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:
and ![\frac{-a}{b}=\frac{-a}{b}](https://tex.z-dn.net/?f=%5Cfrac%7B-a%7D%7Bb%7D%3D%5Cfrac%7B-a%7D%7Bb%7D)
We will use these rules
1) Negative three-fourths divided by Negative two-thirds
![=\frac{-\frac{3}{4} }{-\frac{2}{3} }\\=-\frac{3}{4}\times -\frac{3}{2}\\=\frac{9}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-%5Cfrac%7B3%7D%7B4%7D%20%7D%7B-%5Cfrac%7B2%7D%7B3%7D%20%7D%5C%5C%3D-%5Cfrac%7B3%7D%7B4%7D%5Ctimes%20-%5Cfrac%7B3%7D%7B2%7D%5C%5C%3D%5Cfrac%7B9%7D%7B8%7D)
The quotient is positive.
2) Negative StartFraction 1 over 8 EndFraction divided by 3 and one-fifth
![\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}](https://tex.z-dn.net/?f=%5Cfrac%7B-%5Cfrac%7B1%7D%7B8%7D%20%7D%7B3%5Cfrac%7B1%7D%7B5%7D%20%7D%5C%5C%3D%5Cfrac%7B-%5Cfrac%7B1%7D%7B8%7D%20%7D%7B%5Cfrac%7B16%7D%7B5%7D%20%7D%5C%5C%3D-%5Cfrac%7B1%7D%7B18%7D%20%5Ctimes%20%5Cfrac%7B5%7D%7B16%7D%5C%5C%3D-%5Cfrac%7B5%7D%7B288%7D)
The quotient is negative.
3) 2 and StartFraction 2 over 7 EndFraction divided by negative one-fifth
![\frac{2\frac{2}{7} }{-\frac{1}{5} }\\= \frac{\frac{16}{7} }{-\frac{1}{5} }\\=\frac{16}{7} \times -5\\=-\frac{80}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B2%5Cfrac%7B2%7D%7B7%7D%20%7D%7B-%5Cfrac%7B1%7D%7B5%7D%20%7D%5C%5C%3D%20%5Cfrac%7B%5Cfrac%7B16%7D%7B7%7D%20%7D%7B-%5Cfrac%7B1%7D%7B5%7D%20%7D%5C%5C%3D%5Cfrac%7B16%7D%7B7%7D%20%5Ctimes%20-5%5C%5C%3D-%5Cfrac%7B80%7D%7B7%7D)
The quotient is negative.
4) Negative 6 divided by Five-thirds
![\frac{-6}{\frac{5}{3} }\\=-6 \times \frac{3}{5}\\=-\frac{18}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B-6%7D%7B%5Cfrac%7B5%7D%7B3%7D%20%7D%5C%5C%3D-6%20%5Ctimes%20%5Cfrac%7B3%7D%7B5%7D%5C%5C%3D-%5Cfrac%7B18%7D%7B5%7D)
The quotient is negative.
So, only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.
Option A is correct.