# Long Subtraction Calculator

Created by Anna Szczepanek, PhD
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Jun 05, 2023

Table of contents:

Welcome to Omni's long subtraction calculator! Here we show you step-by-step how to solve any long subtraction problem. Our calculator can deal with whole numbers as well as those with decimal places!

If you need a quick summary of how to do long subtraction, scroll down and read the short explanation we've prepared. Once you've mastered the long subtraction method, check out our calculators dedicated to the remaining three arithmetic operations:

## Long subtraction method

Long subtraction is a popular method of quickly subtracting long numbers, i.e., those that have many digits. If you can correctly subtract a whole number between 0 to 9 from a whole number between  1 and 18 (for example, if you know that 12 - 5 = 7), then nothing can stop you from learning long subtraction over the course of the next five minutes! Here are the steps of the long subtraction method:

1. Put the numbers one under the other so that they are aligned by place value. The number you are subtracting from goes on top, the smaller number beneath it.

That is, your numbers have to be right-aligned - the ones-digits have to be aligned, tens-digits have to be aligned, and so on.

2. In the far-right column, subtract the bottom number from the top number and put the result in the same column (at the bottom).

If the upper-digit is greater than or equal to the bottom-digit, then there is no problem. However, if the upper-digit is smaller than the bottom-digit, then we have to borrow from the subsequent column. We have dedicated a separate section to borrowing in long subtraction.

3. Go to the next column (to the left) and subtract again, long subtraction borrowing if needed, and put the result in the bottom row. Repeat this step for every column.

4. If the upper number has more digits than the lower number, then at some point you encounter a column that has only one digit, i.e., the bottom row is empty. In such case we simply rewrite this number into the result row.

Alternatively, you may imagine filling in the empty places with zeros and then subtracting this zero from the top-row digit.

As you can see, long subtraction of whole numbers is very easy! In the next sections, we explain how to deal with numbers that have decimal places. Next, we elaborate on the mysterious borrowing procedure.

π Want to learn how to handle complex mathematical problems that involve more than one arithmetic operation? Check our distributive property calculator.

## How to borrow in long subtraction?

First of all, remember that we need to borrow only if the top digit in a column is smaller than the bottom digit. When this happens, go one column to the left and look at its top number.

• If this number is greater than 0, then cross it out and replace it with the value of that number minus 1. Then go back to your original column, cross out the top number, and replace it with the value of that number plus 10.

• If this number is equal to 0, then the long subtraction borrowing procedure is more complicated, but only slightly. Zero in a column means that this column has nothing to lend. But to the left there are other columns, and they can come to our rescue! We go through them one by one, looking for the first non-zero column. Then we borrow 10 from this column into the column to the right (that originally contained 0, but after borrowing it contains 10). Now that this column is non-zero, we can borrow from it and give to the next column, and so on, until we come back to our original column.

As always, it's practice that makes perfect, so, to get a better grasp of the long subtraction steps, we recommend that you go through the examples in the last section. Once you're done and want more, go and generate as many examples of long subtraction problems as you wish with the show steps mode of our long subtraction calculator.

## How to do long subtraction of decimal numbers?

Long subtraction of two numbers with decimal places is very similar to what we've just seen in the case of two whole numbers. The key step is to align the numbers correctly. As before, the numbers have to be aligned by place value.

For instance, if we want to subtract 15.413 from 5437.321 using the long subtraction method, we write them down as follows:

\begin{align*} 5437&.321 \\ 15&.413 \end{align*}

As you can see, the numbers we're dealing with have the same number of decimal places, so it was easy to align them, wasn't it?
But what to do with numbers that have a different number of decimal places? Just remember to put the numbers such that the decimal points are aligned. You can then fill in the missing decimal places with zeros.

For instance, if we want to calculate 117.32 - 32.4121 using long subtraction, we set up the problem as follows:

\begin{align*} 117&.3200 \\ 32&.4121 \end{align*}

Once you've written down the numbers correctly, perform the subtraction using the method explained in the previous sections. When you arrive at the decimal point, put the point in the result row and proceed.

## How to use this long subtraction calculator?

Here are the most important things you should know about Omni's long subtraction calculator:

1. Enter two numbers. Our long subtraction calculator will subtract the smaller number from the larger one.

2. The calculator returns the result in a fraction of a second. Look for it beneath the numbers you've entered.

3. Turn on the show steps option if you want the long subtraction calculator to show the step-by-step solution of your long subtraction problem.

