Solve Vertical Addition: 48 + 52 Step-by-Step

Vertical Addition with Carryover

48+52776 \begin{aligned} &48 \\ +& \\ &52 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this problem together.
00:07 Combine two digits at a time.
00:10 Start by adding the ones digits.
00:13 Write the result down, carry one over.
00:17 Now, add the tens digits. Don't forget to add the one you carried.
00:23 Write the tens in place, carry one more to the hundreds.
00:27 Fill any missing digits with zero.
00:31 Finally, add the hundreds digits and put the result in place.
00:35 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

48+52776 \begin{aligned} &48 \\ +& \\ &52 \\ &\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 by their place value.
  • Step 2: Add the digits in the units column.
  • Step 3: Manage any carryover if necessary.
  • Step 4: Add the digits in the tens column along with any carryover.

Now, let's work through each step:

Step 1: Align the numbers.

48
+52
___

Step 2: Add the digits in the units column:
8 (from 48) + 2 (from 52) = 10.
This gives us 0 in the units place and we carry over 1 to the tens place.

Step 3: Add the digits in the tens column, including the carried over 1:

4 (from 48) + 5 (from 52) + 1 (carryover) = 10.

Thus, the digit 0 goes to the tens place, and 1 will be placed in the hundreds place.

Therefore, the full solution looks like this:

48
+52
___
100

Therefore, the solution to the problem is 100100.

3

Final Answer

100

Key Points to Remember

Essential concepts to master this topic
  • Place Value: Always align digits by tens and units columns
  • Technique: Add units first: 8 + 2 = 10, write 0 carry 1
  • Check: Verify by adding horizontally: 48 + 52 = 100 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when digits sum to 10 or more
    Don't write 10 in the units place = wrong answer like 1010! When units add to 10 or more, you must write only the units digit and carry the tens digit to the next column. Always carry over properly to get the correct sum.

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 it mean to 'carry over' in addition?

+

When two digits add up to 10 or more, you write down the units digit and 'carry' the tens digit to the next column. For example, 8 + 2 = 10, so write 0 and carry the 1 to the tens place.

Why do I need to align the numbers vertically?

+

Place value alignment is crucial! The units digits must line up under units, and tens digits under tens. This ensures you're adding the correct place values together.

What if I get confused about which column to add first?

+

Always start with the rightmost column (units place) and work your way left. This is because any carryover from the units affects the tens column, and so on.

How can I double-check my vertical addition?

+

Try adding the numbers horizontally: 48 + 52. You can also break it down: 40 + 50 = 90 and 8 + 2 = 10, so 90 + 10 = 100.

What happens when both columns need carryover?

+

Handle each column one at a time, from right to left. Each carryover only affects the next column to the left, so take your time and work systematically.

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