Master the tricky part of subtraction! Learn when and how to 'regroup' or 'borrow' in subtraction. When you don't have enough ones, we trade 1 ten for 10 ones. It's like trading a dime for 10 pennies! 💰🎯
Practice the important skill of regrouping in subtraction through fun, interactive challenges!
Learn to identify when regrouping is necessary in subtraction problems!
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Practice the regrouping process with visual understanding!
Drag to sort or use ↑↓ buttons to adjust · Correct Order
Put your regrouping skills to work with real-world scenarios!
Test your borrowing skills by matching problems to correct solutions!
🖱️ Drag options below to the correct boxes (computer) or click to move (mobile)
Solve challenging problems that really test your understanding!
Explore 10 detailed knowledge cards covering everything you need to know about regrouping and borrowing!
Borrowing (also called 'regrouping' or 'trading') is what we do when we don't have enough in a place to subtract. Since we can't have negative ones, we borrow 1 ten (which equals 10 ones) from the tens place. It's like breaking a $10 bill into 10 $1 bills when you need more ones!
When ones digit is too small to subtract from, we 'borrow'
Example: In 52 - 38, can't take 8 from 2 (not enough!)
Borrow 1 ten from tens place: 5 tens becomes 4 tens
Trade that 1 ten for 10 ones: 2 ones becomes 12 ones
Now we CAN subtract: 12 - 8 = 4!
Check before you subtract! Look at the ones digits. If the bottom digit is bigger than the top digit, you'll need to borrow. This quick check prepares you!
Forgetting to reduce the tens after borrowing! When you take 1 ten from the tens place, remember to cross out the old digit and write the new smaller number!
Like making change! If you have 5 dimes and 2 pennies ($0.52) but need to give someone 38 cents, you break a dime to get more pennies!
Use actual coins! Start with dimes and pennies. When you don't have enough pennies, trade a dime for 10 pennies. Physical trading helps it click!
Borrowing follows a specific order! First, check if ones are big enough. If not, reduce the tens by 1 and add 10 to the ones. Then subtract normally! The key is remembering that 1 ten equals 10 ones - that's what makes the trade work. Following steps prevents errors!
Step 1: Check ones - Can you subtract? If no, continue...
Step 2: Cross out the tens digit, write one less
Step 3: Add 10 to the ones digit (1 ten = 10 ones!)
Step 4: Now subtract the ones column
Step 5: Subtract the tens column (use the new reduced number)
Write the borrowed numbers small above the digits! This helps you remember what to subtract. Some students use different colors for borrowed numbers!
Forgetting which number changed after borrowing! After taking 1 from tens, make sure you subtract FROM the NEW smaller tens number, not the original!
Multi-step processes are everywhere: following recipes, building projects, solving puzzles. Math teaches you to follow steps in order!
Color-code your work! Use blue for original numbers, red for borrowed/changed numbers. Visual cues help you track what happened!
Before you start subtracting, do a quick check! Look at the ones digits. If the bottom ones digit is bigger than the top ones digit, you'll need to borrow. This quick scan helps you prepare mentally and stay organized. No surprises mid-problem!
Check the ones: 52 - 38 → Can't take 8 from 2, BORROW!
Check the ones: 76 - 43 → Can take 3 from 6, no borrowing
Check the ones: 41 - 27 → Can't take 7 from 1, BORROW!
Check the ones: 95 - 31 → Can take 1 from 5, no borrowing
Rule: If bottom ones > top ones, you must borrow!
Do a 'borrow scan' before solving! Circle problems that need borrowing in one color, non-borrowing in another. This prep makes solving smoother!
Starting without checking, then getting stuck mid-problem! Take 2 seconds to check first - it saves time and prevents errors!
Like checking if you have enough ingredients before cooking. If you don't have enough eggs, you need to 'borrow' from a neighbor or adjust the recipe!
Play 'Borrow or Not?' - Look at subtraction problems and quickly identify which need borrowing, without solving! Builds instant recognition.
Borrowing is all about place value! When we borrow 1 ten and trade it for 10 ones, the NUMBER STAYS THE SAME - we just changed its form! 52 written as 4 tens and 12 ones still equals 52. Understanding this relationship is the secret to mastering borrowing!
1 ten = 10 ones (this is the key to borrowing!)
When we borrow, we move value from tens place to ones place
Example: 52 has 5 tens and 2 ones
After borrowing: 4 tens and 12 ones (same total value: 52!)
Place value makes borrowing work mathematically!
Think 'Same value, different form!' Just like $1 = 100 pennies, 1 ten = 10 ones. We're not changing amounts, just breaking them into smaller pieces!
Thinking we're changing the number when we borrow! We're not - 52 = 50 + 2 = 40 + 12. Same number, different representation!
Currency exchange: $1 = 4 quarters = 10 dimes = 100 pennies. Same value, different forms - just like place value trades!
Build with place value blocks! Show 52 with 5 tens-rods and 2 ones-units. Trade 1 tens-rod for 10 ones-units. Count again - still 52!
How you write borrowing matters! Cross out the old tens digit and write the new smaller one nearby. Add a small '1' before the ones digit to show you added 10. Good notation helps you track changes and prevents mistakes. It's like leaving yourself clear notes!
Cross out the original tens digit (don't erase!)
Write the new tens digit (one less) above or beside it
Write a small '1' before the ones digit to show +10
Example: 52 becomes 4 above 5, and 12 above 2
Clear notation prevents confusion later!
Use a small '1' before the ones digit to show borrowing: 2 becomes '12' with a tiny 1 in front. This reminds you that you borrowed!