## Long subtraction examples

Here we show how to subtract two long numbers with the help of the long subtraction method.

Long subtraction example 1. Compute 21347 - 3275:

1. Setup:
\begin{align*} {2}1{3}47&\\ -\ \ \ 3275& \\ =\quad \quad \ \ \ & \end{align*}
1. We subtract the numbers in the far-right column: 7 - 5 = 2. We put the result 2 at the very bottom of the same column:
\begin{align*} {2}1{3}47&\\ -\ \ \ 3275& \\ =\quad \ \ \ \ 2 & \end{align*}
1. We move onto the next column. As 4 < 7, so we need to borrow from the column to the left. We replace 3 with 3 - 1 = 2 in the column to the left and replace 4 with 14 in the current column. Hence, we subtract 14 - 7 = 7 and so place 7 in the result row.
\begin{align*} {\small{\phantom{12}2\phantom{22}}}& \\ {2}1\sout{3}47&\\ -\ \ \ 3275& \\ =\quad \ \ 72 & \end{align*}
1. We subtract 2 - 2 = 0 and put 0 into the result row:
\begin{align*} {\small{\phantom{12}2\phantom{22}}}& \\ {2}1\sout{3}47&\\ -\ \ \ 3275& \\ =\ \ \ \ 072 & \end{align*}
1. Since 1 < 3, we need to borrow once again. We replace 2 with 2 - 1 = 1 in the far-left column and replace 1 with 11 in the current column. Hence, we subtract 11 - 3 = 8 and place 8 in the result row.
\begin{align*} {\small{1\phantom{2}2\phantom{22}}}& \\ \sout{2}1\sout{3}47&\\ -\ \ \ 3275& \\ = \ \ 8072 & \end{align*}
1. We've run out of the digits in the bottom number, but there are still digits in the upper number. We rewrite 1 into the result row:
\begin{align*} {\small{1\phantom{2}2\phantom{22}}}& \\ \sout{2}1\sout{3}47&\\ -\ \ \ 3275& \\ = 18072 & \end{align*}

Example 2. Solve 4520.12 - 515.9:

1. Setup. We have to be careful to correctly align the numbers:
\begin{align*} 45{20}&.12 \\ -\quad 515&.90 \\ =\quad \quad \ \ &\phantom{.22} \end{align*}
1. We subtract the numbers in the far-right column: 2 - 0 = 2. We put the result 2 at the very bottom of the same column:
\begin{align*} 45{20}&.12 \\ -\quad 515&.90 \\ =\quad \quad \ \ &\phantom{.2}2 \end{align*}
1. We have 1 < 9, so we go to the column to the left (skipping the decimal point!). But it contains 0, so there's nothing to borrow here... Go one more column to the left; thankfully, it contains 2. We replace 2 with 2 - 1 = 1. We go back to the right and replace 0 with 10. Then borrow from this column and replace 10 with 10 - 1 = 9 and, finally, replace 1 with 11 in the original column. Then we subtract 11 - 9 = 2 and put 2 in the result row.
\begin{align*} {\small{19}}& \\ 45\sout{20}&.12 \\ -\quad 515&.90 \\ =\quad \quad \ \ &\phantom{.}22 \end{align*}
1. We've reached the column full of decimal points. We put the point in the result row as well:
\begin{align*} {\small{19}}& \\ 45\sout{20}&.12 \\ -\quad 515&.90 \\ =\quad \quad \ \ &.22 \end{align*}
1. We subtract the numbers in the next column: 9 - 5 = 4 and put 4 into the result row:
\begin{align*} {\small{19}}& \\ 45\sout{20}&.12 \\ -\quad 515&.90 \\ =\quad \ \ \ 4&.22 \end{align*}
1. We subtract the numbers in the next column: 1 - 1 = 0 and put 0 into the result row:
\begin{align*} {\small{19}}& \\ 45\sout{20}&.12 \\ -\quad 515&.90 \\ =\quad \ 04&.22 \end{align*}
1. We subtract the numbers in the next column: 5 - 5 = 0. We put 0 into the result row:
\begin{align*} {\small{19}}& \\ 45\sout{20}&.12 \\ -\quad 515&.90 \\ =\ \ \ 004&.22 \end{align*}
1. We've run out of the digits in the bottom number, but there is still a digit in the upper number. We put 4 into the result row:
\begin{align*} {\small{19}}& \\ 45\sout{20}&.12 \\ -\quad 515&.90 \\ =\ 4004&.22 \end{align*}
Anna Szczepanek, PhD
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