Ordering Rational Numbers - Pre Algebra

1. Which is less, $-\frac{2}{3}$ or $-\frac{3}{4}$?

   $-\frac{3}{4}$. As decimals, $-0.75 < -0.\overline{6}$.

2. Which is greatest: $0.3$, $\frac{1}{3}$ or $0.33$?

   $\frac{1}{3}$. It equals $0.333...$, which is greater than $0.33$ and $0.3$.

3. What integer lies between $-3.6$ and $-2.4$?

   $-3$. It is the only integer from $-3.6$ to $-2.4$.

4. Which is least: $-1.2$, $-1.02$ or $-1.22$?

   $-1.22$. It has the greatest absolute value of the three negatives.

5. Which is greater, $-7$ or $-3$?

   $-3$. It lies to the right of $-7$ on the number line.

6. On a horizontal number line, where does the greater of two numbers lie?

   To the right of the smaller number.

7. One town is at $-5$ degrees F and another at $-12$ degrees F. Which is colder?

   The town at $-12$ degrees F, since $-12 < -5$.

8. Order from least to greatest: $0.5$, $-1$, $-\frac{1}{4}$.

   $-1$, $-\frac{1}{4}$, $0.5$. Negatives come first, and $-1$ is farther left than $-0.25$.

9. Which symbol, $<$ or $>$, belongs between $-2.5$ and $-2.05$ (in that order)?

   $<$. Since $2.5 > 2.05$, the negative $-2.5$ is farther left.

10. When comparing two negative numbers, which one is less?

    The one with the greater absolute value. For example, $-9 < -2$ because $-9$ is farther left.

11. Order from greatest to least: $\frac{3}{5}$, $0.65$, $\frac{5}{8}$.

    $0.65$, $\frac{5}{8}$, $\frac{3}{5}$. As decimals: $0.65 > 0.625 > 0.6$.

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