3.1: Which One Doesn’t Belong: Inequalities
Which inequality doesn’t belong?
$\frac{5}{4} < 2$
$8.5 > 0.95$
$8.5 < 7$
$10.00 < 100$
Let’s compare numbers on the number line.
Which inequality doesn’t belong?
$\frac{5}{4} < 2$
$8.5 > 0.95$
$8.5 < 7$
$10.00 < 100$
Here are the low temperatures, in degrees Celsius, for a week in Anchorage, Alaska.
day | Mon | Tues | Weds | Thurs | Fri | Sat | Sun |
---|---|---|---|---|---|---|---|
temperature | 5 | -1 | -5.5 | -2 | 3 | 4 | 0 |
The lowest temperature ever recorded in the United States was -62 degrees Celsius, in Prospect Creek Camp, Alaska. The average temperature on Mars is about -55 degrees Celsius.
On a winter day the low temperature in Anchorage, Alaska was -21 degrees Celsius and the low temperature in Minneapolis, Minnesota was -14 degrees Celsius.
Jada said: “I know that 14 is less than 21, so -14 is also less than -21. This means that it was colder in Minneapolis than in Anchorage.”
Do you agree? Explain your reasoning.
Another temperature scale frequently used in science is the Kelvin scale. In this scale, 0 is the lowest possible temperature of anything in the universe, and it is -273.15 in the Celsius scale. Each $1^\circ\text{K}$ is the same as $1^\circ\text{C}$, so $10^\circ\text{K}$ is the same as $\text-263.15^\circ\text{C}$.
Decide whether each inequality statement is true or false. Be prepared to explain your reasoning.
$\text-2 < 4$
$\text-2 < \text-7$
$4 > \text-7$
$\text-7 > 10$
Drag each point to its proper place on the number line. Use your observations to help answer the questions that follow.
Andre says that $\frac14$ is less than $\text{-}\frac {3}{4}$ because, of the two numbers, $\frac14$ is closer to 0. Do you agree? Explain your reasoning.
Which number is greater: $\frac14$ or $\frac54$?
Which number is farther from 0: $\frac14$ or $\frac54$?
Which number is greater: $\text{-}\frac {3}{4}$ or $\frac58$?
Which number is farther from 0: $\text{-}\frac {3}{4}$ or $\frac58$?
Is the number that is farther from 0 always the greater number? Explain your reasoning.
We use the words greater than and less than to compare numbers on the number line. For example, the numbers -2.7, 0.8, and -1.3, are shown on the number line.
Because -2.7 is to the left of -1.3, we say that -2.7 is less than -1.3. We write: $$\text-2.7 <\text -1.3$$ In general, any number that is to the left of a number $n$ is less than $n$.
We can see that -1.3 is greater than -2.7 because -1.3 is to the right of -2.7. We write $$\text-1.3 >\text -2.7$$ In general, any number that is to the right of a number $n$ is greater than $n$
We can also see that $0.8 > \text-1.3$ and $0.8 > \text-2.7$. In general, any positive number is greater than any negative number.
The sign of a nonzero number is either positive or negative.