Checking Reasonableness - Pre Algebra

1. How do you check a solution to an equation?

   Substitute it into the original equation. The solution is correct only if both sides come out equal.

2. A student finds that $0.5\%$ of 200 is 100. What is the correct value?

   1. Since $0.5\% = 0.005$, the answer is $0.005 \times 200 = 1$; 100 would be $50\%$ of 200.

3. When a positive number is divided by a number between 0 and 1, how does the quotient compare to the original number?

   The quotient is greater than the original number. For example, $6 \div 0.5 = 12$.

4. Using a compatible number, what is a good estimate of $\frac{2}{5}$ of 598?

   About 240, since 598 is close to 600 and $\frac{2}{5}$ of 600 is 240.

5. How does estimation help check a calculated answer?

   Rounding the numbers gives a quick approximate answer. A result far from the estimate signals an error.

6. A student calculates a person's height as 170 meters. Which unit would make 170 a reasonable height?

   Centimeters. 170 cm is about 1.7 m, a typical adult height.

7. A student says $\sqrt{48} \approx 6.93$. Between which two whole numbers must $\sqrt{48}$ lie?

   6 and 7, because $36 < 48 < 49$. So 6.93 is reasonable.

8. Which addition checks the subtraction $82 - 47 = 35$?

   $35 + 47 = 82$. Adding the difference back to the number subtracted should give the starting number.

9. What value do both sides of $3x - 7 = 2x + 11$ equal when $x = 18$ is substituted?

   47 on each side, since $54 - 7 = 47$ and $36 + 11 = 47$. Equal sides confirm the solution.

10. A student says the mean of 72, 85 and 90 is 95. Why must this be wrong?

    A mean must lie between the least and greatest values, and 95 is greater than 90. The mean is actually 82.33.

11. When a positive number is multiplied by a number between 0 and 1, how does the product compare to the original number?

    The product is less than the original number. For example, $8 \times 0.25 = 2$.

12. A student computes $19.8 \times 5.1 = 1009.8$. What estimate shows the decimal point is misplaced?

    $20 \times 5 = 100$, so the product must be near 100. The correct product is 100.98.

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