7. Timfoler used tis calectatior to work ont the value of $$ 3,12 imes 4,36 $$ Fies ivrote down thee aniswer as il6,03d Wil What kimpla check could lumelo hove used, whithout ursing calcidater, to shievo that his ariswer is incorrect?

Question

7. Timfoler used tis calectatior to work ont the value of $$ 3,12 	imes 4,36 $$ Fies ivrote down thee aniswer as il6,03d Wil What kimpla check could lumelo hove used, whithout ursing calcidater, to shievo that his ariswer is incorrect?

UpStudy AI · Accepted Answer

Timfoler's teammate, Lumelo, wanted to verify whether the calculated product of $$ 3.12 \times 4.36 = 16.03 $$ was correct without using a calculator. A simple and effective method for checking the reasonableness of the answer is **estimation through rounding**. Here's how Lumelo could have approached it:

1. **Round Each Number to Simpler Values:**
   - **3.12** can be rounded to **3**.
   - **4.36** can be rounded to **4**.

2. **Multiply the Rounded Numbers:**
   $$
   3 \times 4 = 12
   $$

3. **Compare the Estimated Product to the Calculated Answer:**
   - The estimated product is **12**.
   - Timfoler's answer is **16.03**.

4. **Analyze the Reasonableness:**
   - The exact product of $$ 3.12 \times 4.36 $$ should be somewhat larger than **12** but not excessively so.
   - $$ 3.12 $$ is slightly more than **3**, and $$ 4.36 $$ is slightly more than **4**, so the product should be a bit more than **12** but likely closer to **13 or 14** rather than **16**.

5. **Conclusion:**
   - Since **16.03** is significantly higher than the estimated **12**, Lumelo could reasonably conclude that there might be an error in the calculation.

**Additional Estimation for Clarity:**

For a more refined estimate, Lumelo could use:

- **3.12 ≈ 3.1**
- **4.36 ≈ 4.4**

Then multiply:
$$
3.1 \times 4.4 = (3 \times 4) + (3 \times 0.4) + (0.1 \times 4) + (0.1 \times 0.4) = 12 + 1.2 + 0.4 + 0.04 = 13.64
$$

This refined estimate suggests that the actual product should be around **13.64**, making **16.03** seem too high and indicating a possible miscalculation.

**Key Takeaway:** **Rounding and estimating can quickly help verify the plausibility of a calculated answer without the need for precise computation tools.**
Lumelo could have rounded the numbers to simpler values, multiplied them, and compared the result to Timfoler's answer to check if it makes sense.

7. Timfoler used tis calectatior to work ont the value of \( 3,12 \times 4,36 \) Fies ivrote down thee aniswer as il6,03d Wil What kimpla check could lumelo hove used, whithout ursing calcidater, to shievo that his ariswer is incorrect?

Real Tutor Solution

Answer

Solution

Extra Insights

Related Questions

Latest Arithmetic Questions