is 7.
- So you can see that.
- And then we subtract, and then we have no remainder.
- So 25 goes into 103.075 exactly 4.123 times, which
- makes sense, because 25 goes into 100 about four times.
- This is a little bit larger than 100, so it's going to be
- a little bit more than four times.
- And that's going to be the exact same answer as the
- number of times that 0.25 goes into 1.03075.
- This will also be 4.123.
- So this fraction, or this expression, is the exact same
- thing as 4.123.
- And we're done!
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