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How many times does 13 go into 35 ?
No that is not correct.
Any more do you want to try again.
Yes that is correct. I will show you an image of that and can you see the next step?
Yes it is 3. Now I will show you another image. Try to figure out what happens next and tell me.
You are right to subtract them. That is to say the "16 - 13" bit was right.
However 6 is not right. Try again.
I am going to give you the next step of the 16549 divided by 13 question.
Notice that the first "0" in the answer at the top (top left) comes from the fact that 0 x 13 = 0.
We get the first remainder by 1 - 0
The remainder of this first bit was 1. This is "worth" ten when it is shifted to the right.
This is added to the 6 which we dropped down and they add to give 16.
Then I note that 1 x 13 = 13. The 1 from this is the next digit of the answer.
Now what do we do ?
To get the numbers to appear centrally click and highlight the cells that you wish to make central.
Then click the right mouse button and choose "Format Cells", choose "Alignment" and then
choose "Center" for the "Horizontal " and "Vertical" text alignment.
Then go to the "Font" option at the top. Select a reasonable size like "16". Click OK.
To get a line at the bottom of a row of numbers:
Select the cells that the numbers are in or will be in.
Click the right mouse button and choose "Format Cells", and choose "Border", then
select the bottom left of the "line style" options. Then select which "Border" you want
and click OK.
I have created the lines of the division entirely using the "Border" option.
I will stop at that point so that this post does not go on for too long, but you could have
an experiment with Excel to see what you can do.
(The next stages are to get a "PRTSC" (Print Screen) and to paste it in Paint and then
to "Crop" the item, do any editing in Paint that it needs and save the file as a GIF file
remembering to make it reasonably small so as not to use excessive memory).
Yes that is fine. Right I have trimmed my image file down so as to just show you the first step
that I did in my answer. Can you work out what the next thing to do is? Remember that we are
dividing 16549 by 13 here. All I have really done is set out the answer, observed that trivially
1 divided by 13 gives us 0 remainder 1 and dropped down the 6 with an arrow.
So we have the appearance of the number 16 as the next bit of the problem that we are trying
to divide by 13. What happens next?
OK. A question for you to attempt:
16549 divided by 13. (Using long division)
[0, 13, 26, 39, 52, 65, 78, 91, 104, 117]
I have prepared an image with the answer.
Now a slightly harder one on long division, but still fairly easy:
0 6 3
------
7 | 4 4 1
0
-
4 4
4 2
---
2 1
2 1
---
0 0
---
Each time we choose the highest number below or equal to the remainder
added to the number dropped down, in the times table of the number we
are dividing by.
[ 0, 7, 14, 21, 35, 42, 49, 56, 63 ]
So for example if the number we are left with is 44 after a 4 is put on
the end of remainder 4 then as you can see 42 is the number in the 7 times
table to put under 44.
If we put anything smaller down say 35 then it would go wrong because we
would end up with the remainder being too high - eg. 44 - 35 = 9
this is too high because with a division by 7 each remainder needs to be
in the range (0, 1, 2, 3, 4, 5, 6).
If we choose the multiple of 7 to be 49 with 44 as the number left, then that
would be too high because the subtraction is 44 - 49 = -5 which is too low
to be in the range (0, 1, 2, 3, 4, 5, 6).
I must admit that long division when I was taught it at school was intended
for dividing by a number of at least 13 so perhaps I should do a more
advanced example next.
Doing 171 divided by 3 using long division:
0 5 7
-------
3 | 1 7 1
0
-
1 7
1 5
---
2 1
2 1
---
0 0
---
Times table reminder: [0, 3, 6, 9, 12, 15, 18, 21, 24, 27]
First step: observe that 1 divided by 3 is 0 remainder 1.
So put the 0 above in the answer, Do 1 minus 0 = 1.
Then drop down the 7 to make it into 17.
Aside: 3 x 5 = 15 so put the 5 up in the answer and subtract the 15.
The result of that is 2, then drop down the 1.
This makes 21.
Aside: 3 x 7 = 21 so put the 7 up in the answer and subtract the 21.
Now we end up with zero and there are no more numbers to drop down
the division is completed.
Often arrows are used to show the numbers (7 and 1 in this case) that
are dropped down. It is rather messy to show this using plain text, but
I have made up a graphical file to help show this.
------------------------------------------------------------------------
The short division version is difficult to display with plain text, but
it looks like this:
---------
3 | 1 7 1
then: the "1" remainder goes in front of the 7 to make it look like 17.
0
---------
3 | 1 [17] 1
the "2" remainder goes in front of the 1 to make it look like 21.
0 5 7
------------
3 | 1 [17] [21]
Notice that all of the calculations are the same, but that some of the information
displayed in long division does not get written down unless you want to add a few
notes down below the division or to the side. It is more compact and okay for simple
case where the thing that we are dividing by is small, but usually if we are dividing
by a number out of range of your times tables then long division is better.
Ah. I see. By the way one of the subtraction questions I was going to ask you was to try 113.7 - 66.328 ?
I know that may look hard, but it is not as difficult as all that if you know about decomposition/borrowing.
I have thought of some material on multiplication and division, but if I post it now it might get a bit buried.
I will leave it for now, but if you want me to post my long division now for you to preview let me know.
The multiplication will take longer because I have still got to work out whether I am going to use a graphic and
have not typed anything, but I have made some notes on paper.
Hello (Mandy) I have noticed that you are logged on....
Whoops! Sorry about that I have got two subtractions muddled in my head.
I meant to ask about the one that went 12.1 - 0.589
I have already done a worked example for 1.3 - 0.716
However if you did not read the worked example (Mandy) then you could still have a go.
