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Subtraction: Whole Numbers

Subtraction of whole numbers has a wide range of practical applications. It's a skill that you'll use nearly every day in real life, and you probably use it even now without even being aware of it. For example, you probably know that if you have three apples and you eat one, you've now got just two apples.

That's one simple way to explain subtraction. But when we get into bigger numbers, there are other things we need to consider, like borrowing. Let's go through the entire process of subtraction of whole numbers, from what it is to how to do it.

Helpful concepts to review for subtraction of whole numbers

First things first: Before diving into subtraction of whole numbers, it's a good idea to brush up on a few topics that will help to make sure that you understand the topic fully, such as whole numbers and addition of whole numbers. You'll use these concepts during subtraction as well. It's also helpful to know that subtraction isn't commutative. This means that the order of the numbers matters, and subtracting a larger number from a smaller number would result in a negative answer: $12-22=-10$ .

What is subtraction of whole numbers?

Subtraction is "the process of taking one number or amount away from another." It's the exact opposite of addition of whole numbers - addition and subtraction are inverse operations. Instead of adding two numbers to calculate the sum, you will be taking away one number from another to find the difference. It's used in everything from the simplest of calculations to complex applications, like working with matrices in precalculus - and beyond. Establishing a strong knowledge of this basic math skill is vital.

Subtraction of whole numbers without borrowing

Subtraction without borrowing is a fairly simple process: You simply take away the second number from the first. Let's look at a picture that shows how counting can help you find the answer to $8-5$ :

If you begin with 8 dots and then take away 3 dots, what's left over (the "remainder") is 5. To help you visualize larger numbers, you can use base-10 blocks instead of individual dots.

Subtraction of whole numbers with borrowing

Subtraction of whole numbers with more than one digit sometimes adds a step to finding the remainder. Let's go over subtraction with borrowing using the following example: $94-78$ .

94 can be broken down into $94+4$ , so we'll represent it here with 9 10-blocks and 4 unit blocks:

78 is the equivalent of $70+8$ , so it's represented by 7 10-unit blocks and 8-unit blocks. This is the number that will be taken away:

Now, we don't have enough unit blocks in the first set to subtract 8. That means we have to break up a 10-block. Now we have 8 10-blocks and 14 unit blocks:

Now we can take away 8 unit blocks and 7 10 unit blocks. The remainder is 1 10-block and 6 unit blocks, or $10+6=16$ :

That means $94-78=16$ .

When you subtract by writing out your problem, you will solve it column-by-column from right to left. Breaking up a 10-block is known as "borrowing", and you'll see it in action in the problem here:

That means

$\begin{array}{cc}& \hfill 3053\\ & \hfill \underset{_}{-\phantom{\rule{10pt}{0ex}}737}\end{array}$

First, subtract the ones column. Because 3 is less than 7, you'll borrow 1 10 from the 5 to make it 13:

$\begin{array}{cc}& \hfill {}_{4}\phantom{\rule{4pt}{0ex}}{}_{13}\\ & \hfill 30\overline{)5}\overline{)3}\\ & \hfill \underset{_}{-\phantom{\rule{10pt}{0ex}}7\phantom{\rule{3pt}{0ex}}3\phantom{\rule{3pt}{0ex}}7\phantom{\rule{3pt}{0ex}}}\\ & \hfill 6\phantom{\rule{3pt}{0ex}}\end{array}$

Next, subtract the tens column, using what's left when you subtract 1 - in this case, 4:

$\begin{array}{cc}& \hfill {}_{4}\phantom{\rule{4pt}{0ex}}{}_{13}\\ & \hfill 30\overline{)5}\overline{)3}\\ & \hfill \underset{_}{-\phantom{\rule{10pt}{0ex}}7\phantom{\rule{3pt}{0ex}}3\phantom{\rule{3pt}{0ex}}7\phantom{\rule{3pt}{0ex}}}\\ & \hfill 1\phantom{\rule{3pt}{0ex}}6\phantom{\rule{3pt}{0ex}}\end{array}$

Move on to subtract the rest of the columns, one by one. To solve our problem, you'll see that we need to borrow again, this time from the thousands column to the hundreds column:

$\begin{array}{cc}& \hfill {}_{2}\phantom{\rule{4pt}{0ex}}{}_{10}\phantom{\rule{4pt}{0ex}}{}_{4}\phantom{\rule{4pt}{0ex}}{}_{13}\\ & \hfill \overline{)3}\overline{)0}\overline{)5}\overline{)3}\\ & \hfill \underset{_}{-\phantom{\rule{10pt}{0ex}}7\phantom{\rule{6pt}{0ex}}3\phantom{\rule{4pt}{0ex}}7\phantom{\rule{3pt}{0ex}}}\\ & \hfill 2\phantom{\rule{5pt}{0ex}}3\phantom{\rule{6pt}{0ex}}1\phantom{\rule{4pt}{0ex}}6\phantom{\rule{3pt}{0ex}}\end{array}$

Because subtraction is the opposite of addition, it is easy to check your work by reworking your problem as an addition problem. For example, to confirm that $33-11=22$ , we can add 11 to both sides of the problem to get rid of the negative number: $33-11+11=22+11$ .

If you get the same number from the problem as your answer, you'll know that you've calculated your subtraction problem correctly, too.

