Answer:
Only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.
Option A is correct.
Step-by-step explanation:
We will solve to find out Which expression has a positive quotient.
We know the division rule: [tex]\frac{-a}{-b}=\frac{a}{b}[/tex] and [tex]\frac{-a}{b}=\frac{-a}{b}[/tex]
We will use these rules
1) Negative three-fourths divided by Negative two-thirds
[tex]=\frac{-\frac{3}{4} }{-\frac{2}{3} }\\=-\frac{3}{4}\times -\frac{3}{2}\\=\frac{9}{8}[/tex]
The quotient is positive.
2) Negative StartFraction 1 over 8 EndFraction divided by 3 and one-fifth
[tex]\frac{-\frac{1}{8} }{3\frac{1}{5} }\\=\frac{-\frac{1}{8} }{\frac{16}{5} }\\=-\frac{1}{18} \times \frac{5}{16}\\=-\frac{5}{288}[/tex]
The quotient is negative.
3) 2 and StartFraction 2 over 7 EndFraction divided by negative one-fifth
[tex]\frac{2\frac{2}{7} }{-\frac{1}{5} }\\= \frac{\frac{16}{7} }{-\frac{1}{5} }\\=\frac{16}{7} \times -5\\=-\frac{80}{7}[/tex]
The quotient is negative.
4) Negative 6 divided by Five-thirds
[tex]\frac{-6}{\frac{5}{3} }\\=-6 \times \frac{3}{5}\\=-\frac{18}{5}[/tex]
The quotient is negative.
So, only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.
Option A is correct.
