Use column addition when adding large numbers. Align the digits by place value (ones, tens, hundreds) and add columns from right to left.
Align the numbers: Write the numbers vertically, aligning ones, tens, hundreds.
Add the ones column:8 + 5 = 13. Write 3 in the ones place and carry 1 to the tens column.
Add the tens column:5 + 7 + 1 \text{ (carried)} = 13. Write 3 in the tens place and carry 1 to the hundreds column.
Add the hundreds column:3 + 4 + 1 \text{ (carried)} = 8. Write 8 in the hundreds place.
Example: 358 + 475
¹ ¹
3 5 8
+ 4 7 5
-----------
8 3 3
Column Subtraction (with Borrowing)
Use column subtraction for larger numbers. Align digits by place value. If the top digit is smaller than the bottom digit in a column, borrow 1 from the column to the left.
Align the numbers: Write the numbers vertically, aligning ones, tens, hundreds.
Subtract the ones column: Since 3 < 6, borrow 1 from the tens column. The 2 in the tens column becomes 1, and the 3 in the ones column becomes 13. Now subtract: 13 - 6 = 7.
Subtract the tens column: Since the remaining 1 is less than 7, borrow 1 from the hundreds column. The 5 in the hundreds column becomes 4, and the 1 in the tens column becomes 11. Now subtract: 11 - 7 = 4.
Subtract the hundreds column: Subtract the remaining digits: 4 - 1 = 3.
Example: 523 - 176
⁴ ¹¹ ¹³ 523
- 1 7 6
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3 4 7
Long Multiplication (2-Digit by 2-Digit)
Multiply the top number by each digit of the bottom number, one at a time, then add the results together.
Align the numbers: Write the numbers vertically.
Multiply by the ones digit: Multiply 43 \times 7 = 301. Write 301 on the first line.
Write placeholder zero: Put a 0 in the ones column of the next line, because you are now multiplying by the tens digit (20).
Multiply by the tens digit: Multiply 43 \times 2 = 86. Write 86 to the left of the 0 (making it 860).
Add partial products: Add 301 + 860 = 1161 to get the final answer.