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

Add fifty units to the number 31.

What is the resulting number?

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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