Solve the Expression: Finding the Value of 43-4

Subtraction Decomposition with Number Breaking

Which expression is equivalent to the given equation?

43−4= 43-4=

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Step-by-step written solution

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1

Understand the problem

Which expression is equivalent to the given equation?

43−4= 43-4=

2

Step-by-step solution

To solve this problem, we need to determine which expression is equivalent to 43−4 43 - 4 .

The expression 43−4 43 - 4 can be broken down as follows:

  • We know that 4=3+1 4 = 3 + 1 , so we can rewrite the expression as 43−(3+1) 43 - (3 + 1) .
  • This expression simplifies by subtracting in stages: first subtract 3 3 , then subtract 1 1 .
  • Therefore, 43−4 43 - 4 is equivalent to 43−3−1 43 - 3 - 1 .

Among the provided choices, option 4, 43−3−1 43 - 3 - 1 , is equivalent to 43−4 43 - 4 .

Thus, the solution to the problem is 43−3−1 43 - 3 - 1 .

3

Final Answer

43−3−1 43-3-1

Key Points to Remember

Essential concepts to master this topic
  • Decomposition Rule: Break the subtracted number into smaller additive parts
  • Technique: Since 4 = 3 + 1, write 43−4=43−3−1 43 - 4 = 43 - 3 - 1
  • Verification: Calculate both ways: 43−4=39 43 - 4 = 39 and 43−3−1=39 43 - 3 - 1 = 39 ✓

Common Mistakes

Avoid these frequent errors
  • Adding parts instead of keeping subtraction throughout
    Don't write 43 - 3 + 1 when breaking down 43 - 4! This changes subtraction to addition and gives 43 instead of 39. Always keep the subtraction operation: 43 - 3 - 1.

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 down 4 into 3 + 1 instead of other combinations like 2 + 2?

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You can use any combination that adds to 4! The key is that 43−4 43 - 4 equals 43−2−2 43 - 2 - 2 or 43−1−3 43 - 1 - 3 . All are mathematically correct.

Does the order matter when I subtract the parts?

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No, order doesn't matter! Since 43−3−1=43−1−3 43 - 3 - 1 = 43 - 1 - 3 , you can subtract the parts in any sequence and get the same result.

How do I know which answer choice matches my decomposition?

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Look for the expression that breaks down your subtrahend correctly. Since we need 4=3+1 4 = 3 + 1 , find the choice with 43 - 3 - 1.

What if none of the choices seem to work?

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Double-check your decomposition! Make sure the parts you're subtracting add up to the original number being subtracted. For example, 3 + 1 = 4 ✓

Is this method useful for larger numbers too?

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Absolutely! Breaking down subtraction is especially helpful with larger numbers. For example, 156−23 156 - 23 could become 156−20−3 156 - 20 - 3 for easier mental math.

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