Solve Two-Digit Addition: 23 + 51 in Vertical Format

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

Lining up numbers by place value ensures you're adding the right digits together! Ones go with ones, tens go with tens. This prevents mixing up place values and getting wrong answers.

Q: Should I always start adding from the right side?

Yes, always start from the ones place! This is the standard method that helps you handle carrying (regrouping) properly when sums are 10 or greater.

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

Try these methods: Add the numbers horizontally: 23 + 51Break apart: (20 + 50) + (3 + 1) = 70 + 4 = 74Use a calculator to verify

Q: Do I need to write the plus sign when doing vertical addition?

Yes! Writing + 51 (with the plus sign) makes it clear you're adding. This helps prevent confusion and shows your work clearly for teachers and yourself.

Two-Digit Addition with Vertical Format

$\begin{aligned} &23 \\ +& \\ &51 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step written solution

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Understand the problem

$\begin{aligned} &23 \\ +& \\ &51 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll use vertical addition, adding two two-digit numbers, 23 and 51. Here’s how to proceed:

Step 1: Align the numbers vertically by their place values.

Arrange the numbers:

$\begin{aligned} &23 \\ + &51 \\ \end{aligned}$

Step 2: Add the units digits, which are 3 and 1.

$3 + 1 = 4$

Step 3: Add the tens digits, which are 2 and 5.

$2 + 5 = 7$

Step 4: Combine both results.

The sum of the units digits is 4, and the sum of the tens digits is 7, giving the final total of:

$\begin{aligned} &23 \\ + &51 \\ \underline{\phantom{76}} & \\ &74 \\ \end{aligned}$

Therefore, the final result of adding 23 and 51 is $74$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value (ones under ones, tens under tens)
Technique: Add columns from right to left: 3 + 1 = 4, then 2 + 5 = 7
Check: Verify by adding horizontally: 23 + 51 = 20 + 50 + 3 + 1 = 74 ✓

Common Mistakes

Avoid these frequent errors

Misaligning digits vertically
Don't write numbers randomly without lining up place values = wrong sums! When digits aren't properly aligned, you might add tens to ones or get confused about which digits to combine. Always line up the rightmost digits (ones place) first, then stack tens above tens.

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

Why do I have to line up the numbers vertically?

Lining up numbers by place value ensures you're adding the right digits together! Ones go with ones, tens go with tens. This prevents mixing up place values and getting wrong answers.

Should I always start adding from the right side?

Yes, always start from the ones place! This is the standard method that helps you handle carrying (regrouping) properly when sums are 10 or greater.

What if I get the same answer adding left to right?

For simple problems like 23 + 51, you might get lucky! But when you need to carry numbers, adding left to right will give wrong answers. Always start from the right to build good habits.

How can I check if my vertical addition is correct?

Try these methods:

Add the numbers horizontally: 23 + 51
Break apart: (20 + 50) + (3 + 1) = 70 + 4 = 74
Use a calculator to verify

Do I need to write the plus sign when doing vertical addition?

Yes! Writing + 51 (with the plus sign) makes it clear you're adding. This helps prevent confusion and shows your work clearly for teachers and yourself.

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