Addition & Subtraction
Addition With and Without Regrouping
To add large numbers, line up the Ones, Tens, Hundreds and Thousands and add each column from the right. When a column adds up to 10 or more, we regroup (carry) 1 to the next column.
For 2,567 + 1,848: ones 7 + 8 = 15 (write 5, carry 1), tens 6 + 4 + 1 = 11 (write 1, carry 1), hundreds 5 + 8 + 1 = 14 (write 4, carry 1), thousands 2 + 1 + 1 = 4. The sum is 4,415.
- Add column by column from the Ones place.
- If a column makes 10 or more, carry 1 to the next column.
Subtraction With Borrowing & Checking
To subtract, line up the places and subtract each column from the right. When the top digit is smaller, borrow 1 from the next column.
We can check a subtraction by adding the answer to the number we subtracted — it should give back the first number. For 645 − 278 = 367, check: 367 + 278 = 645.
- Borrow 1 from the next column when the top digit is too small.
- Check subtraction: answer + number subtracted = first number.
Estimation & Word Problems
Estimation gives a quick, close answer. To estimate a sum or difference, first round each number to the nearest ten or hundred, then add or subtract. For example, 312 + 489 is about 300 + 500 = 800.
In word problems, words like in all and altogether mean add, while left, remaining and how many more mean subtract.
- Round to the nearest ten/hundred, then estimate.
- 'In all' means add; 'left / how many more' means subtract.