Solve the Expression: Finding the Value of 83-6

Subtraction Decomposition with Breaking Apart Numbers

Which expression is equivalent to the given equation?

83−6= 83-6=

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Which expression is equivalent to the given equation?

83−6= 83-6=

2

Step-by-step solution

To solve this problem, we'll convert 83−6 83 - 6 into an equivalent expression.

  • Step 1: Begin by calculating the subtraction 83−6 83 - 6 , which equals 77.
  • Step 2: Since we're looking for an equivalent expression, we should express 6 as a sum of two numbers. Possible pairs include: (3,3) (3,3) , (2,4) (2,4) , (1,5) (1,5) , etc.
  • Step 3: We need an expression that mirrors 77. Among provided choices, one provides 83−3−3 83 - 3 - 3 .
  • Step 4: Check if 83−3−3 83 - 3 - 3 equals 77: Subtract 3 from 83 to get 80, and then subtract another 3 to result in 77.
  • Step 5: This confirms that the original equation 83−6 83 - 6 is indeed equivalent to the expression 83−3−3 83 - 3 - 3 .

Therefore, the expression equivalent to 83−6 83 - 6 is 83−3−3 83 - 3 - 3 .

3

Final Answer

83−3−3 83-3-3

Key Points to Remember

Essential concepts to master this topic
  • Decomposition Rule: Break the subtrahend into parts that equal the original
  • Technique: Express 6 as 3+3, so 83-6 becomes 83-3-3
  • Check: Verify both expressions equal 77: 83-6=77 and 83-3-3=77 ✓

Common Mistakes

Avoid these frequent errors
  • Adding decomposed parts instead of maintaining subtraction
    Don't change 83-6 into 83-3+3 = wrong operation! This changes subtraction to addition and gives 83 instead of 77. Always keep all operations as subtraction when decomposing the subtrahend.

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 can't I just calculate 83-6 directly?

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You absolutely can! This problem is teaching you number decomposition - breaking numbers apart while keeping the same value. This skill helps with mental math and understanding place value.

How do I know which way to break apart the 6?

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Look at the answer choices! The problem gives you options like 3+3, 2+4, or 1+5. Pick the combination that matches one of the given expressions.

Does the order matter when I subtract?

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Yes! Subtraction is not commutative. 83−3−3 83-3-3 works left to right: first 83-3=80, then 80-3=77. The order of operations matters!

Can I use this method with bigger numbers?

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Definitely! Breaking apart numbers makes mental math easier. For example, 156−28 156-28 could become 156−20−8 156-20-8 for easier calculation.

What if none of the choices seem right?

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Double-check your arithmetic! Calculate the original expression and each choice. The correct answer will have the same final result as 83−6=77 83-6=77 .

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