Part A Use mental math to solve the problem 8.02−5.98 . Question 2 Part B Explain the method of mental math that you used to find the answer. Be specific with each step you took.

Answer 1

Part A

To solve \( 8.02 - 5.98 \) using mental math, you can simplify the numbers for easier calculation.

1. Estimate the Numbers: Round \( 8.02 \) to \( 8.00 \) and \( 5.98 \) to \( 6.00 \).
2. Subtract the Rounded Values: Now, compute \( 8.00 - 6.00 = 2.00 \).
3. Adjust for the Small Difference: Since I rounded \( 5.98 \) up to \( 6.00 \) and \( 8.02 \) down to \( 8.00 \), I need to adjust the result slightly. The original numbers are \( 8.02 \) and \( 5.98 \), which means I rounded \( 5.98 \) too high by \( 0.02 \) (since \( 6.00 - 5.98 = 0.02 \)).
4. Adjust the Result: Therefore, I need to subtract \( 0.02 \) from \( 2.00\), giving me \( 2.00 - 0.02 = 1.98 \).

The final answer is \( 1.98 \).

Part B

The method of mental math I used can be broken down into specific steps:

1. Rounding: I rounded both numbers to the nearest whole number for simplicity, which makes subtraction easier.

   • \( 8.02 \) became \( 8.00 \)
   • \( 5.98 \) became \( 6.00 \)

2. Performing the Basic Operation: I subtracted the rounded values:

   • \( 8.00 - 6.00 = 2.00 \)

3. Recognizing the Adjustment: I acknowledged that by rounding \( 5.98 \) to \( 6.00 \), I added \( 0.02 \) more than needed. Therefore, I had to account for that adjustment when I arrived at my initial answer.

4. Final Adjustment: I adjusted by subtracting the excess \( 0.02 \) from my estimated result:

   • \( 2.00 - 0.02 = 1.98 \)

Using these steps, I was able to accurately and efficiently arrive at the correct answer, \( 1.98 \). This method demonstrates how rounding can simplify mental calculations while being mindful of adjustments to maintain accuracy.