Solve Three-Digit Addition: 685 + 315 in Vertical Format

Column Addition with Carrying

685+315776 \begin{aligned} &685 \\ +& \\ &315 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Each time combine 2 digits, and then place
00:06 Let's start by adding units with units
00:09 Place the units, add 1 to tens
00:12 Add tens with tens, remember to add 1 to the calculation
00:16 Place tens in tens, add 1 to hundreds
00:20 Add hundreds with hundreds, remember to add 1
00:24 Place hundreds in hundreds, and add 1 to thousands
00:28 Place 0 in the missing digits
00:32 Add thousands with thousands, remember to add 1
00:35 Place in thousands
00:38 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

685+315776 \begin{aligned} &685 \\ +& \\ &315 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Add the units column
  • Step 2: Add the tens column, including any carry from the units
  • Step 3: Add the hundreds column, including any carry from the tens

Now, let's work through each step:

Step 1: Add the units column.

The units are 55 (from 685685) and 55 (from 315315).
5+5=105 + 5 = 10. Write 00 in the units place and carry over 11 to the tens place.

Step 2: Add the tens column, including any carry from the units.

The tens are 88 (from 685685) and 11 (from 315315), plus the 11 carried over.
8+1+1=108 + 1 + 1 = 10. Write 00 in the tens place and carry over 11 to the hundreds place.

Step 3: Add the hundreds column, including any carry from the tens.

The hundreds are 66 (from 685685) and 33 (from 315315), plus the 11 carried over.
6+3+1=106 + 3 + 1 = 10. Write 00 in the hundreds place and 11 in the thousands place.

Therefore, the solution to the problem is 10001000.

3

Final Answer

1000

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add each column from right to left
  • Technique: When sum ≥ 10, write ones digit and carry tens
  • Check: Verify 685 + 315 = 1000 by adding backwards ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when column sum is 10 or more
    Don't write 10 in a single column position = wrong place values! This creates numbers like 10010 instead of 1000. Always write the ones digit and carry the tens digit to the next column.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &12 \\ +& \\ &~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

What does 'carry over' mean in addition?

+

When adding a column gives you 10 or more, you write down the ones digit and carry the tens digit to the next column. For example, 5 + 5 = 10, so write 0 and carry the 1.

Why do I start adding from the right side?

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You start from the units place (rightmost) because any carrying affects the next column to the left. This ensures you handle all the carrying correctly as you move left.

What if I forget to carry a number?

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Your final answer will be too small! For example, if you forgot to carry in this problem, you might get 900 instead of 1000. Always double-check each column for carries.

How can I check if my addition is correct?

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Try these methods:

  • Add the numbers in reverse order (315 + 685)
  • Use estimation: 700 + 300 = 1000
  • Subtract one number from your answer to get the other

What happens when I carry to a new place value?

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When all columns produce carries, you create a new digit in the next place value. Like in this problem: 685 + 315 creates a new thousands place, making 1000!

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