Solve the Expression: Finding the Equivalent to 91 - 7

Expression Decomposition with Multi-Step Subtraction

Which expression is equivalent to the given equation?

917= 91-7=

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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?

917= 91-7=

2

Step-by-step solution

To solve this problem, we need to find an expression that is equivalent to 917 91 - 7 . Let's work through it step by step.

First, let's compute 917 91 - 7 :

917=84 91 - 7 = 84

Next, we need to find which of the given choices results in 84 84 . The simplest way to do this is to break down the subtraction 917 91 - 7 into two steps, reducing from 91 91 in stages, and match these to the choices:

We can express 7 7 as the sum of two smaller numbers, such as 1+6 1 + 6 . This breakdown results in:

917=91(1+6) 91 - 7 = 91 - (1 + 6)

This can then be rewritten as two separate subtractions:

9116 91 - 1 - 6

Now, compare this with the provided choices:

  • Choice 1: 9116 91 - 1 - 6 , which equals 84 84 .
  • Choice 2: 9132 91 - 3 - 2 , which equals 86 86 .
  • Choice 3: 9124 91 - 2 - 4 , which equals 85 85 .
  • Choice 4: 9115 91 - 1 - 5 , which equals 85 85 .

The expression 9116 91 - 1 - 6 is equivalent to 917 91 - 7 because both evaluations result in 84 84 .

Therefore, the correct answer is 9116 91 - 1 - 6 .

3

Final Answer

9116 91-1-6

Key Points to Remember

Essential concepts to master this topic
  • Equivalence Rule: Expressions with the same result are equivalent
  • Decomposition Technique: Break 7 into 1 + 6, so 91 - 7 = 91 - 1 - 6
  • Verification Check: Calculate each option to confirm only one equals 84 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of checking equivalence
    Don't just look for numbers that add up to 7 without calculating! This leads to choosing wrong expressions that don't equal 84. Always calculate the final result of each expression to verify equivalence.

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 pick any two numbers that add up to 7?

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Great question! While 1+6=7 1 + 6 = 7 , 3+2=5 3 + 2 = 5 , not 7. You must check that the sum of the numbers being subtracted equals the original number being subtracted.

How do I know which breakdown of 7 to use?

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Look at the answer choices! The correct breakdown will match one of the options. For example, since 7=1+6 7 = 1 + 6 , we get 9116 91 - 1 - 6 .

Do I need to calculate every answer choice?

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Yes, it's the safest approach! Calculate each option to see which one equals 84. This prevents mistakes and builds confidence in your answer.

What if multiple expressions seem correct?

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Only one expression will equal exactly 84. If you think multiple answers work, double-check your arithmetic - you likely made a calculation error.

Is there a faster way than calculating everything?

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Once you understand that 917=84 91 - 7 = 84 , you can look for expressions where the numbers being subtracted add up to exactly 7: 1 + 6 = 7, so 9116 91 - 1 - 6 works!

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