Erasing instead of crossing out! Don't erase - cross out so you can see what changed. This helps you check work and spot errors!
Like editing a document with 'track changes' on - you can see what was changed and why. Good record-keeping prevents mistakes!
Practice neat notation on graph paper! Each digit gets its own square. Use different colors for original and borrowed numbers!
Certain subtraction situations ALWAYS need borrowing! When the bottom ones digit is bigger than the top ones digit, borrowing is inevitable. Recognizing these patterns instantly tells you what to expect. Pattern awareness makes borrowing feel automatic!
Any problem where ones bottom > ones top needs borrowing
Example: _2 - _8, _3 - _7, _4 - _9 all need borrowing
After borrowing, ones place becomes 10+ the original
2 becomes 12, 3 becomes 13, 4 becomes 14 after borrowing
Pattern recognition speeds up problem-solving!
Memorize 'red flags': If you see 2 - 8, 3 - 7, 4 - 9 in the ones place, you KNOW you'll borrow. Instant recognition saves time!
Not recognizing patterns and figuring it out each time! Learn which situations always need borrowing - it becomes second nature!
Pattern recognition helps everywhere: recognizing traffic patterns for safety, weather patterns for planning, or habit patterns for improvement!
Make a 'borrowing patterns chart' showing common ones combinations that need borrowing. Keep it handy until patterns are automatic!
Borrowing is tricky, so checking is EXTRA important! The best check is addition: if 63 - 38 = 25, then 25 + 38 should equal 63. You can also estimate or solve again. Any method that confirms your answer is valuable. Always verify borrowing problems!
Method 1: Add your answer to what you subtracted (25 + 38 = 63?)
Method 2: Estimate first (63 - 38 is about 60 - 40 = 20, close to 25 ✓)
Method 3: Solve again carefully, watching borrowed numbers
Method 4: Use number line - count up from 38 to 63 (should equal 25)
If checks don't match, borrow again more carefully!
ALWAYS check borrowing problems! They're more complex, so mistakes are common. Spend 10 seconds checking to catch errors before moving on!
Not checking work, especially with borrowing! These problems have more steps, more chances for errors. Check EVERY borrowing problem!
Double-checking important calculations: bank balances, test scores, measurements for building. In real life, accuracy with numbers matters!
Make checking mandatory! After every borrowing problem, immediately check with addition. Build the habit until it's automatic!
Borrowing happens in real life when we need to break larger units into smaller ones! Whether it's breaking a $10 bill for exact change, converting units in cooking, or calculating time remaining, borrowing helps us solve practical problems accurately!
Money: Had 73 cents (7 dimes, 3 pennies), spent 48 cents (need to break a dime!)
Inventory: Store has 52 toys, sold 38, need 14 more (borrowed to calculate)
Collections: Had 91 cards, gave away 56, left with 35 (borrowing needed)
Cooking: Recipe needs 45 mL, bottle has 82 mL, will have 37 mL left after
Time: Had 63 minutes, used 47 minutes, 16 minutes remaining (borrowed!)
Look for borrowing in daily life! Any time you need to 'make change' or 'break down' a larger unit, that's borrowing in action!
Thinking borrowing only exists on paper! It's one of the most practical math skills - we use it constantly for money, measurements, time, and more!
EVERYWHERE! Shopping (making change), inventory management, time calculations, recipe conversions, measuring remaining amounts, and more!
Create real-life borrowing scenarios! 'You have $73, buy something for $48. How much left?' Use actual money to solve!
Borrowing is the hardest subtraction skill, so it's NORMAL to find it challenging at first! Every mathematician struggled with borrowing when learning. What matters is persistence - keep practicing, learn from mistakes, and celebrate progress. Confidence comes from seeing yourself improve!
Start with simple ones: Practice 52 - 38, 41 - 27 until comfortable
Build up gradually: Try 73 - 48, 91 - 56 as you gain confidence
Celebrate small wins: Got one right? Awesome! Keep going!
Learn from errors: Each mistake teaches you what to watch for
Track your progress: Notice how borrowing gets easier each day!
Keep a success journal! Write down borrowing problems you solved correctly. When it feels hard, look back and see how much you've learned. You're growing!
Giving up because it's hard! Borrowing is SUPPOSED to be challenging - that means your brain is growing! Struggle is part of learning, not a sign you can't do it.
Persistence builds character! When you push through hard math, you learn you can overcome challenges anywhere. Math teaches life skills!
Set tiny goals! 'Today I'll solve 3 borrowing problems correctly.' Tomorrow, try 4. Small consistent wins build big success!
Once you master borrowing with two digits, you can handle ANY borrowing problem! With three-digit numbers, you might need to borrow from hundreds to tens, then tens to ones. But it's the SAME PROCESS repeated! Understanding the pattern makes bigger numbers manageable.
Some problems need borrowing from tens AND hundreds!
Example: 200 - 158 requires multiple borrows
The process is the same, just repeated for each place
Master two-digit borrowing first, then three-digit is easier
Each place value follows the same borrowing rules!
Take it one place at a time! Don't let big numbers intimidate you. Handle each place value one step at a time, just like smaller problems!
Getting overwhelmed by larger numbers! Remember: the process is identical whether subtracting 52 - 38 or 552 - 338. Same steps, bigger numbers!
Larger calculations: subtracting big prices, calculating long distances, figuring out large inventories - real numbers often need multiple borrowing!
Start with two-digit mastery, then gradually introduce three-digit problems. Build confidence before adding complexity!