Solve Three-Digit Addition: 157 + 264 in Vertical Format

Q: What does 'carrying' mean in addition?

Carrying happens when adding digits gives you 10 or more. You write down the units digit and carry the tens digit to the next column. For example: $7 + 4 = 11$ means write 1, carry 1.

Q: Why do I need to align the numbers vertically?

Proper alignment ensures you're adding units to units, tens to tens, etc. If numbers aren't lined up correctly, you'll add different place values together and get the wrong answer!

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

Try these methods: Add the numbers horizontally using mental mathUse a calculator to verifyAdd the numbers in reverse order (264 + 157)

Vertical Addition with Carrying

$\begin{aligned} &157 \\ +& \\ &264 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 joining 2 digits, and then place

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

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

00:14 Combine tens with tens, remember to add 1 to the calculation

00:19 Place tens in tens, add 1 to hundreds

00:25 Combine hundreds with hundreds, remember to add 1

00:30 Place in hundreds

00:33 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

$\begin{aligned} &157 \\ +& \\ &264 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll perform vertical addition:

Write the numbers 157 and 264 in a column, aligning the digits by place value. Start from right (units) to left (hundreds).
Step 1: Add the digits in the units place $7 + 4 = 11$ . Write down 1 and carry over 1 to the tens column.
Step 2: Add the digits in the tens place $5 + 6 = 11$ , plus the carried 1 from the previous step, giving a total of 12. Write down 2 and carry over 1 to the hundreds column.
Step 3: Add the digits in the hundreds place $1 + 2 = 3$ , plus the carried 1 from the previous step, resulting in 4. Write down 4.

After adding each column and managing the carries appropriately, the resulting sum of these numbers is 421.

Therefore, the solution to the problem is $421$ .

Final Answer

421

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers with units, tens, and hundreds lined up
Technique: Start right to left: $7 + 4 = 11$ , write 1 carry 1
Check: Add horizontally: $157 + 264 = 421$ matches vertical result ✓

Common Mistakes

Avoid these frequent errors

Adding columns from left to right instead of right to left
Don't start with hundreds place first = wrong carrying pattern! This creates incorrect carries that compound errors in each column. Always start from the rightmost column (units) and work left, carrying as needed.

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 'carrying' mean in addition?

Carrying happens when adding digits gives you 10 or more. You write down the units digit and carry the tens digit to the next column. For example: $7 + 4 = 11$ means write 1, carry 1.

Why do I need to align the numbers vertically?

Proper alignment ensures you're adding units to units, tens to tens, etc. If numbers aren't lined up correctly, you'll add different place values together and get the wrong answer!

What if I forget to add the carried number?

Always remember the carried digit! Write it small above the next column as a reminder. For example, when $5 + 6 + 1$ (carried) = 12, you must include that carried 1.

How can I check if my vertical addition is correct?

Try these methods:

Add the numbers horizontally using mental math
Use a calculator to verify
Add the numbers in reverse order (264 + 157)

What if there are more than two numbers to add?

The same process works! Stack all numbers vertically with proper alignment, then add each column from right to left. You might carry larger numbers, but the principle stays the same.

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