Addition is the mathematical operation of combining two or more numbers to get a total or sum.

Subtraction is the mathematical operation of taking one number away from another to find the difference.

Regrouping in addition refers to the process of carrying over a value from one column to the next when the sum exceeds the base value (e.g., 10 in base 10).

Regrouping in subtraction involves borrowing from a higher place value when the top digit is smaller than the bottom digit in a column.

To add two-digit numbers without regrouping, simply add the digits in each place value column separately, ensuring the sum is less than 10.

To add two-digit numbers with regrouping, add the digits in the ones place first, carry over if the sum is 10 or more, then add the tens place.

To subtract two-digit numbers without regrouping, subtract the digits in each place value column directly, ensuring the top digit is larger than the bottom.