Printable math worksheet for 7th graders focusing on comparing pairs of rational numbers to determine which is greater.

To solve the problem of comparing rational numbers, we need to determine which number in each pair is greater. Rational numbers can be positive or negative, and their comparison involves understanding their relative positions on the number line. Here's how we can approach each pair:

Step-by-Step Solution:

#### 1. $-\frac{3}{8}, 0$
- Comparison: Any negative number is less than zero.
- Result: $0 > -\frac{3}{8}$
- Answer: $(0)$

#### 2. $\left(-\frac{7}{12}\right), \left(\frac{5}{-8}\right)$
- Simplify $\frac{5}{-8}$ to $-\frac{5}{8}$.
- Compare $-\frac{7}{12}$ and $-\frac{5}{8}$:
- Convert to a common denominator: LCM of 12 and 8 is 24.
- $-\frac{7}{12} = -\frac{14}{24}$, $-\frac{5}{8} = -\frac{15}{24}$.
- Since $-\frac{14}{24} > -\frac{15}{24}$, $-\frac{7}{12} > -\frac{5}{8}$.
- Result: $-\frac{7}{12} > -\frac{5}{8}$
- Answer: $\left(-\frac{7}{12}\right)$

#### 3. $\left(\frac{4}{-9}\right), \left(-\frac{3}{-7}\right)$
- Simplify $\frac{4}{-9}$ to $-\frac{4}{9}$ and $-\frac{3}{-7}$ to $\frac{3}{7}$.
- Compare $-\frac{4}{9}$ and $\frac{3}{7}$:
- Any positive number is greater than any negative number.
- Result: $\frac{3}{7} > -\frac{4}{9}$
- Answer: $\left(\frac{3}{7}\right)$

#### 4. $\left(-\frac{5}{8}\right), \left(\frac{3}{4}\right)$
- Compare $-\frac{5}{8}$ and $\frac{3}{4}$:
- Any positive number is greater than any negative number.
- Result: $\frac{3}{4} > -\frac{5}{8}$
- Answer: $\left(\frac{3}{4}\right)$

#### 5. $\left(\frac{5}{9}\right), \left(-\frac{3}{-8}\right)$
- Simplify $-\frac{3}{-8}$ to $\frac{3}{8}$.
- Compare $\frac{5}{9}$ and $\frac{3}{8}$:
- Convert to a common denominator: LCM of 9 and 8 is 72.
- $\frac{5}{9} = \frac{40}{72}$, $\frac{3}{8} = \frac{27}{72}$.
- Since $\frac{40}{72} > \frac{27}{72}$, $\frac{5}{9} > \frac{3}{8}$.
- Result: $\frac{5}{9} > \frac{3}{8}$
- Answer: $\left(\frac{5}{9}\right)$

#### 6. $\left(\frac{5}{-8}\right), \left(-\frac{7}{12}\right)$
- Simplify $\frac{5}{-8}$ to $-\frac{5}{8}$.
- Compare $-\frac{5}{8}$ and $-\frac{7}{12}$:
- Convert to a common denominator: LCM of 8 and 12 is 24.
- $-\frac{5}{8} = -\frac{15}{24}$, $-\frac{7}{12} = -\frac{14}{24}$.
- Since $-\frac{15}{24} < -\frac{14}{24}$, $-\frac{7}{12} > -\frac{5}{8}$.
- Result: $-\frac{7}{12} > -\frac{5}{8}$
- Answer: $\left(-\frac{7}{12}\right)$

#### 7. $\left(\frac{3}{4}\right), \left(\frac{1}{2}\right)$
- Compare $\frac{3}{4}$ and $\frac{1}{2}$:
- Convert to a common denominator: LCM of 4 and 2 is 4.
- $\frac{3}{4} = \frac{3}{4}$, $\frac{1}{2} = \frac{2}{4}$.
- Since $\frac{3}{4} > \frac{2}{4}$, $\frac{3}{4} > \frac{1}{2}$.
- Result: $\frac{3}{4} > \frac{1}{2}$
- Answer: $\left(\frac{3}{4}\right)$

#### 8. $\left(\frac{12}{10}\right), \left(\frac{3}{5}\right)$
- Simplify $\frac{12}{10}$ to $\frac{6}{5}$.
- Compare $\frac{6}{5}$ and $\frac{3}{5}$:
- Both have the same denominator, so compare the numerators.
- Since $6 > 3$, $\frac{6}{5} > \frac{3}{5}$.
- Result: $\frac{6}{5} > \frac{3}{5}$
- Answer: $\left(\frac{6}{5}\right)$

#### 9. $\left(\frac{3}{2}\right), \left(-\frac{4}{6}\right)$
- Simplify $-\frac{4}{6}$ to $-\frac{2}{3}$.
- Compare $\frac{3}{2}$ and $-\frac{2}{3}$:
- Any positive number is greater than any negative number.
- Result: $\frac{3}{2} > -\frac{2}{3}$
- Answer: $\left(\frac{3}{2}\right)$

#### 10. $\left(\frac{4}{-8}\right), \left(-\frac{3}{-6}\right)$
- Simplify $\frac{4}{-8}$ to $-\frac{1}{2}$ and $-\frac{3}{-6}$ to $\frac{1}{2}$.
- Compare $-\frac{1}{2}$ and $\frac{1}{2}$:
- Any positive number is greater than any negative number.
- Result: $\frac{1}{2} > -\frac{1}{2}$
- Answer: $\left(\frac{1}{2}\right)$

Final Answers:

1. $(0)$
2. $\left(-\frac{7}{12}\right)$
3. $\left(\frac{3}{7}\right)$
4. $\left(\frac{3}{4}\right)$
5. $\left(\frac{5}{9}\right)$
6. $\left(-\frac{7}{12}\right)$
7. $\left(\frac{3}{4}\right)$
8. $\left(\frac{6}{5}\right)$
9. $\left(\frac{3}{2}\right)$
10. $\left(\frac{1}{2}\right)$

Boxed Answer:

\[
\boxed{
(0), \left(-\frac{7}{12}\right), \left(\frac{3}{7}\right), \left(\frac{3}{4}\right), \left(\frac{5}{9}\right), \left(-\frac{7}{12}\right), \left(\frac{3}{4}\right), \left(\frac{6}{5}\right), \left(\frac{3}{2}\right), \left(\frac{1}{2}\right)
}
\]