Problem 48 - Fundamentals of Mathematics

Question

Combine the numbers as indicated. $$892-820-9$$

Step-by-Step Solution

Answer

The result of the operation is 63.

Step 1: Evaluate the First Operation

Begin by solving the first part of the expression: \(892 - 820\). To do this, subtract 820 from 892.\[892 - 820 = 72\]

Step 2: Process the Remaining Operation

Now, take the result from Step 1 and subtract 9 from it. \[72 - 9 = 63\]

Step 3: Combine and Verify

To ensure accuracy, confirm that the operations were combined correctly. The full expression is: \[892 - 820 - 9 = 63\]The calculations in the previous steps confirm that this is correct.

Key Concepts

Subtraction

Subtraction is one of the basic arithmetic operations, where you remove a certain quantity from another. It's like counting backwards on a number line. In this exercise, the subtraction expression involves multiple numbers: starting with 892 and subtracting 820, then subtracting another 9. It involves 'borrowing' or 'regrouping' when you don't have enough value to subtract from the given digit, but that's more of an issue when you subtract individual digits manually. When using subtraction, the key is to align numbers properly, especially with larger numbers.

• The first number (minuend) is what you have.
• The second number (subtrahend) is what you're taking away.
• The result is called the difference.

In this problem, we broke it down step by step, dealing with 892 minus 820 first, then working with that result. This makes it easier to manage, especially with larger numbers or multiple subtractive steps.

Step-by-Step Solutions

Step-by-step solutions are invaluable for grasping complex mathematical concepts like subtraction. They allow you to break down a problem into small, manageable pieces. In the provided example, we started by subtracting the first two numbers: 892 and 820. This simplified the task to focus only on these numbers, making it less intimidating and easier to follow. **Detailed Breakdown:**

• **Step 1:** Start with the first pair of numbers: 892 and 820. Subtracting these gives a simpler interim calculation result, which is 72 in this case.


• **Step 2:** Take the result from Step 1 and subtract the next number in the sequence, which is 9, to obtain the final result of 63.

By dividing the exercise into defined parts, the solution process becomes clear and manageable. This method encourages active engagement and continuous checking at each step to verify correctness.

Verification of Results

Verification of results is crucial in mathematics to ensure the accuracy of calculated answers. It's like double-checking your work. In subtraction, this might involve adding the difference back to the subtractive number to see if you arrive at the original number. In our problem, confirming the final result involves ensuring each operation was accurate: **Validation Processes:**

• Revisit each step: Make sure the subtraction in Step 1 and Step 2 were performed correctly. In this example, verify that 892 minus 820 equals 72 and 72 minus 9 equals 63.


• If you reverse the operation, adding 9 back to 63 should retrieve the interim result 72; adding 820 to this should give you back the original 892.

By understanding how to verify answers, not only do you arrive at correctness, but you also develop confidence in your arithmetic skills, ensuring that your solution can be depended upon in a test or real-world scenario.