Subtraction of whole numbers practice questions

Solve the following problems using whole number subtraction:

a. $8-4=$

$\begin{array}{cc}& \hfill 8\\ & \hfill \underset{_}{-\phantom{\rule{5pt}{0ex}}4}\\ & \hfill 4\end{array}$

b. $16-2=$

$\begin{array}{cc}& \hfill 16\\ & \hfill \underset{_}{-\phantom{\rule{5pt}{0ex}}2}\\ & \hfill 14\end{array}$

c. $9-8=$

$\begin{array}{cc}& \hfill 9\\ & \hfill \underset{_}{-\phantom{\rule{5pt}{0ex}}8}\\ & \hfill 1\end{array}$

d. $54-31=$

$\begin{array}{cc}& \hfill 54\\ & \hfill \underset{_}{-\phantom{\rule{5pt}{0ex}}31}\\ & \hfill 23\end{array}$

e. $271-61=$

$\begin{array}{cc}& \hfill 271\\ & \hfill \underset{_}{-\phantom{\rule{5pt}{0ex}}61}\\ & \hfill 210\end{array}$

f. $7645-522=$

$\begin{array}{cc}& \hfill 7645\\ & \hfill \underset{_}{-\phantom{\rule{5pt}{0ex}}522}\\ & \hfill 7123\end{array}$

Solve the following problems using whole number subtraction with borrowing:

a. $41-9=$

$\begin{array}{cc}& \hfill {}_{3}\phantom{\rule{4pt}{0ex}}{}_{11}\\ & \hfill \overline{)4}\overline{)1}\\ & \hfill \underset{_}{-\phantom{\rule{15pt}{0ex}}9\phantom{\rule{3pt}{0ex}}}\\ & \hfill 3\phantom{\rule{3pt}{0ex}}2\phantom{\rule{3pt}{0ex}}\end{array}$

b. $21-13=$

$\begin{array}{cc}& \hfill {}_{1}\phantom{\rule{4pt}{0ex}}{}_{11}\\ & \hfill \overline{)2}\overline{)1}\\ & \hfill \underset{_}{-\phantom{\rule{15pt}{0ex}}1\phantom{\rule{4pt}{0ex}}3\phantom{\rule{3pt}{0ex}}}\\ & \hfill 8\phantom{\rule{3pt}{0ex}}\end{array}$

c. $439-221=$

$\begin{array}{cc}& \hfill {}_{2}\phantom{\rule{4pt}{0ex}}{}_{13}\\ & \hfill 4\overline{)3}\overline{)3}\\ & \hfill \underset{_}{-\phantom{\rule{15pt}{0ex}}2\phantom{\rule{3pt}{0ex}}2\phantom{\rule{5pt}{0ex}}4\phantom{\rule{3pt}{0ex}}}\\ & \hfill 2\phantom{\rule{3pt}{0ex}}0\phantom{\rule{5pt}{0ex}}9\phantom{\rule{3pt}{0ex}}\end{array}$

d. $230-49=$

$\begin{array}{cc}& \hfill {}_{1}\phantom{\rule{4pt}{0ex}}{}_{12}\phantom{\rule{4pt}{0ex}}{}_{10}\\ & \hfill 2\overline{)3}\overline{)0}\\ & \hfill \underset{_}{-\phantom{\rule{15pt}{0ex}}4\phantom{\rule{5pt}{0ex}}9\phantom{\rule{3pt}{0ex}}}\\ & \hfill 1\phantom{\rule{3pt}{0ex}}8\phantom{\rule{5pt}{0ex}}1\phantom{\rule{3pt}{0ex}}\end{array}$

e. $5679-3701=$

$\begin{array}{cc}& \hfill \phantom{\rule{4pt}{0ex}}{}_{4}\phantom{\rule{4pt}{0ex}}{}_{16}\\ & \hfill \overline{)5}\overline{)6}\phantom{\rule{2pt}{0ex}}7\phantom{\rule{3pt}{0ex}}9\\ & \hfill \underset{_}{-\phantom{\rule{15pt}{0ex}}3\phantom{\rule{4pt}{0ex}}7\phantom{\rule{5pt}{0ex}}0\phantom{\rule{3pt}{0ex}}1}\\ & \hfill 1\phantom{\rule{3pt}{0ex}}9\phantom{\rule{3pt}{0ex}}7\phantom{\rule{5pt}{0ex}}8\end{array}$

f. $23538-956=$

$\begin{array}{cc}& \hfill \phantom{\rule{4pt}{0ex}}{}_{4}\phantom{\rule{4pt}{0ex}}{}_{16}\\ & \hfill \phantom{\rule{3pt}{0ex}}2\overline{)3}\overline{)5}\overline{)3}\phantom{\rule{3pt}{0ex}}8\\ & \hfill \underset{_}{-\phantom{\rule{24pt}{0ex}}9\phantom{\rule{5pt}{0ex}}5\phantom{\rule{5pt}{0ex}}6}\\ & \hfill 2\phantom{\rule{5pt}{0ex}}2\phantom{\rule{5pt}{0ex}}5\phantom{\rule{5pt}{0ex}}8\phantom{\rule{5pt}{0ex}}2\end{array}$

Mastering subtraction of whole numbers with Varsity Tutors

Subtraction is one of the most important math skills students will ever learn. Not only do we use it every day in real life, but mastering more advanced math skills depends on building a solid foundation. If your student needs additional help with subtraction of whole numbers, private math tutoring is one of the best ways to bolster their skills. Working with a tutor allows students to move at their own pace in a low-pressure, judgment-free environment.

Because subtraction of whole numbers is such a vital skill to master, it's important that students get a good grasp of the concept right away. Personalized lessons with a tutor who has experience working with students who need help with basic math skills like subtraction can make a real difference. If you're interested in getting your student more in-depth, personalized help with subtraction of whole numbers, get in touch with the Educational Directors at Varsity Tutors today.

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