Solve Vertical Addition: Finding the Sum of 178 + 12

Q: What does 'carry over' mean in addition?

When adding a column gives you 10 or more, you write down the ones digit and carry the tens digit to the next column. For example: $8 + 2 = 10$, so write 0 and carry 1.

Q: Why do I need to align the numbers by place value?

Place value alignment ensures you're adding units to units, tens to tens, etc. If 12 isn't aligned properly under 178, you might accidentally add wrong digits together!

Q: How can I check if my vertical addition is correct?

Try adding the numbers horizontally: 178 + 12. Break it down: 178 + 10 = 188, then 188 + 2 = 190. If you get the same answer, you're correct!

Q: What happens when I have to carry multiple times?

Handle each column one at a time from right to left. Add the carry from the previous column, then if that sum is 10 or more, carry again to the next column.

Vertical Addition with Carrying

$\begin{aligned} &178 \\ +& \\ &~~12 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 calculate the sum of 2 digits, and then we place

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

00:09 Place the ones, and add 1 to the tens

00:15 Add tens with tens, remember to add 1 to the calculation

00:19 Place in the tens position

00:24 Place 0 in the missing digits

00:27 Add hundreds with hundreds, place in hundreds position

00:30 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

$\begin{aligned} &178 \\ +& \\ &~~12 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will perform vertical addition:

Step 1: Write the numbers vertically, aligning by place value. We have 178 on top and 12 below.
Step 2: Start by adding the units column: $8 + 2 = 10$ . Write 0 below the line and carry over 1 to the next column.
Step 3: Move to the tens column. Add $7 + 1 = 8$ from 178 and the carry over 1, which equals $8 + 1 = 9$ . Write 9 below the line.
Step 4: Finally, add the hundreds column, where we have 1 with no carry over involved. Write 1 below the line.

After completing these steps, the vertical addition gives us the sum: $190$ .

Final Answer

190

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value with units column first
Carrying: When sum exceeds 9, write ones digit and carry tens
Check: Verify 178 + 12 = 190 by adding horizontally ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry when column sum exceeds 9
Don't write 10 in the units column when 8 + 2 = 10! This creates a wrong answer like 1710 instead of 190. Always write the ones digit (0) and carry the tens digit (1) 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' mean in addition?

When adding a column gives you 10 or more, you write down the ones digit and carry the tens digit to the next column. For example: $8 + 2 = 10$ , so write 0 and carry 1.

Why do I need to align the numbers by place value?

Place value alignment ensures you're adding units to units, tens to tens, etc. If 12 isn't aligned properly under 178, you might accidentally add wrong digits together!

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

When a column has only one number (like the hundreds place with just 1), simply bring it down to your answer. Remember to add any carry-over if there is one!

How can I check if my vertical addition is correct?

Try adding the numbers horizontally: 178 + 12. Break it down: 178 + 10 = 188, then 188 + 2 = 190. If you get the same answer, you're correct!

What happens when I have to carry multiple times?

Handle each column one at a time from right to left. Add the carry from the previous column, then if that sum is 10 or more, carry again to the next column.

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