Question

I want to know if I did the below question right

Answer 1

There are various options correct.

Firstly, we can write the fraction as a division, but we need to put parenthesis because of the negative signs:

`(-(4)/(5))/(-(2)/(5))=(-(4)/(5))\, /\, (-(2)/(5))`

We can now drop the sings, since, in a division, two negative sings makes a positive result:

`(-(4)/(5))/(-(2)/(5))=(-(4)/(5))\, /\, (-(2)/(5))=(4)/(5)\, /\, (2)/(5)`

So, the second alternative is correct. Also, we can see that the thirs alternative is wrong, because the first fraction is inverted.

Now, a property of division of fractions is that we can invert the second fraction (the divisior) and turn the division into a multiplication, so:

`(-(4)/(5))/(-(2)/(5))=(-(4)/(5))\, /\, (-(2)/(5))=(-(4)/(5))\cdot(-(5)/(2))`

From here, we can see that the fourth alternative is correct. also, the last alternative is wrong because it invertes the first fraction. The fisrt alternative is also wrong because it inverted both fraction and, in this case, it mase them not equivalent.

So, the alternatives that are equivalent are the second and the fourth.