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Borrowing (Regrouping)

Overview

Knocking on the neighbor's door.

What is it?

Taking a value of 10 from the next highest place value when the top digit is too small to subtract from.

History

Also called 'Decomposition' in modern math teaching.

Key Idea

Slash the neighbor, drop it by 1, give yourself a 10.

Practice This Topic

Concept Guide

Plain English: Imagine trying to pay $8 but you only have a $10 bill. You can't give 8 singles. You have to 'break' the ten into ten ones first. That is borrowing.

Real-world example: Making change at a cash register.

How to do it

  1. Start at the right column.
  2. If Top < Bottom, look left.
  3. Cross out the neighbor, subtract 1 from it.
  4. Add 10 to your current Top number.
  5. Subtract normally.
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Common Pitfall

Subtracting UP! In 52 - 38, students often say 8-2=6. Wrong! You must borrow.

Word Problem
"You need 35 wood to build a chest. You have 52. How much extra do you have?"
Reasoning: 52 - 35. You can't do 2-5. Borrow from 50. 12-5=7. 4-3=1. Answer: 17.

Practice Examples

The Setup
4 12 5 2 - 3 8 ------ 1 4
Borrow 10 from 50.