Okay in this video
I want to talk about just some basic arithmetic and multiplying decimals is
what we're going to do you hear. So
um, I've got three examples here I'm going to do and I'm going to do them in order.
Um, there's really nothing
too tricky about this there's just one little thing you have to remember and then
after that it's just being
I think um, it's knowing your multiplication tables.
Um, so in the first example we'll take one point six five times seven.
Um, you don't have to, my own personal preference is
um, notice the first number has three digits and
the second number has one, I like to put the number with more digits on top.
Um, again you don't have to it's just a matter
of my personal preference and then I'm going to multiply this by the number
seven. When I do this I'm not worried about lining up
decimals or anything like that at this point I'm really not even concerned
there's a decimal um, actually in the problem.
Okay so seven times five is 35. So we'll
drop down the five and carry the three. Seven times six is 42.
42 plus three again will give us, um
45. So we'll drop down the five, we'll have to carry the four
and then seven times one is seven um,
plus four will give us 11. So right now I have the number
um, 1,155 which is clearly not correct.
Um, all you have to do though notice um,
there's only one number that really has a decimal place that's visible
and that's the one point six five and notice
um, if you kinda count if you were to move it to the right
uh, to where the last digit is you'd have to move the decimal places
two places. Okay so
notice the decimal places two places um,
from the end of the number and what you do is you simply take
um, your final answer and you count over that many decimal places as well.
So we had to go um, two decimal places to the left.
So on my final answer I'll move uh, the decimal place over
two places and that will give me my final answer
of 11.55. Um, so let's do another one here hopefully make this
uh, make a little more sense. Okay so now we've got the number two point
three four and again I'm going to multiply that by the number
uh, one point two. Again I'm really not concerned at all with the decimals, I'm just treating
these like a whole numbers at the moment. So two times four
is eight. Two times three is six.
Two times two is four. Okay
and now I'll move on to my next number so one times four
is four. One times three is three.
One times two is two. So now I just add these up
so eight and sometimes people put a zero. When I was a kid they always told us to put an X.
So that's just my own uh, little habit. So you can put a zero or whatever
um, and then we add eight plus zero is
eight. Six and four is ten. So we'll drop down the zero
carry the one, one plus four is five plus three is
eight um, drop the two write down so right now we have the number
2808 and again we just do the same thing.
Notice in the first number if our decimal place was to be at the end
we would have to move it two times.
Let's say two places. Notice
if my decimal place uh, had been on the right
of the bottom number I would have to move it over one place.
What you do is, you add up the
total number of places that the decimals moved over. So you had to move it one, two,
three times total. So that's what's we'll do on the bottom number will move the decimal over one, two,
three times and that will give us our final answer.
So two point three four times one point two
is the number two point eight zero eight.
Okay so let's do uh, one last one here.
So suppose I have the number
um, suppose we got to multiply I think this will be a little longer
um, so 21.95
um, we'll have to multiply this by
1.867.
And again notice um, before I even multiply
again at the very beginning if you look at 21.95 if the decimal place was all
all the way to the right we would have to move it one, two places.
If I look at the number that I multiplied by the bottom
if we put the decimal place all the way to the right to get it in its proper
place I would have to move it one
one, two uh, three places.
So that means my final answer the decimal will have to be moved
a total of five places okay.
So have to remember this and keep this in mind, but again
other than that it's just going to be a matter of you know just multiply and
pretending their whole numbers
and just putting the decimal place um, where it needs to be.
Alright so let's see if we can't um, let me make this a little prettier
so let's see if we can't do this uh. So 21.95
uh, times 1.867 so little tedious here.
Okay so seven times five is 35. So we'll drop down the five
and carry the three. Um, seven times nine is 63, plus three is 66.
So we'll drop down to six carry a six. Seven times one is seven
plus six um, is 13. So we'll drop down
three um, carry the one. Seven times two is 14
add one and that'll give us 15.
Alright so now we've kinda taken care of the seven, so let's see, six times
five is 30. So we'll drop down the zero, carry the three.
Six times nine is 54 plus three is 57,
carry the five. Six times one is six plus five is 11,
carry the one. Six times two is 12
plus one is 13.
Okay so now I've taken care of the six, I have to put um,
two placeholders so eight times five is 40.
So uh, drop down the zero we'll carry the four.
Eight times nine to 72 plus 476
we'll carry the seven. Eight times one
is eight, plus seven is 15. Um, we'll again carry the one.
Eight times two is 16. 16 plus one
is 17. Okay so were almost there
very tedious at least the last number um,
will be easy. So we're just multiply everything by one. So we'll simply get five,
nine, um, one, two
and now we just have to add all these numbers together and at the end just
move the decimal place over the correct number
of times. So in the first column to get my X's or zeros
uh, so we'll get five uh, we'll get six plus
zero which is six. We'll get three plus seven which is 10. So we'll drop down the zero
carry the one. One and five is six, plus one is seven,
plus six is 13, plus five is
18. Again we'll have to carry a one. One and one is two, plus three is five. Plus five is ten. Plus
nine is 19,
carry the one and one and one is two um,
plus seven is nine plus one is ten. We'll drop down the zero
and we'll carry the one. Um, so uh, one and one and two
is four [whew!] very tedious here.
Okay so um, so now I get all we have to do is again back to what we did at the beginning,
we counted.
So I had to move the decimal place over one, two in the first one
one, one, two, three in the second one. So again we had we said we had to move a total of
five places.
So if it starts on the end we would move over one,
two, three, four, five.
So it says that the decimal place should go right there.
Um, so it says 21.95 times 1.867
is gonna be equal to 40.98065.
Um, one thing I would definitely recommend you know just to make sure that you do
have a decimal place and
that the correct um, the correct place you know. If we rounded this off
you know if we took our numbers 21.95 that's roughly equal to uh,
22. If we rounded up. 1.867
that's roughly equal to uh, two. So if we multiply two and 22 we would get 44
but, again 22's bigger than the number that I'm using.
Two is also bigger than the number that I'm using. So I know this
estimate of 44 should be a touch, a touch bigger than the correct answer
um, and well 44 is a little bit bigger than 40.98065 so that seems like a
reasonable answer. So
all I'm saying is you can use estimation at the end real quickly
you know if I had the decimal place where it was 4.09
well that can't be right. Likewise if had the decimal place
you know at 409, um, 409
again you know just as a quick estimate I know that can't be correct something
would be wrong.
Okay so I hope this uh, video makes some sense. I'm going to do some others as well
where you have to divide
Um, numbers involving decimals. So feel free to take a look at that as well.