Solve the Addition Problem: 67 + 5

Addition Decomposition with Strategic Regrouping

67+5= ? 67+5=\text{ ?}

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Step-by-step written solution

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1

Understand the problem

67+5= ? 67+5=\text{ ?}

2

Step-by-step solution

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

  • Step 1: Break down the number 5 into smaller components to simplify the addition. One convenient way is to write 5=3+2 5 = 3 + 2 .
  • Step 2: Add these components sequentially to 67. Start with 67+3 67 + 3 and then add the remaining 2:

Breaking down the addition as described:

1. 67+3=70 67 + 3 = 70

2. 70+2=72 70 + 2 = 72

Thus, calculating step by step confirms:

67+5=67+3+2=72 67 + 5 = 67 + 3 + 2 = 72

Therefore, the expression equivalent to 67+5 67 + 5 as broken into two components is 67+3+2 67 + 3 + 2 .

Analyzing the available choices, the correct equivalent is given by choice 3: 67+3+2 67 + 3 + 2 .

3

Final Answer

67+3+2 67+3+2

Key Points to Remember

Essential concepts to master this topic
  • Decomposition: Break numbers into parts that make addition easier
  • Technique: Use 5=3+2 5 = 3 + 2 to reach friendly number 70
  • Check: Verify 67+3+2=70+2=72 67 + 3 + 2 = 70 + 2 = 72

Common Mistakes

Avoid these frequent errors
  • Adding without strategic decomposition
    Don't just add 67 + 5 = 72 without showing the decomposition! This misses the point of breaking numbers strategically. Always decompose the second number to make mental math easier and reach friendly benchmark 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 break 5 into 3 + 2 instead of other combinations?

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Breaking 5 into 3 + 2 is strategic because adding 3 to 67 gives us 70, which is a friendly number! Then adding 2 more is super easy. Other combinations like 4 + 1 don't create this helpful stepping stone.

What makes 70 a 'friendly number'?

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Numbers ending in 0 are friendly numbers because they're easy to work with mentally. When you reach 70, adding 2 more becomes simple: 70+2=72 70 + 2 = 72 .

Can I use this strategy with bigger numbers?

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Absolutely! For example, with 78+7 78 + 7 , you could break 7 into 2 + 5 to get 78+2+5=80+5=85 78 + 2 + 5 = 80 + 5 = 85 . Always look for ways to reach friendly numbers!

How do I choose which number to decompose?

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Usually decompose the smaller number (like the 5 in this problem). Look at the larger number and think: 'What do I need to add to reach the next friendly number?' That guides your decomposition.

What if there are multiple correct decompositions?

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Sometimes there are! For 67+5 67 + 5 , you could also use 67+1+4=68+4=72 67 + 1 + 4 = 68 + 4 = 72 . Choose the decomposition that feels easiest for you to calculate mentally.

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