Solve the Addition Equation: 89 + 8 = ?

Addition Decomposition with Number Breaking

89+8= ? 89+8=\text{ ?}

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Step-by-step written solution

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1

Understand the problem

89+8= ? 89+8=\text{ ?}

2

Step-by-step solution

To solve the problem of finding the equivalent expression for 89+8 89 + 8 , we can break down the number 8 into components that simplify the addition process. By breaking it down as 8=1+7 8 = 1 + 7 , we can rephrase the addition:

  • Step 1: Break down the number 8 as 8=1+7 8 = 1 + 7 .
  • Step 2: Add 1 to 89, which gives us 90.
  • Step 3: Then add 7 to 90, yielding 97.

Thus, the breakdown of 89+8 89 + 8 can be written as 89+1+7 89 + 1 + 7 , which is equivalent to the original addition.

Now, examining the answer choices:

  • Choice 1 (33+2+5 33 + 2 + 5 ) does not add to 97, it adds to 40.
  • Choice 2 (89+1+6 89 + 1 + 6 ) results in 96, which is incorrect.
  • Choice 3 (89+2+7 89 + 2 + 7 ) results in 98, which is incorrect.
  • Choice 4 (89+1+7 89 + 1 + 7 ) is the correct breakdown, resulting in 97.

Therefore, the correct choice is Choice 4: 89+1+7 89 + 1 + 7 .

3

Final Answer

89+1+7 89+1+7

Key Points to Remember

Essential concepts to master this topic
  • Decomposition: Break one addend into smaller parts that sum to the same value
  • Technique: Convert 8 = 1 + 7 to make 89 + 8 = 89 + 1 + 7
  • Check: All decompositions must equal original sum: 97 = 97 ✓

Common Mistakes

Avoid these frequent errors
  • Breaking numbers randomly without verifying equivalence
    Don't decompose 8 into any random numbers like 2 + 7 = 9 without checking! This creates expressions that don't equal the original sum and give wrong totals. Always verify your breakdown adds to the same value as the original addend.

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 would I break down 8 into 1 + 7 instead of just adding 89 + 8?

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Breaking down numbers helps you practice mental math strategies! Adding 1 first gives you 90, then adding 7 is easier than adding 8 directly to 89.

How do I know which way to break down the number?

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Look for breakdowns that create friendly numbers like multiples of 10. Since 89 + 1 = 90, breaking 8 as 1 + 7 makes the calculation simpler.

What if I break 8 into different parts like 3 + 5?

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That works too! 89+3+5 89 + 3 + 5 also equals 97. The key is making sure your parts add up to 8 and help with easier mental calculation.

Do all the answer choices add up to 97?

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No! That's the trick. Only 89+1+7 89 + 1 + 7 equals 97. The others give different sums:

  • 33 + 2 + 5 = 40
  • 89 + 1 + 6 = 96
  • 89 + 2 + 7 = 98

Is there a faster way to check my answer?

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Yes! Add up each choice quickly: if it doesn't equal 97 (which is 89 + 8), then it's wrong. This helps you eliminate incorrect options fast.

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