I’m guessing that you mean if a/b is the original quotient, where a and b are whole numbers, then:
(a+13)/(b-7)=-4.
So a+13=-4(b-7)=-4b+28, therefore a+4b=28-13=15. The table below shows some possible values for a and b:
| a |
b |
a+13 |
b-7 |
(a+13)/(b-7) |
a/b |
| 11 |
1 |
24 |
-6 |
24/-6=-4 |
11/1 |
| 7 |
2 |
20 |
-5 |
20/-5=-4 |
7/2 |
| 3 |
3 |
16 |
-4 |
16/-4=-4 |
3/3 |
We can also have negative values for b, e.g., b=-2, a=23, (a+13)/(b-7)=36/-9=-4, a/b=23/-2.
I think perhaps the answer you’re looking for is 7/2.