1.2: Whole Number Subtraction
Have you ever seen seals at the zoo? They are fascinating animals.
Jonah loves working with the seals. In fact, he learns more and more about them every day. One day when he arrived at work, Jonah discovered that there had been a new baby seal pup born the night before. The workers at the zoo had weighed the new pup and his mother just that morning. The mother seal had weighed 157 pounds when she had been weighed alone. The combined weight of both the Mother and pup was 171 pounds.
What did the new pup weigh?
To figure this out, you will need to understand how to subtract whole numbers. Pay close attention and you will learn all that you need to know in this Concept.
Guidance
Just like you have been adding whole numbers for a long time, you have been subtracting them for a long time too. Let’s think about what it means to subtract.
Subtraction is the opposite of addition. Hmmm.... What does that mean exactly? It means that if you can add two numbers and get a total, then you can subtract one of those numbers from that total and end up with the other starting number.
In other words, Subtraction is the opposite of addition. When you add two numbers you get a total, when you subtract two numbers, you get the difference.
\begin{align*}15-9=\underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
This is a pretty simple example. If you have fifteen of something and take away nine, what is the result? Think about how we can do this problem. First, we need to rewrite the problem vertically, just like we did when we were adding numbers. Remember to line up the digits according to place value.
\begin{align*}15\\ \underline{ - \ 9}\\ 6\end{align*}
This could probably be completed using mental math.
What about if you had more digits?
\begin{align*}12, 456 - 237 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
Our first step is to line up these digits according to place value. Let’s look at what this will look like in our place value chart.
Ten Thousands | Thousands | Hundreds | Tens | Ones |
---|---|---|---|---|
1 | 2 | 4 | 5 | 6 |
2 | 3 | 7 |
Wow! This problem is now written vertically. We can go ahead and subtract.
\begin{align*}12,456\\ \underline{ \ - \ \ 237}\end{align*}
To successfully subtract these two values, we are going to need to regroup.
What does it mean to regroup?
When we regroup we borrow to make our subtraction easier. Look at the ones column of the example. We can’t take 7 from 6, so we borrow from the next number. The next number is in the tens column, so we can “borrow a 10” to subtract. If we borrow 10, that makes the 5 into a 4. We can make the 6 into 16 because \begin{align*}10 + 6 = 16\end{align*}. There’s the 10 we borrowed.
Let’s put that into action.
Be careful-be sure you subtract according to place value. Don’t let the regrouping mix you up.
Our answer is 12,219.
Now try a few of these on your own. Subtract the following whole numbers.
Example A
\begin{align*}674 - 59 =\underline{\;\;\;\;\;\;\;}\end{align*}
Solution: 615
Example B
\begin{align*}15,987 - 492 =\underline{\;\;\;\;\;\;\;}\end{align*}
Solution: 15,495
Example C
\begin{align*}22,456 - 18, 297 =\underline{\;\;\;\;\;\;\;}\end{align*}
Solution: 4,159
Remember the Mother and the new baby seal pup? Well now that you have learned how to subtract whole numbers, you are ready to go back and look at that problem.
Here is the original problem once again.
Have you ever seen seals at the zoo? They are fascinating animals. Jonah loves working with the seals. In fact, he learns more and more about them every day. One day when he arrived at work, Jonah discovered that there had been a new baby seal pup born the night before. The workers at the zoo had weighed the new pup and his mother just that morning. The mother seal had weighed 157 pounds when she had been weighed alone. The combined weight of both the Mother and pup was 171 pounds.
What did the new pup weigh?
To figure this out, we will need to write a subtraction problem. We know that the mother seal weighed 157 pounds and the combined weight of the mother and new pup was 171 pounds.
If we subtract 157 from 171, we will have the weight of the new pup.
\begin{align*}171 - 157 =\underline{\;\;\;\;\;\;\;}\end{align*}
The answer is 14. The seal pup weighed fourteen pounds.
Vocabulary
Here are the vocabulary words that are found in this Concept.
- Difference
- the answer to a subtraction problem
- Regroup
- when you need to borrow from the next column in subtraction
Guided Practice
Subtract the following values.
\begin{align*}567 - 391 =\underline{\;\;\;\;\;\;\;}\end{align*}
Answer
To subtract these values, we first have to line up the values according to place value. Then we subtract. Don't forget to regroup.
567 - 391 = 176
Interactive Practice
Subtraction
Video Review
These videos will help you with subtracting whole numbers.
Khan Academy Basic Subtraction
James Sousa Example of Subtracting Whole Numbers
Practice
Subtract the following values.
1. \begin{align*}56 - 21 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
2. \begin{align*}50 - 23 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
3. \begin{align*}267 - 19 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
4. \begin{align*}345 - 127 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
5. \begin{align*}560 - 233 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
6. \begin{align*}1600 - 289 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
7. \begin{align*}5400 - 2334 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
8. \begin{align*}8990 - 7865 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
9. \begin{align*}12340 - 3456 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
10. \begin{align*}23410 - 19807 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
11. \begin{align*}35611 - 9037 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
12. \begin{align*}22410 - 11807 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
13. \begin{align*}54600 - 21807 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
14. \begin{align*}88419 - 32817 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
15. \begin{align*}93415 - 10007 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
16. \begin{align*}67419 - 39807 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
17. \begin{align*}123410 - 119807 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
18. \begin{align*}334410 - 219807 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
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Absolute Value
The absolute value of a number is the distance the number is from zero. Absolute values are never negative.Decimal point
A decimal point is a period that separates the complete units from the fractional parts in a decimal number.Difference
The result of a subtraction operation is called a difference.Regroup
In subtraction, to regroup is to borrow from the next column.Image Attributions
Here you'll learn how to subtract whole numbers.