Questions: Multi-Digit Addition

Question 1

What is the sum of 3,846 + 2,975?

• A. 5,711
• B. 6,711
• C. 6,821
• D. 6,811

Answer: (C)

Starting from the ones: 6+5=11, write 1 carry 1; tens: 4+7+1=12, write 2 carry 1; hundreds: 8+9+1=18, write 8 carry 1; thousands: 3+2+1=6. Result: 6,821. A common error is forgetting one or more carries, which produces 6,811 or 6,711.

Question 2

When adding 4,567 + 2,489, you can determine the thousands digit by computing 4 + 2 = 6 without checking for a carry from the hundreds column.

• T. True
• F. False

Answer: False

Carries from lower columns can change a higher column's digit. Here: ones 7+9=16 (write 6, carry 1); tens 6+8+1=15 (write 5, carry 1); hundreds 5+4+1=10 (write 0, carry 1); thousands 4+2+1=7. The answer is 7,056, not 6,056. Never assume a column's digit is final until you check whether the column to its right generated a carry.

Question 3

A school collected 1,248 cans in the first week and 976 in the second week. Explain how place-value alignment helps you find the correct total.

Model answer: Align 1,248 and 976 so ones are under ones, tens under tens, etc. Then add column by column from the right: 8+6=14 (write 4, carry 1); 4+7+1=12 (write 2, carry 1); 2+9+1=12 (write 2, carry 1); 1+0+1=2. Total: 2,224.

Alignment enforces the rule that only like units combine. Without it, you might add a tens digit to a ones digit, mixing units and producing a nonsense answer. The carries represent legitimate trading — 10 ones become 1 ten, 10 tens become 1 hundred — which is exactly what place value describes.