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G.2 Subtract using expanded form: up to three digits

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What is subtraction using expanded form?

Expanded form subtraction is a method where we break numbers into their place values (hundreds, tens, and ones) before subtracting. This helps us understand how subtraction works with each place value.

Example:
  • 267 = 200 + 60 + 7
  • 135 = 100 + 30 + 5
  • Subtract: (200 - 100) + (60 - 30) + (7 - 5) = 100 + 30 + 2 = 132
Note

Expanded form makes large numbers easier to work with by showing the value of each digit separately.

How to subtract without regrouping

When each digit in the top number is larger than the digit below it, we can subtract directly without changing the numbers.

Steps:
  • Expand both numbers: 475 = 400 + 70 + 5 and 253 = 200 + 50 + 3
  • Subtract hundreds: 400 - 200 = 200
  • Subtract tens: 70 - 50 = 20
  • Subtract ones: 5 - 3 = 2
  • Add the results: 200 + 20 + 2 = 222
Note

Always check that each place value in the first number is larger before subtracting directly.

Understanding regrouping in expanded form

Regrouping (sometimes called borrowing) happens when a digit in the top number is smaller than the digit below it. We need to adjust the numbers before we can subtract.

Example with Regrouping:
  • 742 = 700 + 40 + 2 and 318 = 300 + 10 + 8
  • We can't do 2 - 8, so regroup: take 10 from 40
  • Now: 700 + 30 + 12
  • Subtract: (700 - 300) + (30 - 10) + (12 - 8) = 400 + 20 + 4 = 424
Note

When regrouping, remember you're moving value from one place value to another, not just changing numbers.

Double regrouping with expanded form

Sometimes we need to regroup more than once when multiple place values need adjustment before subtracting.

Double Regrouping Steps:
  • 825 = 800 + 20 + 5 and 467 = 400 + 60 + 7
  • First regrouping: take 10 from 20 → 800 + 10 + 15
  • Second regrouping: take 100 from 800 → 700 + 110 + 15
  • Subtract: (700 - 400) + (110 - 60) + (15 - 7) = 300 + 50 + 8 = 358
Note

Take your time with double regrouping. Work step by step to avoid mistakes.

Special cases numbers with zeros

When numbers have zeros in the tens or ones place, we need to regroup carefully to make subtraction possible.

Working with Zeros:
  • 803 = 800 + 0 + 3 and 526 = 500 + 20 + 6
  • We have 0 tens, so regroup from hundreds: take 100 from 800
  • Now: 700 + 100 + 3
  • Regroup again: take 10 from 100 → 700 + 90 + 13
  • Subtract: (700 - 500) + (90 - 20) + (13 - 6) = 200 + 70 + 7 = 277
Note

Zeros tell us we definitely need to regroup from a higher place value.