Solve Addition Pattern: From 40+40=80 to 41+41

Addition Patterns with Number Relationships

40+40=80 40+40=80

Use the above equation to help solve the following problem:

41+41=? 41+41=\text{?}

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

40+40=80 40+40=80

Use the above equation to help solve the following problem:

41+41=? 41+41=\text{?}

2

Step-by-step solution

To solve 41+4141 + 41, notice that it can be related to 40+40=8040 + 40 = 80 by adding one to each of the constituent numbers 4040. This can be expressed as:

41+41=(40+1)+(40+1)41 + 41 = (40 + 1) + (40 + 1).

Breaking it down, we have:

  • 40+40=8040 + 40 = 80
  • Add 1+11 + 1 to this result, which is 22.

Thus, the total becomes:

80+2=8280 + 2 = 82.

Therefore, the sum of 41+4141 + 41 is 82\textbf{82}.

3

Final Answer

82 82

Key Points to Remember

Essential concepts to master this topic
  • Pattern Recognition: Use known sums to find related calculations efficiently
  • Technique: Break down 41+41 as (40+1)+(40+1) = 80+2
  • Check: Verify 41+41=82 by counting up from 80+2=82 ✓

Common Mistakes

Avoid these frequent errors
  • Adding only one extra unit instead of two
    Don't think 41+41 = 80+1 = 81! Since both numbers increased by 1, you need to add 2 total (1+1). Always count how many extra units you're adding from both numbers.

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

Why can't I just add 1 to get 81?

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Because both numbers changed from 40 to 41! When you have 41+41 41+41 , you're adding two numbers that each increased by 1, so you need to add 1+1=2 1+1=2 to the original sum.

How do I know this pattern works for other numbers?

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This decomposition method works for any addition! Break each number into parts: (a+b)+(c+d)=(a+c)+(b+d) (a+b)+(c+d) = (a+c)+(b+d) . Try it with 42+42=(40+2)+(40+2)=80+4=84 42+42 = (40+2)+(40+2) = 80+4 = 84 !

Is there a faster way to solve this?

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Yes! Once you understand the pattern, you can think: "Each number went up by 1, so the sum goes up by 2." So 80+2=82 80+2=82 directly!

What if the numbers were different, like 40+42?

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Great question! You'd still use the same approach: 40+42=40+(40+2)=80+2=82 40+42 = 40+(40+2) = 80+2 = 82 . Break the harder number into known parts plus extras.

How can I check my answer without using the pattern?

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You can always add directly: 41+41 41+41 by counting or using column addition. Both methods should give you 82 - if they don't match, recheck your work!

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