Solve Vertical Addition: 104 + 153 Step by Step

Q: Why do I start adding from the right side?

We start from the units column because that's how our place value system works! If there's any carrying needed, it flows naturally from right to left, just like counting.

Q: Do I always get the same answer if I add the other way?

Yes! Addition is commutative, meaning $104 + 153 = 153 + 104 = 257$. The order doesn't matter, but the column alignment still does.

Q: How can I check my work without a calculator?

Try estimation first: $100 + 150 = 250$, so 257 seems reasonable. Then add the columns again carefully to double-check each step.

Q: What happens if there are zeros in the middle?

Zeros are easy! In the tens column: $0 + 5 = 5$. Just remember that zero plus any number equals that same number.

Vertical Addition with Three-Digit Numbers

$\begin{aligned} &104 \\ +& \\ &153 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 we'll calculate the sum of 2 digits, and then we'll place

00:06 We'll start by adding ones with ones, and place in ones

00:11 Add tens with tens, place in tens

00:15 Add hundreds with hundreds, place in hundreds

00:20 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

$\begin{aligned} &104 \\ +& \\ &153 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will perform vertical addition:

Step 1: Align the numbers by place value:
$\begin{aligned} &104 \\ + &153 \\ &\underline{\phantom{706}} \\ \end{aligned}$
Step 2: Add the numbers starting from the rightmost digit (units).
The units column: $4 + 3 = 7$
Step 3: Move to the tens column and add.
The tens column: $0 + 5 = 5$
Step 4: Finally, add the hundreds column.
The hundreds column: $1 + 1 = 2$

Putting it all together, the result of adding 104 and 153 is:

$\begin{aligned} &104 \\ + &153 \\ &\underline{257} \\ \end{aligned}$

Therefore, the solution to the problem is $257$ .

Final Answer

257

Key Points to Remember

Essential concepts to master this topic

Alignment Rule: Stack numbers by place value columns (hundreds, tens, units)
Technique: Add column by column from right to left: $4 + 3 = 7$
Check: Verify each column adds correctly: units 7, tens 5, hundreds 2 ✓

Common Mistakes

Avoid these frequent errors

Misaligning place values when stacking numbers
Don't stack 104 and 153 without proper alignment = wrong column additions! When digits aren't aligned by place value, you add wrong numbers together. Always line up hundreds with hundreds, tens with tens, and units with units.

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 start adding from the right side?

We start from the units column because that's how our place value system works! If there's any carrying needed, it flows naturally from right to left, just like counting.

What if I get confused about which digits to add?

Draw vertical lines between columns to separate hundreds, tens, and units. This makes it crystal clear which digits belong together: $1|0|4 + 1|5|3$

Do I always get the same answer if I add the other way?

Yes! Addition is commutative, meaning $104 + 153 = 153 + 104 = 257$ . The order doesn't matter, but the column alignment still does.

How can I check my work without a calculator?

Try estimation first: $100 + 150 = 250$ , so 257 seems reasonable. Then add the columns again carefully to double-check each step.

What happens if there are zeros in the middle?

Zeros are easy! In the tens column: $0 + 5 = 5$ . Just remember that zero plus any number equals that same number.

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