Solve Vertical Addition: 65 + 18 Step by Step

Vertical Addition with Two-Digit Regrouping

65+18776 \begin{aligned} &65 \\ +& \\ &18 \\ &\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, and remember 1 above
00:12 Combine tens with tens, remember to add 1 to the calculation
00:19 Place in the tens position
00:23 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

65+18776 \begin{aligned} &65 \\ +& \\ &18 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

Let's solve the problem of adding two numbers, 65 and 18, step-by-step using vertical addition:

  • Step 1: Write the numbers vertically, aligning the tens and ones digits as follows:

+65+1876 \begin{array}{c} \phantom{+}65 \\ +18 \\ \underline{\phantom{76}} \\ \end{array}

  • Step 2: Add the digits in the ones column. These digits are 5 and 8.

5+8=13 5 + 8 = 13

  • Since the sum is 13, we place the 3 in the ones column and carry over the 1 to the tens column.
  • Step 3: Move to the tens column. Add the digits in this column: 6 (from 65) and 1 (from 18), plus the 1 we carried over from the ones column.

6+1+1=8 6 + 1 + 1 = 8

  • Step 4: Write 8 in the tens place.

+65+187683 \begin{array}{c} \phantom{+}65 \\ +18 \\ \underline{\phantom{76}} \\ 83 \\ \end{array}

Therefore, the sum of 65 and 18 is 83\mathbf{83}.

3

Final Answer

83

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers with ones digits and tens digits lined up
  • Regrouping: When ones sum ≥ 10, carry the ten to tens column
  • Verification: Check by adding in reverse order: 18 + 65 = 83 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry when ones column sum exceeds 9
    Don't write 13 in the ones place when 5 + 8 = 13! This ignores place value rules and gives 1318 instead of 83. Always carry the 1 to the tens column and write only 3 in the ones place.

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

Why do I need to line up the digits vertically?

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Lining up digits ensures you're adding ones to ones and tens to tens. If digits aren't aligned properly, you'll add numbers from different place values and get the wrong answer!

What does 'carry over' mean exactly?

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When two digits add up to 10 or more, you carry over the extra ten to the next column. For example, 5+8=13 5 + 8 = 13 means write 3 and carry the 1 ten to the tens column.

Do I always need to carry when adding?

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No! You only carry when the sum in a column is 10 or greater. If 4+3=7 4 + 3 = 7 , just write 7 - no carrying needed.

How can I check if my addition is correct?

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Try these methods:

  • Add in reverse order: 18 + 65 should equal 65 + 18
  • Estimate: 65 + 18 is about 70 + 20 = 90, close to 83
  • Use subtraction: 83 - 18 should equal 65

What if I have to carry more than once?

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That's normal! Some problems require carrying multiple times. Just work through each column step by step, always remembering to add any carried number to the next column's sum.

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