Solve for the Missing Number: 82 minus ? equals 7

Inverse Subtraction with Substitution Methods

If

=7 \colorbox{yellow}\\=7

Solve the following subtraction problem:

82= 82- \colorbox{yellow}\\=

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

If

=7 \colorbox{yellow}\\=7

Solve the following subtraction problem:

82= 82- \colorbox{yellow}\\=

2

Step-by-step solution

To solve this problem, we'll use the substitution method for the subtraction equation provided:

  • Step 1: Identify the value represented by the symbol. We are given that the yellow box equals 7.
  • Step 2: Substitute the value 7 into the subtraction problem: 82782 - 7.
  • Step 3: Perform the subtraction operation: 827=75 82 - 7 = 75

Therefore, the solution to the problem is 75 75 .

3

Final Answer

75 75

Key Points to Remember

Essential concepts to master this topic
  • Rule: Use substitution to replace symbols with known values
  • Technique: Convert 82 - ? = 7 to 82 - 7 = 75
  • Check: Verify by substituting: 82 - 75 = 7 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the position of the unknown value
    Don't think 82 - 7 = 82 when the yellow box equals 7! This ignores the subtraction operation completely. Always substitute the known value (7) into the correct position and perform the calculation: 82 - 7 = 75.

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 do I substitute 7 for the yellow box in the subtraction problem?

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The yellow box is a symbol representing the same value in both equations. Since the first equation tells us the yellow box equals 7, we use that same value everywhere the symbol appears.

How do I know which number to subtract from which?

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Look at the order in the equation! In 82yellow box 82 - \text{yellow box} , you subtract the yellow box value (7) from 82, giving you 82 - 7 = 75.

What if I got 89 by adding instead of subtracting?

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This happens when you ignore the subtraction sign! Always pay attention to the operation symbol. The problem shows subtraction (-), not addition (+).

Can I check my answer a different way?

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Yes! You can work backwards: 75 + 7 = 82. If your answer plus 7 equals the original number (82), then you solved it correctly.

Why isn't the answer 70 or 80?

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These come from estimation errors. 70 would mean 82 - 12 = 70, and 80 would mean 82 - 2 = 80. Neither gives us the required result of 7 when we check our work.

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