To rewrite the given fractions with positive denominators, we need to adjust the sign of the numerator if the denominator is negative. Here are the steps for each fraction:
### (a) [tex]\(\frac{5}{-4}\)[/tex]
1. The given fraction is [tex]\(\frac{5}{-4}\)[/tex].
2. To make the denominator positive, we multiply both the numerator and the denominator by [tex]\(-1\)[/tex]:
[tex]\[
\frac{5 \times -1}{-4 \times -1} = \frac{-5}{4}
\][/tex]
3. So, [tex]\(\frac{5}{-4} = \frac{-5}{4}\)[/tex].
### (b) [tex]\(\frac{-7}{-4}\)[/tex]
1. The given fraction is [tex]\(\frac{-7}{-4}\)[/tex].
2. To make the denominator positive, we multiply both the numerator and the denominator by [tex]\(-1\)[/tex]:
[tex]\[
\frac{-7 \times -1}{-4 \times -1} = \frac{7}{4}
\][/tex]
3. So, [tex]\(\frac{-7}{-4} = \frac{7}{4}\)[/tex].
### (c) [tex]\(\frac{15}{-7}\)[/tex]
1. The given fraction is [tex]\(\frac{15}{-7}\)[/tex].
2. To make the denominator positive, we multiply both the numerator and the denominator by [tex]\(-1\)[/tex]:
[tex]\[
\frac{15 \times -1}{-7 \times -1} = \frac{-15}{7}
\][/tex]
3. So, [tex]\(\frac{15}{-7} = \frac{-15}{7}\)[/tex].
### (d) [tex]\(\frac{-14}{-5}\)[/tex]
1. The given fraction is [tex]\(\frac{-14}{-5}\)[/tex].
2. To make the denominator positive, we multiply both the numerator and the denominator by [tex]\(-1\)[/tex]:
[tex]\[
\frac{-14 \times -1}{-5 \times -1} = \frac{14}{5}
\][/tex]
3. So, [tex]\(\frac{-14}{-5} = \frac{14}{5}\)[/tex].
### Summary:
- [tex]\(\frac{5}{-4} = \frac{-5}{4}\)[/tex]
- [tex]\(\frac{-7}{-4} = \frac{7}{4}\)[/tex]
- [tex]\(\frac{15}{-7} = \frac{-15}{7}\)[/tex]
- [tex]\(\frac{-14}{-5} = \frac{14}{5}\)[/tex]
Thus, the fractions with positive denominators are:
[tex]\((a) \frac{-5}{4}\)[/tex]
[tex]\((b) \frac{7}{4}\)[/tex]
[tex]\((c) \frac{-15}{7}\)[/tex]
[tex]\((d) \frac{14}{5}\)[/tex]
