Solve Vertical Addition: 10 + 32 Step-by-Step

Vertical Addition with Two-Digit Numbers

10+32776 \begin{aligned} &10 \\ +& \\ &32 \\ &\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
00:08 Place in the correct position
00:11 Add tens with tens
00:14 Place in the correct position
00:16 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

10+32776 \begin{aligned} &10 \\ +& \\ &32 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Align the numbers vertically so that each digit lines up according to its place value. Arrange 10 and 32 as follows:

10+32776 \begin{aligned} &10 \\ +& \\ &32 \\ &\underline{\phantom{776}} \end{aligned}

  • Step 2: Add the digits in the rightmost column (units place). Add 00 (from 10) and 22 (from 32) to obtain 22.

Write the result 22 beneath the line in the units column:

10+3277672 \begin{aligned} &10 \\ +& \\ &32 \\ &\underline{\phantom{776}} \\ &\phantom{7}2 \\ \end{aligned}

  • Step 3: Move to the next column to the left (tens place) and add 11 (from 10) and 33 (from 32) to obtain 44.

Write the result 44 to the left of the 22 in the tens column:

10+3277642 \begin{aligned} &10 \\ +& \\ &32 \\ &\underline{\phantom{776}} \\ &42 \\ \end{aligned}

Therefore, the solution to the problem is 42 42 .

3

Final Answer

42

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up digits by place value before adding
  • Technique: Add rightmost column first: 0 + 2 = 2
  • Check: Verify by adding horizontally: 10 + 32 = 42 ✓

Common Mistakes

Avoid these frequent errors
  • Adding digits without proper alignment
    Don't just add numbers left to right like 1+0+3+2=6! This ignores place value and gives completely wrong answers. Always align digits vertically by place value first.

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 need to line up the numbers vertically?

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Place value matters! Each digit represents a different value based on its position. The 1 in 10 means ten, while the 3 in 32 means thirty. Lining them up ensures you add the right values together.

What if one number has fewer digits than the other?

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That's normal! In this problem, 10 has a 0 in the units place. You can think of it as adding 0 + 2 = 2. The shorter number just has invisible zeros in the empty places.

Do I always start adding from the right side?

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Yes! Always start with the rightmost column (units place) and work left. This follows the same pattern you'll use later with carrying in more complex problems.

How can I check if my answer is correct?

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Try adding the numbers in your head or use the commutative property: 10+32=32+10 10 + 32 = 32 + 10 . You can also subtract: 4210=32 42 - 10 = 32

What's the difference between vertical and horizontal addition?

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Vertical addition helps you see place values clearly and prepares you for harder problems with carrying. Horizontal addition like 10 + 32 works for simple problems but gets messy with larger numbers.

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