R1 · Lesson 2: Add & Subtract Multi-Digit Numbers

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Why this matters for Grade 6: Standard 6.NS.2 requires fluency with multi-digit addition and subtraction as the foundation for the division algorithm. You also need these skills to compute with decimals (6.NS.3) and to evaluate algebraic expressions (6.EE.2).

Learn It

Adding & Subtracting — and Estimating

Addition with regrouping: Line up digits by place value and add from right to left. Regroup (carry) when any column's sum is 10 or more.

Example 1: 3,482 + 1,759

3,482
+ 1,759
──────
5,241

Step-by-step: ones: 2+9=11, write 1 carry 1 · tens: 8+5+1=14, write 4 carry 1 · hundreds: 4+7+1=12, write 2 carry 1 · thousands: 3+1+1=5 → 5,241

Subtraction with regrouping: Line up digits, subtract right to left. When the top digit is too small, regroup (borrow) from the next place.

Example 2: 6,005 − 2,387

6,005
− 2,387
──────
3,618

Check: 3,618 + 2,387 = 6,005 ✓
Ones: can't do 5−7, borrow from tens (which is 0, so borrow from hundreds, which is also 0 — borrow from thousands). After regrouping: 15−7=8, tens: 9−8=1 (after giving 1 to ones), hundreds: 9−3=6 (after giving 1 to tens column chain), thousands: 5−2=3 → 3,618

Estimation: Round each number to its lead digit, then add or subtract. A fast sanity check before you commit to an answer.

Example 3: Estimate 412 + 289
Round to the nearest hundred: 400 + 300 = 700.
The exact answer (701) is close — the estimate worked!

Try It · Guided

Work These Together

1. What is 4,316 + 2,578?

Hint

Ones: 6+8=14, write 4 carry 1. Tens: 1+7+1=9. Hundreds: 3+5=8. Thousands: 4+2=6. Answer: 6,894.

2. Which is the best estimate for 597 + 314?

Hint

Round to the nearest hundred: 600 + 300 = 900.

Practice · On Your Own

You Try

3. Subtract: 8,000 − 3,456

Hint

8,000 − 3,456: borrow across zeros. Regroup step by step: 8,000 → 7,999+1 at ones place. 10−6=4 ones, 9−5=4 tens, 9−4=5 hundreds, 7−3=4 thousands → 4,544.

4. Solve: 5,274 + 3,819

Hint

Ones: 4+9=13, write 3 carry 1. Tens: 7+1+1=9. Hundreds: 2+8=10, write 0 carry 1. Thousands: 5+3+1=9. Answer: 9,093.

5. A school supply room has 2,450 pencils. Students use 876 during the week. How many pencils are left?

Hint

2,450 − 876: ones: 0 < 6, borrow → 10−6=4; tens: 4 (after lending) − 7, borrow → 14−7=7 (tens become 3); hundreds: 3 (after lending) − 8, borrow → 13−8=5; thousands: 1 − 0 = 1. Answer: 1,574.

★

Exit Ticket

Show What You Know

6. What is 7,631 − 4,285?

Hint

Ones: 1 < 5, borrow → 11−5=6. Tens: 2 (after lending) < 8, borrow → 12−8=4. Hundreds: 5 (after lending) − 2=3. Thousands: 7−4=3. Answer: 3,346.

7. Which is the best estimate for 712 − 289?

Hint

Round to hundreds: 700 − 300 = 400.

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