Solve Vertical Addition: 2789 + 456 Step by Step

Vertical Addition with Carrying Strategy

2789+  456776 \begin{aligned} &2789 \\ +& \\ &~~456 \\ &\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 we'll place
00:06 Let's start by combining ones with ones
00:09 Place the ones, add 1 to tens
00:12 Combine tens with tens, remember to add 1 to the calculation
00:19 Place tens in tens, add 1 to hundreds
00:23 Combine hundreds with hundreds, remember to add 1
00:29 Place hundreds in hundreds, and add 1 to thousands
00:33 Place 0 in the missing digits
00:37 Combine thousands with thousands, remember to add 1
00:41 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

2789+  456776 \begin{aligned} &2789 \\ +& \\ &~~456 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve the addition of 2789+4562789 + 456, we'll proceed with vertical addition:

  • Step 1: Align the numbers by their digits:
    02789+04560000 \begin{array}{c} \phantom{0}2789 \\ +\phantom{0}456 \\ \underline{\phantom{0000}} \\ \end{array}
  • Step 2: Start adding from the rightmost column (ones place):
    9+6=159 + 6 = 15. Write down 55 and carry over 11 to the tens place.
  • Step 3: Add the tens place:
    8+5=138 + 5 = 13, and add the carry over 11, getting 1414. Write down 44 and carry over 11 to the hundreds place.
  • Step 4: Add the hundreds place:
    7+4=117 + 4 = 11, and add the carry over 11, getting 1212. Write down 22 and carry over 11 to the thousands place.
  • Step 5: Add the thousands place:
    Since we only have 22 and a carry of 11, the result is 33.
  • Step 6: Compile the result across all columns:
    3245 3245

Therefore, the solution to the addition problem is 32453245.

3

Final Answer

3245

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value columns (ones, tens, hundreds)
  • Technique: Start from ones: 9 + 6 = 15, write 5 carry 1
  • Check: Add left to right: 2000 + 700 + 80 + 9 + 400 + 50 + 6 = 3245 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over to the next column
    Don't just write down 15 when 9 + 6 = 15 without carrying = wrong final answer! This ignores place value and creates errors in every following column. Always write the ones digit and carry the tens digit to the next column.

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

Why do I need to carry when adding?

+

When the sum in any column is 10 or more, you have more than 9 units in that place value. The extra amount needs to move to the next higher column to maintain proper place value.

What if I forget to add the carried number?

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Your answer will be wrong! The carried number represents tens, hundreds, or thousands depending on the column. Always remember to add it before moving to the next column.

Can I add from left to right instead?

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It's much harder that way! Adding from right to left (ones to thousands) makes carrying systematic and prevents mistakes with place values.

How do I check my vertical addition?

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Try these methods:

  • Add again using the same process
  • Add horizontally: 2789+456=32452789 + 456 = 3245
  • Subtract: 3245456=27893245 - 456 = 2789

What if the numbers have different lengths?

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No problem! Just imagine zeros in the empty spots. For example, treat 456 as 0456 when adding to 2789. The alignment by place value stays the same.

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