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Subtraction with Larger Numbers
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Introduction

In this lesson, you will learn the steps of subtraction. When doing subtraction with numbers that are too large to do in your head, there are steps you can follow to help you do the subtraction correctly.


These videos illustrate the lesson material below. Watching the videos is optional. In the video called "Steps for Subtraction," only steps 1-3 are relevant to this lesson.


Steps for Subtraction


  1. Stack by place value with the biggest number on top.
  2. Regroup when needed. This is needed when the top number is smaller than the bottom number in a place value column.
  3. Subtract in columns by place value, starting on the right and going left.

Here are a few examples to illustrate these steps.

Example 1
\(9-3\)

Step one instructs you to stack by place value with the biggest number on top. Place 9 on top of 3, since 9 is the bigger number. There is only one digit in each number, so both numbers will be placed in the one's column. Your equation should look something like this:

Equation showing 9 minus 3.

Figure 1

Now that you have the problem set up, you can subtract. The answer is 6.

Equation showing 9 minus 3. The answer, 6, is orange.

Figure 2

Example 2
\( 56-42\)

Arrange according to number size and place value. 56 is the bigger number so it must be on top of 42. There are two digits in each number, so you will align the 6 and 2 in the ones column and align the 5 and 6 in the ten's column.

Equation 56 minus 42.

Figure 3

Subtract the columns by place value, starting on the right and moving to the left: \(6-2=4\) and \(5-4=1\). The final answer is 14.

Equation 56 minus 42. The answer, 14, is orange.

Figure 4

Regrouping

Regrouping is the second step in the subtraction process. It isn’t always necessary, as in the examples above, but it is an important step to understand.

Example 3
\(25-7\)

Equation 25 minus 7.

Figure 5

In this example, step one was already performed by lining up the numbers by place value (ones on top of ones) with the largest number on top. You might consider adding a zero in front of the 7, just to see how the numbers line up.

For step two, notice that 5 is greater than 7. To make this equation solvable, you need to regroup by borrowing from the tens column.

When you borrow from a column, you don’t just add one to the original number. You add the full value of what you borrow. Since you are borrowing from the tens column, one 10 should be added to the ones column. You will do some simple addition to add the borrowed 10 to the 5 ones. This gives you 15 in the ones column (refer to Figure 6).

Equation 25 minus 07, with the zero in light gray. This figure shows how to use borrowing in subtraction. The 2 and 5 are both slashed, with an orange 15 above the 5 and an orange 1 above the 2.

Figure 6

Now you can solve this equation. Start on the right (in the ones column) and move to the left.

Equation 25 minus 07, with the zero in light gray. This figure shows how to use borrowing in subtraction. The 2 and 5 are both slashed, with 15 above the 5 and 1 above the 2. The answer, 18, is orange.

Figure 7

The final answer is: \(25-7=18\).

Example 4
\(452-273\)

Equation 452 minus 273.

Figure 8

The numbers are already arranged as instructed by step one. Now, determine if the problem needs regrouping. Notice in the ones column that 2 is smaller than 3, and in the tens column 5 is smaller than 7. Both columns will need to borrow from the column on their left (see Figure 9).

Equation 452 minus 273, with numbers 5 and 2 slashed and replaced by an orange 4 above the 5 and an orange 12 above the 2. An orange 9 is in the ones column of the answer.

Figure 9

As always, start with the ones column. Just as the first example, add 10 to the 2 in the ones column, making it a 12. Consequently, this will turn the 5 in the ten's column to a 4. Note that you haven’t changed the number; you’re just rearranging where the numbers are according to place value.

Next, do the same thing for the tens column that you did for the ones column. Borrow from the number to the left. In this case, that means borrowing from the hundreds column. Since you are borrowing from the hundreds column, you get ten groups of 10 added to our tens column. Do some simple addition to add the borrowed group of tens to the original 4 tens. This gives you 14 tens (Figure 10).

Equation 452 minus 273, with 452 slashed and replaced by a 12 above the 2, a 4 above the 5 (which is also slashed and replaced with an orange 14), and an orange 3 above the 4. In the answer box there is a 9 is in the ones column and an orange 7 in the tens column.

Figure 10

Move on to the next column. \(3-2\) works as a problem, so you will simply solve the rest of the equation. Therefore, \(452 - 273 = 179\).

Equation 452 minus 273 equals 179, with 452 slashed and replaced by a 12 above the 2, a 4 above the 5 (which is also slashed and replaced with 14), and a 3 above the 4. In the answer box is 179 and the 1 is orange.

Figure 11


Things to Remember


  • The steps of subtraction:
    1. Arrange numbers according to size and place value.
    2. Regroup as needed.
    3. Subtract place values—right to left.
  • When borrowing from a column, you don’t just add one to the original number. You add the full value of what you borrow.

Practice Problems

Evaluate the following expressions:
  1. \(64 - 32 = ?\) (
    Solution
    x
    Solution: 32
    Details:
    Using place value to subtract, put the 6 in the tens place and the 4 in the ones place.

    This is a box with two vertical columns: Tens and Ones. The number 6 is placed in the tens column and the number 4 is placed in the ones column.

    Next, put the 3 in the tens place and the 2 in the ones place.

    This is the same image as the previous one except there is now a number 3 placed below number the 6 and in the tens column and there is a number 2 placed below the number 4 in the ones column.

    Subtract the numbers in the ones place.
    \(4 − 2 = 2\)


    This is the same image as the previous one except that now there is a blue answer box below both columns. There is also a subtraction symbol to the left of the tens column. In the ones column of the blue answer box is a number 2.


    Finally, subtract the numbers in the tens place.
    \(6 − 3 = 3\)

    This is the same image as the previous image except now there is also a number 3 in the tens column of the blue answer box .

    The answer: \(64 − 32 = 32\)
    )
  2. \(357 - 34 = ?\) (
    Solution
    x
    Solution: 323
    Details:
    Using place value to subtract. Place the 3 in the hundreds place, the 5 in the tens place and the 7 in the ones place.

    This image displays three columns. At the top of each column, reading from left to right are the titles, 'Hundreds, Tens, Ones.' Numbers are under the titles in the columns. Under the hundreds column is the number 3. Under the tens column is the number 5. Under the ones column is the number 7.

    Now, place the 3 in the tens place and the 4 in the ones place.

    This is the same as the previous image except a 3 is placed below number 5 in the Tens column and 4 is placed below number 7 in the Ones column.

    Subtract the numbers in the ones place column. \(7 − 4 = 3\)

    This is the same as the previous image except there is now a subtraction symbol to the left of all the numbers and a blue solution box spanning the three columns at the bottom. In the solution box in the ones column is a number 3.

    Subtract the numbers in the tens place column. \(5 − 3 = 2\)

    This is the same as the previous image except there is now a 2 in the tens column of the solution box at the bottom.

    Subtract the numbers in the hundreds column. Since 3 is the only number in this column, the answer is 3. Or in other words, 3 subtract 0 is 3.

    This is the same as the previous image except there is now a 3 in the hundreds column of the solution box at the bottom. So the solution at the bottom now reads 323..

    The answer to \(357 − 34\) is \(323\).
    )
  3. \(963 - 69 = ?\) (
    Solution
    x
    Solution:
    894
    )
  4. \(884 - 500 = ?\) (
    Solution
    x
    Solution:
    384
    )
  5. \(800 - 263 = ?\) (
    Video Solution
    Transcript)
  6. \(577 - 284 = ?\) (
    Solution
    x
    Solution:
    293
    )
  7. \(954 - 597 = ?\) (
    Video Solution
    | Transcript)

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