Decompose — Definition, Formula & Examples
Decompose means to break a number or shape into smaller parts that add up to the original. For example, you can decompose 15 into 10 + 5.
To decompose a quantity is to express it as a sum, difference, or product of two or more component values, preserving the total value of the original quantity.
How It Works
When you decompose a number, you split it into pieces that are easier to work with. You might break a number apart by place value, like splitting 47 into 40 + 7. You can also decompose to make addition or subtraction simpler: for instance, to add 8 + 6, you might decompose 6 into 2 + 4, then add 8 + 2 to get 10, and finally add the remaining 4. The key rule is that your parts must combine back to equal the original number.
Worked Example
Problem: Decompose 365 by place value.
Step 1: Identify the hundreds digit. 3 hundreds equals 300.
Step 2: Identify the tens digit. 6 tens equals 60.
Step 3: Identify the ones digit. 5 ones equals 5.
Answer: 365 = 300 + 60 + 5
Why It Matters
Decomposing numbers is a foundational skill used throughout elementary arithmetic. It helps you add and subtract mentally by breaking problems into friendlier pieces, and it builds the place-value understanding needed for multiplication and long division.
Common Mistakes
Mistake: Breaking a number into parts that do not add back to the original.
Correction: Always check your work by adding the parts together. If you decompose 53, your pieces (such as 50 + 3) must sum to exactly 53.