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Addition & Subtraction

Long Addition

If we are unable to add mentally because there are too many numbers to add or because the numbers are too large, we can use a written addition method which is called long addition or adding in columns. This way of laying out an addition problem allows us to easily find the sum of multiple large or small numbers. Long addition is quite easy once you understand how to do it.

Setting Up the Calculation

Start off by writing the numbers above each other, ensuring that the units column of all numbers are vertically aligned. Numbers with no or the same amount of decimal places can just be aligned to the right. Continue by putting a line underneath the last number and a plus sign to the left of this number (just to show that this is an addition).

Performing the Calculation

To get the answer, you have to add all the numbers in a column - starting on the right and going left. So in the example, we would have added 5 and 9 first. The answer is 14. If we get an answer which is higher than 9 (as in this case), we have to annotate then next column with a small number (1). This is because we cannot put tens into the units column, tens into the hundreds column and so on. In the example, the answer to the first sum is 14 so we put a 4 in the units column and annotate the tens column with a 1 because one extra ten has to go into it. When calculating the next number we then add the 1 to the addition, so in the tens column, we got 5 instead of 4 because we had to add the one transferred from the units column. You may also have to annotate with a column with 2 or 3 when adding more than two numbers together as you could get 20+ or even 30+.  You have to add all columns (always annotating with small numbers underneath where necessary) until there are no columns left. If you have gotten more than 9 as the sum of the numbers in the last column, you will have to add a digit on the left, creating a new column (this is not the case in the example on the right. At the end, you will have the answer to your sum written underneath the line. Below are some examples with various different situations. Long Subtraction Now that you know how long addition works, you should look at long or column subtraction. The overall concept is the same, so it should be quite simple to understand.

Setting up the Calculation

Again you have to write all the numbers above each other making sure that they are right aligned (the units columns of all numbers should be vertically aligned). Then add a line under the last number and a minus sign to its left to show that you are subtracting (and not adding).

Performing the Calculation

Now again work your way from right to left, this time subtracting the bottom number from the top number in each column. Have a look at the example on the right. In the first column we have to do 2 - 1 which is 1. Write the answer to each column underneath the line. If you have a number on the bottom that is larger than the top number, your answer would be negative. To prevent this from happening we simply take 1 away from the next column and add it to our current column so that the number is big enough to be subtracted (without getting a negative result). This has also be done in the example: we have taken away one from the hundreds column and added it to the tens column. This allowed us to subtract 8 from 17 (instead of 7), giving us a positive answer (9). After you have subtracted all columns, the answer will be written underneath. In this case, we had to do 1-1 in the last column which is equal to 0. As a result, the solution is one digit shorter than the original numbers. We have added a few examples underneath to clarify this explanation. Multiplication & Division After this lesson on addition and subtraction, you should try to do some multiplication and division or you can return to the library to choose a new topic. Please share this page if you like it or found it helpful!
Long Addition You can decide where to put your small annotations when adding in columns. Just remember to include them in the sum with the other numbers in the column . Long Subtraction
Example 1 In example 1, we added the numbers in the same column together. In the last column we got a sum of 15, so we had to add a digit (1) on the left
Example 2 In example 2, we have two very large numbers which we were able to add together using long addition. Again, we had to add a digit on the left.
Example 3 In example 3, we have added three numbers together. We were able to easily find the sum of the three numbers by using addition in columns. In the tens column, we got a number larger than 9 and had to annotate the hundreds digit with a 1.
Example 1 In example 1, we subtracted the bottom number from the top number in each column.
Example 2 In the second example, we have to take one from the hundreds column in order to be able to subtract the tens column without getting a negative result.
Multiplication & Division Estimation Standard Form
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Chapter 1.0:  Learning Outcomes Students will be able to solve simple addition & subtraction problems mentally (existing knowledge)! Students will be able to find solutions to complex addition problems with up to three large numbers being added together! Students will be able to use long subtraction to solve problems involving two large numbers!
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