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Long Division

Learn how to do long division the easy way. (Includes Worksheet and examples)
by

Yazzi McDonough

on 13 March 2015

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Transcript of Long Division

Long Division
What is Long Division
Like its name, 'long division', is dividing with larger numbers.
The method is not regularly applied due to the current technology; however, research has proven its usefulness.
It is used in order to minimize complicated mental calculations.
Where is Long Division Used?
Although hard to believe, a lot of the pointless methods you learn in Maths you use in real life; most without you even realising it.
Long division is applied similarly with simple division. Planning and sharing are the major areas where this method is used. For an example, if you need to figure out how many cupcakes you would need to give to a certain amount of people, division is required.
How to Do Long Division
As you will soon find out, long division is not for the weak minded. It requires an open mind and a lot of attention.
We will be doing two step-by-step example questions.
_____
2 5) 3 5 0
Lets start off with the problem 350/25. We will put it in an algorithm.
Next we divide the first digit, 3, by the divisor, 25 and place it above.

2 5
)
3
5 0
3/25 = 0
0
Now we times the divisor by the answer and place it below.

0
2 5
) 3 5 0
25 x 0 = 0
0
Following that, we subtract the answer from the number above it
0
2 5)
3
5 0

0
3
3-0 = 3
Next we bring the second digit down alongside the answer
0
2 5) 3
5
0
0
3
5
Then we use this new number, 35, and divide it by the divisor, 25 and place the answer on the top.
0
2 5
) 3 5 0
0

3 5
1
35/25 = 1
Now we multiply that answer with the divisor and place it at the bottom.
0
1
2 5
) 3 5 0
0
3 5
2 5
25 x 1 = 25
Next we subtract these two totals and place the answer below.
0 1
2 5) 3 5 0
0

3 5
2 5
1 0
35 - 25 = 10
We then place the final digit with the lowest answer and divide the total with the divisor.
0 1
2 5
) 3 5 0
0
3 5
2 5
1 0 0
4
100/25 = 4
Finally, we multiply the answer by the divisor and place it below. We then subtract to see if there are any remainders. Which in this problem, there is not.
0 1
4
2 5
) 3 5 0
0
3 5
2 5
1 0 0
0 0 0
0 0 0
25 x 4 = 100

100-100 = 0
0 1 4
After a long calculation, we find our answer of 14. These are the steps we toke:
Now lets do another problem

_____
16)524
First we have to divide the first digit by the divisor and place above.
0
Next we multiply that answer with the divisor and put below.
0
Now the bottom number is subtracted from the one above and placed below.
__
5
2
The second digit is then brought down to the lower line.

This created number on the bottom line is then divided by the divisor and placed along the answer line.
3
4 8
This new answer is multiplied by the divisor and put on a lower line.

The lowest answer is then subtracted from the one above and placed below.
____
0 4
4
The third digit now joins the bottom row on the end.

This lowest answer is divided by the divisor and the answer is taken to the highest line.

0 3 2
The previous result is then multiplied by the divisor and put on lower row.

These lowest number is subtracted from the one above and placed on another line.

2
____
0 1 2
r12
The final number is then placed on the answer line and is represented as 'remainder 12'.
Now it's Your Turn!
It's your go now to try some 'fun' long division questions!
You will be shown a question in which you are expected to answer. Click the next page to see the answers and working out.
Remember, you can go back any time to refresh your memory!
Question 1:
___
43)559
013
Solution:

013
43)559
0
55
43
129
129
000
Question 2:
___
50)967
019 r17
Solution:
019 r17
50)967
0
96
50
467
450
017
Question 3:
You have been selected to make party bags for a 10 year old birthday party tomorrow. There will be 43 children and you have 568 jelly snakes. What is the most amount of snakes you can put in a bag if each is equal?
13
Solution:
013 r9
43)568
0
56
43
128
129
009
The End!
I hope that you have learned something about long division, whether it be the formula or just how confusing and pointless it can get.
Thank you for your time.
Instead of using remainders, we can give the number a decimal place.
032
16)524
0
52
48
044
032
012
This is the equation from before:
Now instead of adding the remainder, we place a decimal point on the question line.
.0
0
We now take this fourth digit down on the bottom row.

Now we divide the divisor by this new number and place it with the answer


.7
Using this top decimal point, we times it by the divisor and place it on a further line


Now we do some subtraction between the two lower numbers to ensure no further decimals.


0008
01 1 2
It equals eight, therefore, we must repeat the steps we just took until the answer is 0.


We add another 0 to the question line and bring this down to the '0008' line.


0
0
Now we divide this answer by the divisor and place on the answer line.
5
00080
Next the divisor is multiplied by this recent number, the '5', and placed on a new line.
00000
Finally, we check for any remainders by subtracting the two bottom lines and adding the answer on another new line.
In this question, there is no remainders, meaning that our final answer is '32.75'. If you want to check that it is correct, simply multiply the divisor and the answer.
Solution (decimals)
019 .34
50)967.00
0
96
50
467
450
0170
0150
00200
00200
00000
_____
50)967
019,34
OR
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