SECTION 1-WHOLE NUMBER ARITHMETIC

SUBTRACTION

In addition we were interested in finding the total of like quantities. In subtraction we will be interested in finding the difference between like quantities. What we will basically asking ourselves is the following question:
"If I have a certain amount of a certain object, and some of them are being taken away from me, how much am I left with?"
Thus if you had 8 CD's and you lost 2, then you would be left with "8-2" or 6 CD's

Before you get started: You should have no trouble subtracting with single digit numbers. If you need help with subtracting single digit numbers then go to the appendix.

In some ways subtraction is similar to addition.

We will still take it one column at a time stating from the rigth hand column.
Except this time instead of adding the numbers, we will be subtracting them.
If we cannot perform the subtraction we will borrow from the left-hand column.
Once we borrow two things will occur.
- The number that we borrowed from will be now be considered as being reduced by 1
- The number in the column we are currently working on will now be considered as being increased by 10, thereby allowing the subtraction to occur.

This will illustrated in the next three examples.

Subtraction example 1

57 - 28

first line the numbers up as shown
                        57
                      - 28
Now we can immediately detect that in the first column we have 7 - 8.
Now 8 cannot be subtracted from 7, so we need to borrow from the 5.
Take one from the 5, and think of it as 4 (Note: the 5 has a strike through it, and a blue 4 appears above it).
Then using this borrowed one, think of the 7 as 17 (Note: the red one immediately above the 7).
Now 17 - 8 = 9
Write the 9 directly below the first column.

41 57 - 28 9

Moving on we have the 5 (which we now consider to be 4) - 2.
4 - 2 =2
Write the 2 directly below the second column.

4 57 - 28 29

57 - 28 = 29
Here's a way to check your answer (Put that calculator down!): Add your solution (29) to the number you are subtracting (28), and you should get the original starting number (57)
         28
        +29
8+9=17. Write down 7 and carry 1.
1 28 +29 7

2+2+1=5
28 +29 57

There you have it 28 + 29 = 57 thereby confirming our solution

Subtraction example 2

3,731 - 3,128

first line the numbers up as shown
                        3731
                      - 3128
Now we can immediately detect that in the first column we have 1 - 8.
Now 8 cannot be subtracted from 1, so we need to borrow from the 3.
Take one from the 3, and think of it as 2 (Note: the 3 has a strike through it, and a blue 2 appears above it).
Then using this borrowed one, think of the 1 as 11 (Note: the red one immediately above the 1).
Now 11 - 8 = 3
Write the 3 directly below the first column.

21 3731 - 3128 3

Moving on we have the 3 (which we now consider to be 2) - 2.
2 - 2 =0
Write the 0 directly below the second column.

2 3731 - 3128 03

Moving on to the third column we have "7-1"
7-1=6
Write the 6 in the third column

3731 - 3128 603

Now we reached the last column.
In this column we have "3 - 3".
3-3=0
Usually we would write the 0 down directly below the fourth column, but since is the final column we can simply omit it. Think of it: When was the last time you saw the number six hundred and three written as 0603?

3731 - 3128 603

3731 - 3128 = 603
Here's a way to check your answer (Put that calculator down!): Add your solution (603) to the number you are subtracting (3128), and you should get the original starting number (3731)
         3128
         +603
3 + 8 = 11. Write down the first 1 and carry the second 1.
1 3128 +603 1

2+0+1=3
3128 +603 31

1+6=7
3128 +603 731

There is noting to add to the 3, so just write a three in that column
3128 +603 3731

There you have it 3128 + 603 = 3731 thereby confirming our solution

Subtraction example 3

3,157 - 289

first line the numbers up as shown
                      3,157
                      - 289
Now we can immediately detect that in the first column we have 7 - 9.
Now 9 cannot be subtracted from 7, so we need to borrow from the 5.
Take one from the 5, and think of it as 4 (Note: the 5 has a strike through it, and a blue 4 appears above it).
Then take that borrowed one and think of the 7 as 17 (Note: the red one immediately above the 7).
Now 17 - 9 = 8, which is written directly below the first column.

41 3,157 - 289 8

Moving on we have the 4 (formerly 5) - 8.
Borrow from the 1, and for here on think of it as 0. Notice that the 1 now is striked though and 0 appears above it.
Think of the 4 as 14. Notice the 1 directly above the 4
14 - 8 =6 which is now written directly below the second column.

1 04 3,157 - 289 68

Moving on we have 0 - 2
Borrow from the 3 and think of the 0 as 10.
The effects of this move are shown below

1 2 0 3,157 - 289 868

In the last column we have a 2 with nothing to subtract from it
Write the 2 in that column

2 3,157 - 289 2,868

3,157 - 289 = 2,868

Assignment 1: confirm this solution by adding 289 and 2,868. Your solution should be 3,157.

In the above three examples we were able to borrow from the next column, when it was required. But what if we could not borrow from the neighboring column? The answer is to borrow across two columns. You will see this portrayed in the next two examples

Subtraction example 4

100 - 38

Now 8 cannot be taken from 0, so we would like to borrow from the second column.
However, the second column is another zero so we have to go on to the third column
Reduce the 1 in the third column to 0, and make the second column's 0 into 10
                      01
                      100
                      -38
      
Now take the second column, which we currently think of as 10 and reduce it to 9
Using that borrowed one think of the first column's 0 as 10

091 100 -38

Now subtract 8 from 10 leaving 2

091 100 -38 2

Moving on we have our imagined 9 minus 3.
9 - 3 = 6

09 100 -38 62

Finally we are left with the last column, which we are now considering to be 0. We could just drop the zero down to the solution giving us an answer of "062", but it is not required to add a zero to the left hand side of the solution (see example 2).
100 -38 62

100 - 38 = 62
Assignment 2: confirm this soultion by adding 62 and 32. Your answer should be 100

Subtraction example 5

201 - 65

First line up the numbers

                     201
                     -65

In the first column we have "1 - 5"
We cannot subtract 5 from 1 so we have to borrow
The column to the immediate left is 0 so we cannot borrow from it.
Moving on to the third column we have 2. Borrow from the 2 and think of it as 1.
That borrow will make the 0 in the second column to appear as 10.

11 201 -65

We still can't subtract 5 from 1, but now we can borrow from the second column.
We are now perceiving the second column as 10. Borrow from from it, making it a 9. The result of this borrow is our 1 is now perceived as 11.

191 201 -65
11-5 = 6

191 201 -65 6
9 - 6 = 3

19 201 -65 36
In the last column we have a 1, with nothing to subtract from it.
1 - 0 = 1

1 200 -65 135

201 - 65 = 135
Assignment 3: Verify this solutin by adding 65 and 135.

After completing a few exercises on your own, you'll be ready to graduate to the multiplication section.

Click on the "generate a subtraction problem" button to see your exercise. Place your answer in the text box and then click the "check my answer" button. The computer will then tell you whether or not your answer is correct.

After you complete the problem, you can generate another problem by first clicking the "reset button" and then clicking the "generate a subtraction problem" button. Continue as many times as you wish, and then:

All text, images, and source code c2003 Martin Selditch.