Solve Addition Problem: Finding the Sum of 19 + 41

Two-Digit Addition with Regrouping

19+41= 19+41=

Solve the addition problem:

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

19+41= 19+41=

Solve the addition problem:

2

Step-by-step solution

To solve the addition problem 19+41 19 + 41 , let's perform the following steps:

  • Step 1: Align the numbers according to place value, so we have:

19+41\begin{array}{c c} & 19 \\ + & 41 \\ \hline \end{array}

  • Step 2: Add the units digits (9 and 1). 9+1=109 + 1 = 10. This result implies a 0 in the units place and a carry-over of 1 to the tens column.
  • Step 3: Add the tens digits plus any carry-over. We have 1+4+1(carry)=61 + 4 + 1 (carry) = 6.

Thus, combining these we get: 19+4160\begin{array}{c c} & 19 \\ + & 41 \\ \hline & 60 \\ \end{array}

Therefore, the sum of 19+41 19 + 41 is 60 \textbf{60} .

3

Final Answer

60 60

Key Points to Remember

Essential concepts to master this topic
  • Place Value: Always align digits by ones and tens columns
  • Technique: Add ones first: 9 + 1 = 10, write 0 and carry 1
  • Check: Verify by adding in reverse: 41 + 19 = 60 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when sum exceeds 9
    Don't just write 10 in the ones place = impossible digit placement! When ones sum to 10 or more, you must write the ones digit and carry the ten to the next column. Always remember to add the carried digit to the tens column.

Practice Quiz

Test your knowledge with interactive questions

If we have 67 blocks in total, how many blocks will remain if we remove 5 tens and 4 ones?

FAQ

Everything you need to know about this question

What does 'carry over' mean in addition?

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When adding digits gives you 10 or more, you write the ones digit and carry the tens digit to the next column. For example: 9 + 1 = 10, so write 0 and carry the 1 to the tens place!

Why can't I just write 10 in the ones place?

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Each place can only hold one single digit (0-9). When you get 10, that's really 1 ten and 0 ones, so the 1 belongs in the tens column!

How do I know when I need to regroup?

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You need to regroup whenever adding any column gives 10 or more. In 19 + 41, since 9 + 1 = 10, you must regroup by carrying the 1 to the tens place.

What if I forget to add the carried number?

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You'll get the wrong answer! In this problem, forgetting the carried 1 would give you 50 instead of 60. Always remember: tens digit + tens digit + any carried amount.

Is there an easier way to add 19 + 41?

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You could think: 19 is close to 20, so 20 + 41 = 61, then subtract 1 to get 60. But learning the standard algorithm helps with bigger numbers!

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