Calculate the Sum: Solving 52 + 9 Step by Step

Addition Decomposition with Breaking Numbers

52+9= ? 52+9=\text{ ?}

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Step-by-step written solution

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1

Understand the problem

52+9= ? 52+9=\text{ ?}

2

Step-by-step solution

To find the sum of 52 and 9, we'll perform simple addition:

  • Step 1: Consider the expression 52+952 + 9.

  • Step 2: Break down the number 9 into simpler parts. One natural way is 9=8+19 = 8 + 1.

  • Step 3: Now express the addition as 52+9=52+(8+1)52 + 9 = 52 + (8 + 1).

  • Step 4: Compute the sum: First add 52+8=6052 + 8 = 60, and then 60+1=6160 + 1 = 61.

  • Step 5: The expression matching 52+952 + 9 is 52+8+152 + 8 + 1.

Now, looking at the available choices, the choice that matches 52+952 + 9 is Choice 4: 52+8+1 \text{Choice 4: } 52 + 8 + 1

Therefore, the correct representation of the expression 52+952 + 9 is Choice 4: 52+8+1 \text{Choice 4: }52 + 8 + 1

3

Final Answer

52+8+1 52+8+1

Key Points to Remember

Essential concepts to master this topic
  • Rule: Break numbers into parts that make calculation easier
  • Technique: Decompose 9 as 8 + 1: 52 + 8 = 60, then 60 + 1 = 61
  • Check: Verify the decomposition equals original: 52 + 8 + 1 = 52 + 9 ✓

Common Mistakes

Avoid these frequent errors
  • Adding numbers in the wrong decomposition order
    Don't randomly break numbers without checking equivalence = wrong representation! Breaking 52 + 9 as 33 + 8 + 2 changes the original sum completely. Always ensure your decomposed parts add up to the original 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 9 into 8 + 1 instead of other combinations?

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Breaking 9 as 8 + 1 is strategic! Adding 8 to 52 gives us a nice round number (60), making the final step easier. You could use 7 + 2 or 6 + 3, but 8 + 1 creates the simplest path.

Do all the answer choices equal 61?

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No! Only 52 + 8 + 1 equals 61. The other choices like 33 + 8 + 2 = 43 give completely different sums. The question asks which expression represents 52 + 9, not which equals 61.

Can I break 52 instead of 9?

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Yes! You could write 52 + 9 as (50 + 2) + 9 or other combinations. However, the answer choices specifically show 52 staying together, so focus on decomposing the 9.

How do I know which decomposition is correct?

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Check that your broken parts add up to the original number. For 9: does 8 + 1 = 9? ✓ Does 6 + 3 = 9? ✓ But we need the one that matches 52 + 9 exactly!

Is this the same as the associative property?

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Very close! This uses the associative property: 52 + 9 = 52 + (8 + 1) = (52 + 8) + 1. We're regrouping the addition to make calculation easier.

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