Solve Three-Digit Addition: 986 + 757 in Vertical Format

Multi-digit Addition with Column Carrying

986+757776 \begin{aligned} &986 \\ +& \\ &757 \\ &\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 consider combining 2 digits, and then place
00:06 Let's start by combining ones with ones
00:09 Place the ones, add 1 to the tens
00:12 Combine tens with tens, remember to add 1 to the calculation
00:18 Place tens in tens, add 1 to hundreds
00:24 Combine hundreds with hundreds, remember to add 1
00:29 Place hundreds in hundreds, and add 1 to thousands
00:34 Place 0 in the missing digits
00:37 Combine thousands with thousands, remember to add 1
00:40 Place in thousands
00:43 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

986+757776 \begin{aligned} &986 \\ +& \\ &757 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Identify the given numbers - 986 and 757.
  • Step 2: Apply the vertical addition method.
  • Step 3: Perform the calculation column by column, starting from the right. Carry over if necessary.

Now, let's work through each step:

Starting with the units column:
6+7=13 6 + 7 = 13 . Since 13 is greater than 9, we write down 3 and carry over 1 to the tens column.

Next, in the tens column:
8+5=13 8 + 5 = 13 , and adding the carry over 1 gives us 14. Again, we write down 4 and carry over 1 to the hundreds column.

Finally, in the hundreds column:
9+7=16 9 + 7 = 16 , and adding the carry over 1 gives us 17. Here, we write down 17 as there are no other columns to carry over to.

Therefore, the final sum is 1743 1743 .

To verify, let's match this result with the given choices. The correct choice is: 1743 1743 .

3

Final Answer

1743

Key Points to Remember

Essential concepts to master this topic
  • Column Rule: Always start from the rightmost column and work left
  • Carrying Technique: When sum exceeds 9, write ones digit and carry tens (13 = 3 write, 1 carry)
  • Verification Check: Add the digits in your answer: 1+7+4+3 = 15, reasonable for 986+757 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to add the carried digit
    Don't just add 8+5=13 in tens column without the carried 1 = wrong answer 1633! This ignores the carried value from the previous column. Always add the carried digit: 8+5+1=14.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &90 \\ +& \\ &~~9\\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

What does it mean to 'carry' in addition?

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When adding digits gives you a number 10 or greater, you write down the ones digit and carry the tens digit to the next column. For example, 6+7=13, so write 3 and carry the 1.

Why do we start from the right column?

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We start from the units column because that's where carrying begins! If you start from the left, you won't know what to carry over from the smaller place values.

What if I forget to carry a number?

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Your answer will be wrong by multiples of 10! Always double-check each column to make sure you've added any carried digits from the previous step.

How can I check my addition is correct?

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Try these methods:

  • Reverse check: Add the numbers in different order (757+986)
  • Estimation: Round to nearest hundreds (1000+800=1800, close to 1743)
  • Digit sum: Add all digits in your answer for reasonableness

What if my final answer has more digits than either original number?

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That's totally normal! When adding large numbers, the sum often has one more digit than the original numbers. 986+757=1743 has 4 digits while the addends have 3 digits.

Can I use this method for any addition problem?

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Yes! This column addition method works for any whole number addition problem, whether it's 2-digit, 3-digit, or even larger numbers. The steps stay exactly the same.

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