Subtraction with Borrowing - Definition, Examples, Quiz, FAQ, Trivia
Learn step-by-step subtraction with regrouping through visual examples and practice activities
What is Subtraction with Borrowing?
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Subtraction with borrowing (also called regrouping) is a method we use when subtracting numbers where the digit in the top number is smaller than the digit directly below it in the bottom number.
Why do we need to borrow? When we can't subtract a larger number from a smaller one, we "borrow" from the next higher place value. This helps us solve problems that seem tricky at first!
Think of borrowing like this: When you don't have enough ones to subtract, you can borrow one ten from the tens place and turn it into ten ones. This gives you enough to subtract.
Key Concept
When the top digit is smaller than the bottom digit, borrow from the next higher place value to make subtraction possible.
How to Borrow Step by Step
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Let's learn the borrowing process using the problem 52 - 27:
Step-by-Step Guide
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-2 7
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-27
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25
Remember
When you borrow from the tens place, you're taking one ten and turning it into ten ones. That's why we reduce the tens digit by 1 and add 10 to the ones digit.
Practice Problems and Examples
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Let's practice subtraction with borrowing using different examples:
Example 1: Two-digit Subtraction
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Solution: Borrow 1 from 6 (making it 5) and add to 3 (making it 13). Then 13-8=5 and 5-2=3. Answer: 35
Example 2: Three-digit Subtraction
-168
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Solution:
1. Ones place: 5-8 → borrow from tens (2 becomes 1, 5 becomes 15) → 15-8=7
2. Tens place: 1-6 → borrow from hundreds (4 becomes 3, 1 becomes 11) → 11-6=5
3. Hundreds place: 3-1=2
Answer: 257
Example 3: Word Problem
Maria has 72 cookies. She gives 38 to her friends. How many cookies does she have left?
-38
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Solution: Borrow from 7 (making it 6) and add to 2 (making it 12). Then 12-8=4 and 6-3=3. Answer: 34 cookies
Practice Tip
Always start subtracting from the ones place and move left. Check your answer by adding it to the subtracted number - you should get the original number!
Subtraction Quiz
Test your subtraction skills with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about subtraction with borrowing:
Math Trivia
Discover interesting facts about subtraction and mathematics:
Ancient Subtraction
The earliest evidence of subtraction comes from ancient Egypt around 1800 BC. Egyptians used a number system based on multiples of 10, similar to our modern system.
Brain Math
Research shows that solving subtraction problems activates different parts of your brain than addition problems. Subtraction requires more visual-spatial processing!
Subtraction Symbol
The minus sign (-) first appeared in a 1489 book by German mathematician Johannes Widmann. Before this, subtraction was often written with the letter "m" for "minus".
Around the World
Different countries teach subtraction differently! In some European countries, they use a method called "equal additions" instead of borrowing.
