When you add or subtract two-digit numbers, a single column sometimes holds too much or too little.
If the ones reach ten, you carry one over to the tens; if the ones are too small to subtract, you borrow ten from the tens.
Slide the two numbers and watch, column by column, how carrying and borrowing play out in a vertical sum.
Why Do We Need Carrying?
🧺 Let's Put Apples in Baskets!
①One basket holds up to 10 apples
②7 + 6 = 13? The basket overflows!
③Move 10 to a new basket, leave 3
④This is "carrying"
Addition with Carrying
47
36
seegongsik.com
Showing the carrying process in vertical addition
💡 Carrying Steps
①Add ones place first
②If ≥ 10 → carry 10 to next place, write only the rest
③Add tens places + 1 (the carry)
Subtraction with Borrowing
63
28
seegongsik.com
Showing the borrowing process in vertical subtraction
💡 Borrowing Steps
①When you can't subtract ones
②Borrow 10 from tens place
③Add 10 to ones, subtract
④Tens place decreases by 1
Summary
Addition with Carry
47 + 36 → Ones: 7+6=13 (write 3, carry 1) → 83
Sum ≥ 10 → carry 10 to next place
Subtraction with Borrow
63 - 28 → Ones: 3<8 → 13-8=5, Tens: 5-2=3 → 35
Can't subtract → borrow 10 from next place
🎯 Remember!
①Always start from ones place
②Carry: > 10 → carry 1
③Borrow: not enough → borrow 10
④Mark carries/borrows to avoid mistakes
⑤Check: result + subtractor = original
Examples and Unit Test
Example 1
Calculate 58 + 27 using vertical addition.
1
Ones: 8 + 7 = 15. Write 5 and carry 1 to the tens.
2
Tens: 5 + 2 + 1(carry) = 8. So 58 + 27 = 85.
▸ 85
When the ones sum is 10 or more, carry 1 to the tens place.
Example 2
Calculate 72 − 35 using vertical subtraction.
1
Ones: you cannot take 5 from 2. Borrow 10 from the tens: 12 − 5 = 7.
2
Tens: after lending, 7 − 1 = 6, then 6 − 3 = 3. So 72 − 35 = 37.
▸ 37
When the ones cannot subtract, borrow 10 from the tens place.