Addition and Subtraction
Here we will look at using the column method for adding and subtracting big numbers using the column method. This is a fundamental skill for all mental mathematics.
Skill 1: Addition
The idea behind the column method of addition is firstly adding the ones, then the tens, then the hundreds and so on. Here’s an example broken down into 5 steps.
Example: Use the column method to find the result of 2,347 + 851.
1) Firstly, write both the numbers one above the other, making sure the ones line up, the tens line up, and so on. Then, draw a line underneath the numbers.
2) Now, we first add the ones,
7+1=8
And write the result underneath the ones column.
3) Then, add the tens,
4+8=12
Now, since the result is a 2-digit number, don’t write the whole thing below the line – we want to carry the 1, which means we write the 2 below the line in the tens column and write the 1 above the hundreds column (technically, it is a hundred).
4) Now when adding the next column, the hundreds, make sure to add the extra 1 that we obtained:
1+3+5=9
Write the results underneath the hundreds column.
5) Finally, since there is only one value in the next column, we simply write that value underneath the line (you can think of 581 and 0581 and add 0 to 2 if it helps).
Then, once there are no more columns left, your answer will be the number underneath the line.
Skill 2: Subtraction
The column method for subtraction is similar in principle to that for addition – start with the values in the “ones” column on the right and move left – but there are a couple of small differences.
Example: Use to the column method to evaluate 3,407 - 1,625.
1) Firstly, write both the numbers one above the other, making sure the ones line up, the tens line up, and so on. Then, draw a line underneath the numbers.
2) Now, we first subtract the one,
7-5=2
And write the result underneath the ones column.
3) Then, we want to subtract the tens but that would give us a negative number. So, instead we “borrow” a 1 from the next column along. So, the 0 becomes a 10 and the 4 is reduced to a 3. Then, do the subtraction:
10-2=8
Write the result underneath the tens column.
4) Now we want to subtract the hundreds but run into the same problem as in step 3), so we borrow a 1 so that in the hundreds column: 3 becomes 13, and in the thousands: 3 is reduced to 2. Then, do the subtraction:
1+3+5=9
Write the result underneath the hundreds column.
5) Lastly, subtract the two values in the thousands column:
2-1=1
Write the result underneath the thousands column.
Then, once there are no more columns left, your answer will be the number underneath the line.
Notes:
• If you need to subtract a big number from a smaller (as in, you expect to get a negative answer), do the column method with the bigger number on top and then simply stick a minus sign in front of your answer.
• If you need to borrow a 1 but the next digit along is a zero, then reduce the zero to a 9, and look to the next digit along and borrow the 1 from it, instead (meaning you then have to reduce that digit by 1, as well the other digit you just reduced).
Example Questions
1. Using the column method, evaluate 590 + 4,455.
A correct application of the column method should look something like
Therefore, the solution is
4,455+590=5,045.
2. Using the column method, evaluate 1,105 - 822.
A correct application of the column method should look something like
Therefore, the solution is
1,105-822=283.
3. Using the column method, evaluate 345 + 353 = 698
345 + 353 = 698
4. Using the column method, evaluate 10020 - 9099
10020 - 9099 = 921
5. Using the column method, evaluate 991 - 1293
Here we can see the second number is larger, meaning our answer will be minus.
Here we write the second number over the first number:
We then perform the subtraction.
1293 - 991 = 302
lastly we add a minus sign to our answer
991 - 1293= - 302
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