Long AdditionWe can use long addition, if numbers are too large in order for us to work out the results in our heads. By laying out the calculation in this way, many large numbers can be added together easily.
Setting Up the Calculation
To perform long addition, the calculation must be set up correctly. You have to write all numbers above each other so that their units, tens, hundreds, etc. columns are aligned. The picture above shows this for the number 1437.25. After draw a line below the last number and write a plus sign to the left of the bottom number to indicate that this is an addition. This will become clearer in a second when working through an example.
Performing the Calculation
Once the calculation is set up, you can perform the calculation. Here are the basic steps to performing long addition:
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Chapter 1.0: Learning OutcomesStudents 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!
Addition & Subtraction
Once the calculation been set up:1.Add all numbers in a column, starting from the right. Write the sum below the line. 2.If the sum is a two digit number, the tens digit is carried (added) to the next column to the left.3.Repeat this until you have added up all the columns.
This may sound confusing but is actually very easy to apply as we will see in the examples that follow.
Perform long addition to find 235 + 719 = ?
For clarity, the column headings and a line for the carried numbers is shown (this is usually excluded).
It can be seen how the numbers in each column have been added. In the units column, the sum was 14. Thus a 4 was written down for the sum of the units column and the 1 was carried into the next (tens) column and added to the sum of the tens column to give 5.
Perform long addition to find 67638 + 92294 = ?
This is an example of a slightly more complex scenario as the numbers are larger.
It can be seen that a one is carried into the hundred thousands column. As a result, the sum has one more digit than the original numbers.
Perform long addition to find 79 + 214 + 18 = ?
In this example, 3 numbers are being added together. Note that the columns and the line for carried numbers have been removed: this is what a typical calculation will look like.
Notice, that in the units column we obtained a sum of 21 and thus a 2 has been carried forward into the tens column.
Note that there is no specific rule on where and how to write annotations for number carried into the next column. However, you should make sure that they are clearly visible for you and that you include them in the sum for the next column.
Long SubtractionSimilarly as with long addition, long subtraction is used if we want to subtract numbers that are too complicated to subtract in our heads. The procedure is very similar to that for long addition.
Setting Up the Calculation
As with long addition, you have to write all numbers (usually only two) above each other so that their units, tens, hundreds, etc. columns are aligned. Then, draw a line below the last number and write a plus minus to the left of the bottom number to indicate that this is a subtraction.Performing the CalculationOnce the calculation is set up, follow these basic steps to performing long subtraction:
Once the calculation been set up:1.Subtract the bottom number(s) from the top number, starting from the right. Write the intermediate result below the line. 2.If the bottom number is larger than the top number, to prevent the intermediate result from being negative, we subtract one from the next column (to the left) of the top number and add it to our current column.3.Repeat this until you have subtracted all the columns.
Perform long subtraction to find 272 - 181 = ?
For clarity, the column headings are included and the subtracted numbers are shown in a separate line.
It can be seen how in each column we have subtracted the bottom from the top number. In the tens column, we had to subtract one from the hundredths column (top number only) for the intermediate result to be non-negative. The zero in the hundreds column is usually omitted.
Perform long subtraction to find 124 - 92 = ?
The columns and their respective headings have been excluded in this example. This is what a long subtraction calculation should look like.
Again, we had to subtract one from the hundreds column in order to obtain a non-negative intermediate result in the tens column. This time the zero was omitted as we would do in a real-life problem.
1 Solve the following problems using long addition.(a)271 + 98 = ? (b) 1340 + 972 = ? (c)23 + 98 + 214 = ?(d)291 + 543 + 1942 = ? (e)1754 + 7153 + 736 + 46 = ?2 Solve the following problems using long subtraction.(a)921 - 97 = ? (b) 872 - 461 = ?(c)1734 - 527 = ?(d)1310 - 76 - 453 = ?