Evaluate the Expression: Solving 66-9 Step by Step

Subtraction Decomposition with Number Breaking

Which expression is equivalent to the given equation?

66−9= 66-9=

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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?

66−9= 66-9=

2

Step-by-step solution

To solve the problem, we need to find an equivalent expression for 66−966 - 9.

  • We start with the original expression 66−966 - 9 and consider simplifying it.
  • Notice that the number 9 can be broken into two smaller numbers: 6 and 3, such that 6+3=96 + 3 = 9.
  • This means we can rewrite the expression 66−966 - 9 as 66−6−366 - 6 - 3.

Now, let's verify:

Perform 66−6=6066 - 6 = 60.
Then perform 60−3=5760 - 3 = 57.

Therefore, the expression 66−6−366 - 6 - 3 simplifies to 57, which is the same as the result of 66−966 - 9.

Hence, the expression 66−6−366 - 6 - 3 is equivalent to 66−966 - 9.

Therefore, the correct choice is 66−6−366 - 6 - 3.

Thus, the solution to the problem is 66−6−366 - 6 - 3.

3

Final Answer

66−6−3 66-6-3

Key Points to Remember

Essential concepts to master this topic
  • Decomposition Rule: Break the subtrahend into smaller, easier parts
  • Technique: Split 9 into 6 + 3, then compute 66 - 6 - 3
  • Check: Verify both expressions equal 57: 66 - 9 = 66 - 6 - 3 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting the decomposed parts
    Don't write 66 - 6 + 3 = 63! This changes the operation and gives the wrong result. When decomposing subtraction, all parts must be subtracted. Always keep the minus sign in front of each decomposed part.

Practice Quiz

Test your knowledge with interactive questions

If we have 85 blocks in total, how many blocks will remain if we remove 4 tens and 1 one?

FAQ

Everything you need to know about this question

Why break 9 into 6 and 3 instead of other numbers?

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You can break 9 into any combination that adds to 9! Like 5+4, 7+2, or 8+1. The key is that all parts must be subtracted to keep the expression equivalent.

Does the order matter when I subtract the parts?

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No, the order doesn't matter for subtraction! 66−6−3 66 - 6 - 3 gives the same result as 66−3−6 66 - 3 - 6 because we're subtracting both numbers.

How do I know if my decomposition is correct?

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Check that your decomposed parts add up to the original number. Since 6 + 3 = 9, then 66−9 66 - 9 equals 66−6−3 66 - 6 - 3 .

Can I use this method with bigger numbers?

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Absolutely! This decomposition strategy works great with larger numbers. For example, 85−17 85 - 17 could become 85−10−7 85 - 10 - 7 to make mental math easier.

What if I make a mistake in my mental math?

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Always double-check by calculating both expressions. Compute 66−9 66 - 9 directly, then compute your decomposed version. If they don't match, recheck your arithmetic!

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