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Chapter 1: Problem 12

Solve. Be sure to check. $$ w=256 \div 16 $$

Short Answer

Expert verified
w = 16

Step by step solution

01

- Understand the Equation

To solve for the variable \( w \), we need to understand the division equation given: \( w = 256 \div 16 \). This means we need to divide 256 by 16.
02

- Perform the Division

Divide 256 by 16. To do this, set up the division: \[ \frac{256}{16} = 16 \].
03

- Write Down the Result

The result of dividing 256 by 16 is 16. Therefore, \( w = 16 \).
04

- Verify the Result

To check the result, multiply 16 by 16 and see if it equals 256. \[ 16 \times 16 = 256 \]. Since this is correct, the solution \( w = 16 \) is verified.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Basic Math Operations
Understanding basic math operations helps in solving more complex problems easily. In this exercise, the primary operation is division.
Division is one of the four fundamental arithmetic operations, alongside addition, subtraction, and multiplication. It is essentially the process of calculating how many times one number is contained within another number.
The equation given is: \[ w = 256 \div 16 \] This means we need to divide 256 by 16. Knowing and mastering division is crucial as it is used in daily tasks like distribution of items or even dividing tasks into smaller manageable parts.
Division Verification
Verifying your result ensures that the solution is correct. After solving any division problem, you should always check your work.
In this exercise, once we have found the value of the variable \( w = 16 \), we should confirm it by performing the reverse operation: multiplication.
The verification process involves multiplying the result back with the divisor to see if you get the original number. Hence, to verify: \16 \times 16 = 256 .\
Since the product is indeed 256, our division was performed correctly, confirming that 16 is the correct answer.
Mathematical Steps
Solving any mathematical problem involves a series of steps that guide you to the solution.
Here are the steps broken down for this particular division problem:
.
  • **Step 1 - Understand the Equation**: The given equation is \( w = 256 \div 16 \). Here, we need to identify that the goal is to divide 256 by 16.

  • **Step 2 - Perform the Division**: Set up the division: \ \frac{256}{16} =16\.

  • **Step 3 - Write Down the Result**: After dividing, the result is 16. Thus, \ w = 16 \.

  • **Step 4 - Verify the Result**: Confirm by reversing the operation: \ 16 \times 16 = 256 \. The verification step ensures that the division is done correctly.
These steps are integral in making sure you understand and solve the equation correctly without errors.

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