4.B.1 — Add multi-digit whole numbers (standard algorithm).
Step 01 of 04
Standard addition algorithm. Write the numbers stacked, lined up by place value (ones over ones, tens over tens). Add column by column, starting from the ONES (right side).
Step 02 of 04
Worked example. 4,275 + 1,847.
4,275+1,847
Ones: 5 + 7 = 12. Write 2, carry the 1 to tens. Tens: 7 + 4 + 1 = 12. Write 2, carry 1. Hundreds: 2 + 8 + 1 = 11. Write 1, carry 1. Thousands: 4 + 1 + 1 = 6.
4,275+1,847=6,122
Step 03 of 04
Why carry? When a column total is 10 or more, the extra ten moves up to the next column (because that column is 10× the value of this one). The carry is just bookkeeping the extra ten.
Step 04 of 04
Multiple addends. Same procedure with three or more numbers — just add up each column.
243+156+89=?
Ones: 3 + 6 + 9 = 18. Write 8, carry 1. Tens: 4 + 5 + 8 + 1 = 18. Write 8, carry 1. Hundreds: 2 + 1 + 0 + 1 = 4. Result: 488.
Key insight
Stack with place values aligned. Add columns right to left. Carry the tens-digit when a column total exceeds 9. Same recipe regardless of how many digits.
4.B.2 — Subtract multi-digit whole numbers.
Step 01 of 04
Standard subtraction algorithm. Stack with the bigger number on top. Line up place values. Subtract column by column starting from the ONES.
Step 02 of 04
Worked example — no borrowing. 7,956 − 4,213.
Ones: 6 − 3 = 3. Tens: 5 − 1 = 4. Hundreds: 9 − 2 = 7. Thousands: 7 − 4 = 3. Result: 3,743.
Step 03 of 04
With borrowing. When the top digit is smaller, borrow 10 from the next column.
5,032 − 2,547.
Ones: 2 − 7 → borrow. 10 + 2 = 12. 12 − 7 = 5. Tens digit is now 2 (was 3). Tens: 2 − 4 → borrow. 12 − 4 = 8. Hundreds is now 9 (was 0 — borrow from thousands first, then give to tens). After all borrows: 4,9_2 becomes the working top. Hundreds: 9 − 5 = 4. Thousands: 4 − 2 = 2. Result: 2,485.
Step 04 of 04
Borrowing across zeros is the trickiest case. You "domino" backwards: each zero becomes 9 as you pull from further left.
Example: 3,002 − 1,475. Ones can't take 5 from 2 — borrow. Tens is 0, borrow from hundreds (also 0), borrow from thousands (3 → 2). Hundreds becomes 9, tens becomes 9 (it gave to ones), ones is now 12. 12 − 5 = 7. Continue: 9 − 7 = 2, 9 − 4 = 5, 2 − 1 = 1. Result: 1,527.
Key insight
Stack, align, subtract right-to-left. Borrow 10 from the next column when needed. Borrowing across zeros chains backwards — each 0 becomes 9. Always check by adding the answer back to the subtrahend.
4.B.3 — Add and subtract word problems.
Step 01 of 04
Decide the operation from the question.
| "How many in all?" | →add |
| "How many altogether?" | →add |
| "How many MORE / LESS?" | →subtract |
| "What's the difference?" | →subtract |
| "How many are LEFT?" | →subtract |
Step 02 of 04
Single-step example. A library has 4,752 books. They donate 1,318. How many remain?
4,752−1,318=3,434 books
"Remain" or "left" → subtract.
Step 03 of 04
Multi-step example. A truck carries 8,450 lbs. After dropping 1,275 lbs at one stop and 2,830 lbs at another, how much is left?
Two subtractions (or add the two drops first, then subtract once).
1,275+2,830=4,105
8,450−4,105=4,345 lbs
Step 04 of 04
Always check that the answer makes sense. If the question asks "how much is left" and your answer is bigger than the starting amount, something went wrong.
Key insight
Match keywords to operations. Multi-step problems chain operations — compute one piece at a time. Always reread the question after solving to make sure the answer matches what's asked.
4.B.4 — Estimate sums and differences.
Step 01 of 04
Estimation trades exactness for speed and sense-checking. Round each number first, then add or subtract.
Decide which place to round to based on what precision you need — usually the highest place that's not the leading digit.
Step 02 of 04
Worked example. Estimate 3,827 + 6,142 by rounding to the nearest hundred.
3,827→3,800,6,142→6,100
3,800+6,100=9,900
Exact answer: 9,969. Estimate is within 70 — close enough for a quick check.
Step 03 of 04
Estimation for sense-checking. If your exact calculation gives an answer FAR from the estimate, you probably made a mistake somewhere.
If you computed 3,827+6,142=996, the estimate ≈10,000 tells you something is wrong (off by a factor of 10 — probably misplaced a digit).
Step 04 of 04
Round both numbers to the SAME place for a fair estimate. Mixing precision (one to thousands, one to ones) makes the estimate less useful.
Key insight
Round each number, then operate. Estimation is for sense-checking and quick mental math. Round both to the same place for the cleanest estimate.