Solve Two-Digit Addition: 53 + 68 Using Column Method

Q: What does 'carry over' actually mean?

When adding digits gives you 10 or more, you write the ones digit in that column and carry the tens digit to the next column left. It's like making change - 11 ones becomes 1 ten and 1 one!

Q: Why do I need to line up the numbers vertically?

Place value alignment is crucial! The ones digits must be under ones digits, tens under tens. If they're not lined up, you'll add the wrong place values together.

Q: What if I forget to add the carried number?

Your answer will be 10 less than it should be! In this problem, forgetting to add the carried 1 would give you 111 instead of 121. Always remember: tens column = 5 + 6 + carried 1.

Q: Can I add from left to right instead?

It's much harder! Starting from the ones column (right) lets you handle carrying naturally. Left-to-right addition requires mental math that's more error-prone.

Q: How do I know if my carrying is correct?

Ones column: 3 + 8 = 11 → write 1, carry 1Tens column: 5 + 6 + 1 = 12 → write 2, carry 1Result: 121Each carried number should be exactly 1!

Column Addition with Carrying

$\begin{aligned} &53 \\ +& \\ &68 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 write down

00:06 Let's start by combining ones with ones

00:09 Write down the ones, and remember to carry 1 up

00:12 Combine tens with tens, remember to add 1 to the calculation

00:19 Write down the tens in the tens place, and carry 1 to hundreds

00:23 Write down the tens in the tens place, and carry 1 to hundreds

00:29 Combine hundreds with hundreds, and write in the appropriate position

00:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &53 \\ +& \\ &68 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll add the numbers 53 and 68 using vertical addition. Follow these steps:

Step 1: Align the numbers vertically by place value:

\begin{aligned} &53 \\ + &68 \\ \end{aligned}

Step 2: Add the units digits (rightmost column):

$3 + 8 = 11$

The result is 11. Write down 1 in the units column, and carry over 1 to the tens column.

Step 3: Add the tens digits (leftmost column), including the carry:

$5 + 6 + 1 = 12$

Write down 2 in the tens column, and carry over 1 to the hundreds column. This gives us a final result:

\begin{aligned} &121 \\ \end{aligned}

Therefore, the correct answer is $121$ .

Final Answer

121

Key Points to Remember

Essential concepts to master this topic

Alignment: Line up digits by place value before adding
Technique: Start from ones column: 3 + 8 = 11, write 1 carry 1
Check: Verify by adding horizontally: 50 + 3 + 60 + 8 = 121 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write down the full two-digit sum like writing 11 in the ones place = messy columns and wrong answer! This makes your final answer too large. 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

What does 'carry over' actually mean?

When adding digits gives you 10 or more, you write the ones digit in that column and carry the tens digit to the next column left. It's like making change - 11 ones becomes 1 ten and 1 one!

Why do I need to line up the numbers vertically?

Place value alignment is crucial! The ones digits must be under ones digits, tens under tens. If they're not lined up, you'll add the wrong place values together.

What if I forget to add the carried number?

Your answer will be 10 less than it should be! In this problem, forgetting to add the carried 1 would give you 111 instead of 121. Always remember: tens column = 5 + 6 + carried 1.

Can I add from left to right instead?

It's much harder! Starting from the ones column (right) lets you handle carrying naturally. Left-to-right addition requires mental math that's more error-prone.

How do I know if my carrying is correct?

Ones column: 3 + 8 = 11 → write 1, carry 1
Tens column: 5 + 6 + 1 = 12 → write 2, carry 1
Result: 121

Each carried number should be exactly 1!

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