Number Splitting & Regrouping
Decomposing numbers for easier addition.
Core Concepts
Number Splitting (or decomposition) is the process of breaking a number down into its place value components (Hundreds, Tens, Ones). This is the foundation for mental math because it allows you to handle big numbers in small, manageable chunks.
Expanded Form
Writing a number as the sum of its place values.
• 45 = 40 + 5
• 123 = 100 + 20 + 3
Solved Examples
Example 1: Splitting a 2-Digit Number
Question: Split 72.
• Tens: 7 tens = 70.
• Ones: 2 ones = 2.
• Answer: 70 + 2.
Example 2: Splitting a 3-Digit Number
Question: Split 358.
• Hundreds: 300.
• Tens: 50.
• Ones: 8.
• Answer: 300 + 50 + 8.
Example 3: Addition using Splitting
Question: Add 23 + 45.
• Step 1: Split both numbers.
• 23 = 20 + 3
• 45 = 40 + 5
• Step 2: Add the Tens together.
• 20 + 40 = 60
• Step 3: Add the Ones together.
• 3 + 5 = 8
• Step 4: Combine.
• 60 + 8 = 68.
Example 4: Splitting with Zeros
Question: Split 405.
• Hundreds: 400.
• Tens: 0 (Skip or write 00).
• Ones: 5.
• Answer: 400 + 5.
