Question

for each of the relationships described below, write an inequality that relates the rational numbers.

1. seven feet below sea level is farther below sea level than 4\\(\frac{1}{2}\\) feet below sea level.
2. sixteen degrees celsius is warmer than zero degrees celsius.
3. three and one - half yards of fabric is less than five and one - half yards of fabric.
4. a loss of $500 in the stock market is worse than a gain of $200 in the stock market.
5. a test score of 64 is worse than a test score of 65, and a test score of 65 is worse than a test score of 67\\(\frac{1}{2}\\).
6. in december, the total snowfall was 13.2 inches, which is more than the total snowfall in october and november, which was 3.7 inches and 6.15 inches, respectively.

Explanation:

Step1: Problem 1

Seven feet below sea level is -7, \(4\frac{1}{2}\) feet below sea level is \(-4\frac{1}{2}\). Farther below means more negative, so \(-7 < -4\frac{1}{2}\).

Step2: Problem 2

Warmer means higher temperature, so \(16 > 0\) (in °C).

Step3: Problem 3

Three and a half is \(3\frac{1}{2}\), five and a half is \(5\frac{1}{2}\). Less than means \(3\frac{1}{2} < 5\frac{1}{2}\).

Step4: Problem 4

Loss of $500 is -500, gain of $200 is +200. Worse loss means more negative, so \(-500 < 200\).

Step5: Problem 5

Worse score means lower, so \(64 < 65\) and \(65 < 67\frac{1}{2}\).

Step6: Problem 6

Total snowfall in Oct and Nov: \(3.7 + 6.15 = 9.85\). December is 13.2, more than means \(13.2 > 9.85\).

Answer:

1. \(\boldsymbol{-7 < -4\frac{1}{2}}\)
2. \(\boldsymbol{16 > 0}\) (°C)
3. \(\boldsymbol{3\frac{1}{2} < 5\frac{1}{2}}\)
4. \(\boldsymbol{-500 < 200}\)
5. \(\boldsymbol{64 < 65}\) and \(\boldsymbol{65 < 67\frac{1}{2}}\)
6. \(\boldsymbol{13.2 > 3.7 + 6.15}\) (simplifies to \(\boldsymbol{13.2 > 9.85}\))