Solve Vertical Addition: 257 + 51 Step-by-Step

Vertical Addition with Carrying Digits

257+  51776 \begin{aligned} &257 \\ +& \\ &~~51 \\ &\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 Start by combining ones with ones
00:09 Place the ones
00:12 Combine tens with tens
00:16 Place tens in tens, add 1 to hundreds
00:20 Place 0 in the missing digits
00:23 Combine hundreds with hundreds remember to add 1, place in hundreds
00:26 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

257+  51776 \begin{aligned} &257 \\ +& \\ &~~51 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we'll proceed with vertical addition of 257 and 51:

  • Align the numbers by place values as follows:
257+  51 \begin{aligned} & 257 \\ +& ~~51 \\ \hline \end{aligned}

Start adding from the right-most side (units column):

Units Column: 7+1=87 + 1 = 8. There is no carrying over needed as the sum is below 10.
Tens Column: 5+5=105 + 5 = 10. Here, we write down 0 and carry over 1 to the hundreds column.
Hundreds Column: 2+0=22 + 0 = 2 from the original numbers plus the 1 carried over gives 33.

The resulting sum is:

257+  51308 \begin{aligned} & 257 \\ +& ~~51 \\ \hline & 308 \\ \end{aligned}

Therefore, the solution to the problem is 308308.

3

Final Answer

308

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up numbers by place value columns (ones, tens, hundreds)
  • Technique: Add right to left: 7+1=8, 5+5=10 (write 0, carry 1)
  • Check: Verify 308 by adding left to right: 200+50+57+1=308 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when sum exceeds 9
    Don't write down 10 in the tens column when 5+5=10 = wrong answer 257+51=3010! The 10 means write 0 and carry 1 to the next column. Always carry the tens digit to the left column when any column sum is 10 or more.

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 we add from right to left instead of left to right?

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We start with the ones column because carrying works from smaller to larger place values. If you start left, you might miss carries that affect the final answer!

What does 'carry over' actually mean?

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When a column adds up to 10 or more, you write the ones digit and carry the tens digit to the next column left. Like 5+5=105+5=10: write 0, carry 1.

How do I know when to carry a number?

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Carry whenever your column sum is 10 or greater. Write down the ones digit, then add the tens digit to the next column to the left.

What if there's no number in a column to add?

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Treat missing digits as zero. In this problem, 51 has no hundreds digit, so we add 2+0=22+0=2 in the hundreds column (plus any carried digit).

Can I check my answer a different way?

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Yes! Try estimation: 257 is close to 260, and 51 is close to 50. So 260+50=310, which is very close to our answer of 308 ✓

What if I make a mistake while adding?

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No worries! Cross out your work neatly and start over. It's better to redo it carefully than to have the wrong answer.

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