I am going to see with this post whether I am allowed to post a graphics file.
Hopefully this will illustrate 1.300 - 0.716
Note that I have included the headings "units, tenths, hundredths, thousandths".
Obviously in an exam you would not waste time writing these things unless they were asked for.
However, Mandy, it may be a good idea to put these things in a few times to get the
hang of place value concepts.
OK let's see whether the graphic works...
Right. How about I do that instead. Now 1.3 - 0.716 ?
It can be set out like this:
1.300 -
0.716
------
------
0 - 6 will give us a negative number. So what do we do ?
Yes that's fine.
It looks like I am going to be in for more of today than I previously expected.
Hi anonimnystefy. Thanks for your welcome post.
I think we need to finish off the subtraction bit. I will do 1.3 - 0.716 as an example:
It is helpful to add two extra zeros on the end of 1.3 - this does not effect what the number actually
is and enables us to line up the two numbers correctly:
1 . 3 0 0 -
0 . 7 1 6
----------
----------
Now 0 - 6 won't work because it is a negative result. Looking to the left the next number is a
zero so that is no good. Looking to the left again we have a "3", we can reduce this to 2 and
drop a 9 to the right instead of the first zero and increase the second zero to ten.
So we end up with something like this (of course there will be a few crossings out in a hand written
test or assignment - the 3 and the first 0 are crossed out in this case).
1 . 2 9 [10] -
0 . 7 1 6
-------------
8 4
-------------
Note that I have filled in the two numbers 4 and 8 which are now easy to work out.
Now 2 - 7 is going to be negative as well so let's borrow from the 1 to the left.
The 1 at the top left gets crossed out and replaced by a 0.
Then we have to add 10 to the 2 because this is worth ten times as much in this column:
0 . [12] 9 10
0 . 7 1 6
-----------------
0 . 5 8 4
-----------------
As you can see I have finished off the answer. 12 - 7 is now easy. The left most column is
very easy 0 - 0 = 0 .
Notice that I have added the decimal point being careful to get it in the right place.
If you so wish you could do 12.1 - 0.589 as a similar problem to check that you have
understood what I have explained.
It would be interesting if you post it to this site or via email so I can see if you are correct
and doing it correctly and I will help if you need some help.
I think we had better delay the multplication and division for a bit. I was jumping ahead a
bit because I thought that you were coping very well with the addition.
You can of course make up your own examples and try them to see if you can do them
check them with a calculator and obviously if you have managed to find something that
you are stuck on by all means post it here or email it to me. Practice is a good way to
learn some basic maths. You cannot learn maths as you might read a novel.
I do entirely understand about your dyslexia. If you cannot do times tables from 2 to 9
then you will not be able to do multiplication and division very well. We need to discuss
this a little and it might be better if we discuss that and a few other things about what
other topics to deal with etc. we can discuss this via email if you prefer.
Yes that's fine.
See you on Sunday.
I know this is a difficult one, but how about 12.1 - 0.589 ?
(I need to know whether you can do the 1.3 - 0.716 question though, if you can't do that one then you
won't be able to do the one above.)
Of course you can ask questions and add posts in between now and Sunday and we could exchange a few
posts at disjointed times. You have done these questions better and more quickly than I had thought you would.
I could do with knowing whether you want to do multiplication and division and what sort of question.
You are almost there with subtraction already and at the rate you did those other questions it shoudn't take very
long. I found it difficult to keep up and I was the one setting the questions.
Just to test you as to what you know already how about:
3.46 x 7 ?
3.46 x 0.7 ?
1.89 divided by 7 ?
Very good. Correct answer.
Can you see how to do 5 .69 - 3.78 ?
If you can do it then go ahead. I wll explain it if you need help.
Another one you might like to try is: 1.3 - 0.716 ?
Notice here that the decimals are not the same length so care is needed with positioning
and place value.
OK. How about you try 20.37 - 18.66 ???
Try to indicate how you worked out the answer as well as you can.
There are limits to what you can do in plain text.
I will probably be able to see if you have used a sensible method.
Good luck.
Right now the subtraction can be done quite easily:
9 . [16] 9 -
8 . 7 8
-------------
1 . 9 1
-------------
By the way I need to mention a few points before I teach you any bad habits.
There are limits to what I can display at this speed, online via a maths forum.
I have had to adapt the way I would usually write subtractions considerably.
If you have to attend an exam on subtraction (and other topics) then please follow
the conventions in your course about how to present your answer.
When I was taught how to do subtraction I would cross out the "1" and put a zero
The "0" to the right would be crossed out and replaced by a 9.
The 16 would be written with the "1" superscripted slightly to indicate that it had been
put in afterwards etc. Method marks are often more important than getting the correct answer.
Right first let's write it out in full:
1 0 . 6 9
8 . 7 8
-----------
-----------
Now the first bit is easy. 9 - 8 = 1.
So in the answer the number one can be written straight away.
1 0 . 6 9
8 . 7 8
-----------
1
-----------
Now in the next stage 6 - 7 = -1 this is a problem because we need a number between
0 and 9. I would then look to the left of the top number. In the next column there is a "0".
This is no good: We cannot decompose a zero.
So: Look at the far left at the top. We have a one so we can take 1 away from this to get
zero. Then we can drop off a "9" in the next column to the right. Then drop off a "10" to
the right of this (notice that we are just redistributing the number here - 10.0 = 9.0 + 1.0).
9 . 16 9
8 . 7 8
------------
1
------------
Right I will give you a minute to look at that and ask any questions about that bit....
I have noticed that you are quite good at these sums. Are you okay with 10.69 - 8.78 ?
Do you want to have a go at that one ?