Sure, let's analyze each rational number step by step to determine whether it is positive or negative.
### (a) [tex]\(\frac{-5}{2}\)[/tex]
In this fraction, the numerator is [tex]\(-5\)[/tex] (negative) and the denominator is [tex]\(2\)[/tex] (positive). When we have a fraction with one negative part (either numerator or denominator), the fraction as a whole is negative.
Thus, [tex]\(\frac{-5}{2}\)[/tex] is negative.
### (b) [tex]\(\frac{-3}{-2}\)[/tex]
Here, both the numerator [tex]\(-3\)[/tex] and the denominator [tex]\(-2\)[/tex] are negative. When both the numerator and the denominator are negative, their negatives cancel out, resulting in a positive value.
Therefore, [tex]\(\frac{-3}{-2}\)[/tex] is positive.
### (c) [tex]\(1 \frac{1}{4}\)[/tex]
This is a mixed number. It consists of an integer part [tex]\(1\)[/tex] and a fractional part [tex]\(\frac{1}{4}\)[/tex], both of which are positive. Since both parts are positive, the entire mixed number is positive.
Thus, [tex]\(1 \frac{1}{4}\)[/tex] is positive.
### (d) [tex]\(\frac{+4}{5}\)[/tex]
In this fraction, the numerator is [tex]\(4\)[/tex] (positive) and the denominator is [tex]\(5\)[/tex] (positive). When both the numerator and the denominator are positive, the fraction as a whole is positive.
Therefore, [tex]\(\frac{+4}{5}\)[/tex] is positive.
### Summary:
- (a) [tex]\(\frac{-5}{2}\)[/tex] is negative.
- (b) [tex]\(\frac{-3}{-2}\)[/tex] is positive.
- (c) [tex]\(1 \frac{1}{4}\)[/tex] is positive.
- (d) [tex]\(\frac{+4}{5}\)[/tex] is positive.
