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Break Apart Strategy to Find The Sum Calculator

Reviewed by Calculator Editorial Team

The break apart strategy is a fundamental math technique that helps students and learners break down complex numbers into more manageable parts to simplify addition, subtraction, and other operations. This method is particularly useful for visual learners and those who struggle with mental math.

What is the Break Apart Strategy?

The break apart strategy involves decomposing numbers into parts that are easier to work with. For example, when adding 17 and 24, you can break 17 into 10 and 7, and 24 into 20 and 4. Adding these parts together (10 + 20 = 30 and 7 + 4 = 11) gives you the total sum of 41.

This method is based on the associative property of addition, which states that the way in which numbers are grouped does not change their sum. The break apart strategy helps students understand place value and reinforces number sense.

Associative Property of Addition: (a + b) + c = a + (b + c)

By breaking numbers apart, students can perform calculations more efficiently and build a stronger foundation in mathematics.

How to Use the Break Apart Strategy

To use the break apart strategy effectively, follow these steps:

  1. Identify the numbers: Determine the numbers you need to add or subtract.
  2. Break apart the numbers: Decompose each number into parts that are easier to work with. Common breaks include tens, fives, and ones.
  3. Add or subtract the parts: Perform the operation on the broken-down parts.
  4. Combine the results: Add or subtract the results of the broken-down parts to get the final answer.

Tip: The break apart strategy works best when the numbers are broken into multiples of 10, 5, or other friendly numbers.

Examples of Break Apart Strategy

Let's look at a few examples to see how the break apart strategy works in practice.

Example 1: Adding Two Numbers

Problem: 23 + 18

Solution:

  1. Break 23 into 20 and 3.
  2. Break 18 into 10 and 8.
  3. Add the tens: 20 + 10 = 30.
  4. Add the ones: 3 + 8 = 11.
  5. Combine the results: 30 + 11 = 41.

Final Answer: 23 + 18 = 41

Example 2: Subtracting Two Numbers

Problem: 45 - 27

Solution:

  1. Break 45 into 40 and 5.
  2. Break 27 into 20 and 7.
  3. Subtract the tens: 40 - 20 = 20.
  4. Subtract the ones: 5 - 7 = -2.
  5. Combine the results: 20 + (-2) = 18.

Final Answer: 45 - 27 = 18

Example 3: Adding Three Numbers

Problem: 19 + 26 + 14

Solution:

  1. Break 19 into 20 - 1.
  2. Break 26 into 20 + 6.
  3. Break 14 into 10 + 4.
  4. Add the tens: 20 + 20 + 10 = 50.
  5. Add the remaining parts: -1 + 6 + 4 = 9.
  6. Combine the results: 50 + 9 = 59.

Final Answer: 19 + 26 + 14 = 59

Break Apart Sum Calculator

Use the calculator below to practice the break apart strategy with different numbers. Simply enter the numbers you want to add, and the calculator will show you how to break them apart and find the sum.

FAQ

What is the break apart strategy used for?
The break apart strategy is used to simplify addition, subtraction, and other operations by breaking numbers into more manageable parts.
How does the break apart strategy help with mental math?
Breaking numbers into parts that are easier to work with helps students perform calculations more efficiently and reinforces number sense.
Can the break apart strategy be used for multiplication and division?
While the break apart strategy is most commonly used for addition and subtraction, it can also be applied to multiplication and division with some adaptation.
Is the break apart strategy suitable for all ages?
Yes, the break apart strategy is suitable for students of all ages, from early elementary to advanced learners.
How can I teach the break apart strategy to my students?
Use visual aids, manipulatives, and real-world examples to help students understand and practice the break apart strategy.