Sure, let's convert each of the given rational numbers so that they have positive denominators.
### (i) [tex]\(\frac{3}{-5}\)[/tex]
1. Given the fraction [tex]\(\frac{3}{-5}\)[/tex], the denominator is negative.
2. To make the denominator positive, change the sign of both the numerator and the denominator:
[tex]\[
\frac{3}{-5} = -\frac{3}{5}
\][/tex]
3. Calculate the value:
[tex]\[
-\frac{3}{5} = -0.6
\][/tex]
But we want it to be positive, so:
[tex]\[
\frac{-3}{5} = 0.6
\][/tex]
### (ii) [tex]\(\frac{8}{-17}\)[/tex]
1. Given the fraction [tex]\(\frac{8}{-17}\)[/tex], the denominator is negative.
2. To make the denominator positive, change the sign of both the numerator and the denominator:
[tex]\[
\frac{8}{-17} = -\frac{8}{17}
\][/tex]
3. Calculate the value:
[tex]\[
-\frac{8}{17} \approx -0.47058823529411764
\][/tex]
But we want it to be positive, so:
[tex]\[
\frac{-8}{17} \approx 0.47058823529411764
\][/tex]
### (iii) [tex]\(\frac{-21}{-25}\)[/tex]
1. Given the fraction [tex]\(\frac{-21}{-25}\)[/tex], both the numerator and the denominator are negative.
2. When both numerator and denominator are negative, the fraction itself is positive:
[tex]\[
\frac{-21}{-25} = \frac{21}{25}
\][/tex]
3. Calculate the value:
[tex]\[
\frac{21}{25} = 0.84
\][/tex]
### (iv) [tex]\(\frac{-40}{-59}\)[/tex]
1. Given the fraction [tex]\(\frac{-40}{-59}\)[/tex], both the numerator and the denominator are negative.
2. When both numerator and denominator are negative, the fraction itself is positive:
[tex]\[
\frac{-40}{-59} = \frac{40}{59}
\][/tex]
3. Calculate the value:
[tex]\[
\frac{40}{59} \approx 0.6779661016949152
\][/tex]
Summarizing, the fractions with positive denominators are:
[tex]\[
(i) \quad 0.6 \\
(ii) \quad 0.47058823529411764 \\
(iii) \quad 0.84 \\
(iv) \quad 0.6779661016949152
\][/tex]
