Tiffany is driving a truckload of hay bales to one of her customers at a nearby farm. On the way, Tiffany pulls into a weigh station - her truck weighs 24,380 pounds. After delivering the hay, she pulls back into the same weigh station, and learns that her truck now weighs 23,120 pounds. How can Tiffany use this information to figure out the weight of the hay she delivered?

In this concept, you will learn how to subtract whole numbers.

### Subtracting Whole Numbers

Subtraction is the opposite of addition.This means that if you add two numbers and get a total, then you can subtract one of the original numbers from the total and end up with the other original number. When you add two numbers you get the **sum**, when you subtract two numbers, you get the **difference**.

Let's look at an example.

\begin{align*}15-9=\underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, rewrite the problem vertically. Remember to line up the digits according to place value.

\begin{align*}15\\ \underline{ - \ 9}\\ 6\end{align*}

The difference is 6.

Let's look at an example with more digits.

\begin{align*}12, 456 - 237 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

The first step is to line up these digits according to place value. Let’s look at this in a place value chart.

Ten Thousands |
Thousands |
Hundreds |
Tens |
Ones |
---|---|---|---|---|

1 |
2 |
4 |
5 |
6 |

2 |
3 |
7 |

This is what the problem looks like when written vertically.

\begin{align*}12,456\\ \underline{ \ - \ \ 237}\end{align*}

To successfully subtract these two values, you are going to need to **regroup**. Regrouping is when you borrow from the next place value column to make subtraction easier.

Look at the ones column of the example. You can’t take 7 from 6, so you borrow from the next number. The next number is in the tens column, so you borrow a 10. When you take the 10, you reduce the 5 in that column to a 4 (you had 5 tens, you gave 1 ten away). You then turn your 6 into 16 with your borrowed 10.

Let’s put that into action.

Be sure you subtract according to place value.

The answer is 12,219.

### Examples

#### Example 1

Earlier, you were given a problem about Tiffany and her heavy hay.

Tiffany’s truck weighed 24,380 pounds with the hay, and 23,120 pounds without it.

The difference between those two weights is the weight of the hay. To figure out the difference, Tiffany can subtract the smaller number from the larger number.

\begin{align*}24380-23120\end{align*}

First, write the problem vertically.

\begin{align*} \ \ \ \ 24380\\
\underline {- \ 23120}\end{align*}

Next, subtract, regrouping if necessary.

\begin{align*}24380&\\ \underline {- \ 23120}&\\ 1260\\\end{align*}

The difference is 1,260.

The total weight of the hay delivered was 1,260 pounds.

#### Example 2

Find the difference.

\begin{align*}567-391=\_\_\_\_\_\end{align*}

To subtract these values, first line up the values according to place value.

\begin{align*}\quad 567\\ \ \underline{- \ 391}\end{align*}

Then, go ahead and subtract, regrouping (borrowing) if necessary.

\begin{align*}_4 \qquad &\\ \cancel{5} ^1 6 \ 7&\\ \underline{- \ 3 \ 9 \ 1}&\\ 1 \ 7 \ 6&\\\end{align*}

The answer is 176.

#### Example 3

Find the difference.

\begin{align*}674 - 59 =\underline{\;\;\;\;\;\;\;}\end{align*}

First, rewrite the problem vertically, lining up the numbers according to place value.

\begin{align*}674&\\ \underline{- \ \ 59}&\\ \end{align*}

Then subtract each column right to left, borrowing as necessary.

\begin{align*}_6 \quad \ &\\ 6 \cancel{7}\, ^14&\\ \underline{-\ \ \ \ 5 \ \ 9}&\\ 6 \ \ 1 \ \ 5&\\\end{align*}

The answer is 615.

#### Example 4

Find the difference.

\begin{align*}15,987 - 492 =\underline{\;\;\;\;\;\;\;}\end{align*}

First, rewrite the problem vertically, lining up the numbers according to place value. \begin{align*}15987&\\ \underline{- \ \ \ 492}&\\ \end{align*}Then subtract each column right to left, borrowing as necessary. \begin{align*}_8 \quad \ \ \ &\\ 1 \, 5 \cancel{9} ^1 8 \ 7&\\ \underline{-\ \ \ 4 \, \ 9 \ 2}&\\ 1 \ 5 \ \ 4 \ \, 9 \ 5&\\\end{align*}

The answer is 15,495.

#### Example 5

Find the difference.

\begin{align*}22,456 - 18, 297 =\underline{\;\;\;\;\;\;\;}\end{align*}

First, rewrite the problem vertically, lining up the numbers according to place value. \begin{align*}22456&\\ \underline{- 18297}&\\ \end{align*}Then subtract each column right to left, borrowing as necessary. \begin{align*}_1 \quad \ _3 \, \ _{^{1}4}\quad &\\ \cancel{2} ^{1}2\cancel{4} \cancel{5} ^{1}6&\\ \underline{-\ \ 1 \ \ 8 \ \ 2 \ \ 9 \ \ 7}&\\ 4 \ \, 1 \ \, 5 \, \ 9&\\\end{align*}

The answer is 4,159.

### Review

Find the difference.

- \begin{align*}56-21 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}50-23 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}267-19 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}345-127 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}560-233 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}1,600 - 289 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}5,400 - 2,334 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}8,990 - 7,865 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}12,340 - 3,456 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}23,410 - 19,807 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}35,611 - 9,037 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}22,410 - 11,807 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}54,600−21,807 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}88,419−32,817 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}93,415−10,007 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}67,419−39,807 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}123,410−119,807 =\underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}334,410−219,807 =\underline{\;\;\;\;\;\;\;}\end{align*}

### Review (Answers)

To see the Review answers, open this PDF file and look for section 1.2.