Problem 519 - Prealgebra

Question

Subtract and then check by adding. $$10,000-15$$

Step-by-Step Solution

Answer

9,985

Step 1: Subtract the Numbers

Subtract 15 from 10,000 to find the difference.\[ 10,000 - 15 = 9,985 \]

Step 2: Check by Adding

Add the difference (9,985) and the subtracted number (15) to ensure it equals the original number (10,000).\[ 9,985 + 15 = 10,000 \]

Key Concepts

subtraction

Subtraction is one of the fundamental arithmetic operations. It represents the process of removing objects from a collection. In simpler terms, it answers the question 'how many are left?'

In our exercise, we subtract 15 from 10,000. To do this, we line up the numbers by their place values and start subtracting from the rightmost digit (the ones). If a digit in the minuend (the number you are subtracting from) is smaller than the corresponding digit in the subtrahend (the number you are subtracting), you need to borrow from the next left digit. But in this exercise, there's no need for borrowing.

After performing the subtraction, we find that: \[ 10,000 - 15 = 9,985 \]

addition

Addition is the mathematical process of combining two numbers to get a total or sum. In our exercise, addition serves as a verification method to check if our subtraction was correct. We do this by adding the subtracted amount back to the difference we obtained from the subtraction.

By adding 9,985 (the result from the subtraction) to 15 (the number we initially subtracted), we should get back the original number, 10,000. Performing the addition: \[ 9,985 + 15 = 10,000 \] This confirms that our subtraction was done correctly.

Understanding addition is crucial because it plays a significant role in daily life, from calculating expenses to measuring quantities in recipes.

arithmetic verification

Arithmetic verification helps check the accuracy of basic operations like addition and subtraction. It's an essential step to ensure that the calculations are correct, which is especially important in more complex problem-solving situations.

In our exercise, we use addition to verify the result of subtraction. By reversing the subtraction process through addition, we can confirm that our answer is accurate. If the numbers don't match, it indicates an error in the calculation.

Verification acts as a safeguard against mistakes and builds confidence in solving math problems. It's like double-checking your work to ensure accuracy.

In summary:

• Always double-check your results
• Use the inverse operation (addition to check subtraction) for verification
• Verification enhances understanding and accuracy in math