Subtraction Algorithm

Contributor: Erika Wargo. Lesson ID: 12390

Algorithm is not a new kind of music; it's a series of steps used to complete a task. In this case, the task is subtraction, and the algorithm is easy and fun, with games, practice and a simple video!

categories

Arithmetic, Whole Numbers and Operations

subject
Math
learning style
Visual
personality style
Beaver
Grade Level
Intermediate (3-5)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!

Audio: Image - Button Play
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It was a nice day, and they were hungry for blueberry pie. So, they went to the farm, where Tina collected 981 blueberries and Pablo collected 456.

  • How many more blueberries did Tina collect than Pablo?

Subtraction is separating one group into two groups or taking one number away from another.

When subtracting one number from another number, the answer is called the difference. A common method used to subtract numbers is called the standard subtraction algorithm.

Whoa!

  • What does that mean?

An algorithm is a set of steps that are used to complete a task.

In this lesson, the steps are used to perform subtraction.

The standard algorithm for subtraction has three steps:

  1. Line up the numbers vertically by place value, starting with the ones place.

The greater number is written, or stacked, above the number with a smaller value.

  1. Begin subtracting in the ones place and then move to the left. Ask yourself:
  • Do I need to borrow and regroup before subtracting?
  • Is the value of the top digit greater than the value of the bottom digit in this place value position?
  1. Borrow and regroup, if necessary.
  1. Repeat Step 2 with the other place values.

It is also helpful to use grid paper to help you line up the digits in each number.

Example 1

721 - 358

Step 1

Line up the numbers by place value.

Since both numbers have three digits in them, each digit in the first number should be lined up with another digit in the second number:

   

7

2

1

 

-

3

5

8

         

 

  • How do you know if you have to borrow and regroup?
  • How many times do you think you will have to borrow and regroup?

Step 2

Begin subtracting in the ones place.

  • Think: Can I subtract 8 ones from 1 ones?

No, so you need to borrow and regroup.

Step 3

Borrow and regroup.

The 2 tens and 1 ones becomes 1 ten and 11 ones. In the ones place, 11 - 8 = 3.

Move to the tens place and continue following the subtraction steps:

     

1

 
   

7

2

11

 

-

3

5

8

       

3

 

  • Think: Can I subtract 1 tens from 5 tens?

No, so you need to borrow and regroup.

Borrow and regroup from the hundreds. The 7 hundreds and 1 tens becomes 6 hundreds and 11 tens.

   

6

11

 
   

7

2

11

 

-

3

5

8

   

3

6

3

 

Subtract the tens place: 11 - 5 = 6.

Subtract the hundreds place: 6 - 3 = 3.

363 is the difference.


A subtraction answer can be checked by adding the difference to the number subtracted. The sum of the addition should equal the starting number.

To check: 363 + 358 = 721, which is the number we started with:

   

1

1

 
   

3

6

3

 

+

3

5

8

   

7

2

1

 

Example 2

At the beginning of the lesson, you were asked the following question:

Tina collected 981 blueberries and Pablo collected 456.

  • How many more blueberries did Tina collect than Pablo?

Using the standard algorithm, line up the digits and subtract, starting with the ones place:

     

7

 
   

9

8

11

 

-

4

5

6

   

5

2

5

 

Tina collected 525 more blueberries than Pablo.

Now, watch a few more examples in Math Antics - Multi-Digit Subtraction (below). Listen for the answers to these questions and write the answers on a piece of paper, if necessary:

  • How is multi-digit subtraction different from multi-digit addition?
  • How do you determine if you need to borrow?

Image - Video

In the Got It? section, you will practice subtracting numbers!

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