Solve Vertical Addition: 193 + 22 Step-by-Step

Vertical Addition with Carrying

193+  22776 \begin{aligned} &193 \\ +& \\ &~~22 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this problem together.
00:07 Each time, combine two digits. Then, write them down.
00:11 Start by adding the ones place. Add ones with ones.
00:16 Write down the result in the ones place.
00:19 Next, add tens with tens.
00:22 Write down the tens in the tens place. Add 1 to the hundreds.
00:27 Fill in any missing digits with 0.
00:31 Add hundreds with hundreds. Don't forget to add 1, writing in the hundreds place.
00:36 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

193+  22776 \begin{aligned} &193 \\ +& \\ &~~22 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, let's perform vertical addition of the numbers 193 and 22:

  • Step 1: Align the Numbers
    193
    + 22
    ------
  • Step 2: Add the Units Column
    The rightmost column is the units place. Add the digits 33 and 22:
    3+2=53 + 2 = 5.
    Write down 55 in the units place of the answer.
  • Step 3: Add the Tens Column
    Move to the next column which is the tens place. Add the digits 99 and 22:
    9+2=119 + 2 = 11.
    Since it's 11 (which is greater than 10), we write 11 under the tens column and carry over 11 to the hundreds column.
  • Step 4: Add the Hundreds Column
    Finally, add the digits in the hundreds place, considering the carryover:
    1+1=21 + 1 = 2.
    Write down 22 in the hundreds place of the answer.
  • Step 5: Write the Final Answer
    Combine the results from each column:
    215.

Therefore, the sum of 193 and 22 is 215 215 .

3

Final Answer

215

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value with units column rightmost
  • Technique: Add column by column: 9+2=119 + 2 = 11, write 1 carry 1
  • Check: Verify by adding horizontally: 193+22=215193 + 22 = 215

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry when sum exceeds 9
    Don't just write 11 in the tens place = wrong answer like 1115! This ignores place value completely. Always write the units 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 'carrying' mean in addition?

+

When two digits add up to 10 or more, you write down the units digit and 'carry' the tens digit to the next column. For example: 9+2=119 + 2 = 11, so write 1 and carry 1.

Why can't I just write 11 in the tens column?

+

Each column can only hold one digit! Writing 11 would mean you have 11 tens, which should actually be written as 1 hundred and 1 ten in separate columns.

How do I know which column to start adding from?

+

Always start from the rightmost column (units place) and work your way left. This ensures you handle any carrying correctly as you move through each place value.

What if there's nothing to add in a column?

+

If one number doesn't have a digit in that place (like the hundreds place in 22), treat it as zero. So in the hundreds column: 1+0=11 + 0 = 1 plus any carried digit.

How can I check if my answer is right?

+

Try these methods:

  • Add horizontally: 193+22193 + 22
  • Subtract backwards: 21522=193215 - 22 = 193
  • Estimate: 200+20220200 + 20 ≈ 220, so 215 makes sense!

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