How do you divide #-5/7 div -35/-7#?

This problem uses a rule of fractions - when dividing a fraction by another fraction, invert the denominator fraction and multiply. This will make way more sense by working through the problem!

We start with #(-5/7)/-(35/-7)#

So what we do is take the denominator fraction, the #-(35/-7)# fraction, and invert it into #-((-7)/35)#. We then change the operation from division to multiplication, so the whole thing now looks like this:

#(-5/7)*-((-7)/35)#

Let's deal with all the negative signs first. There are 3 of them, each one is #(-1)#. It doesn't matter if the negative is in front of the fraction (such as with #(-5/7)#), in the numerator, or in the denominator. Each one is a #(-1)# and can be multiplied together. So let's do that now.

#(-1)(-1)(-1) = -1#

So we know the answer will be negative.

Now let's focus on the rest of the problem. I'm going to ignore the negative signs (because we've just dealt with them) and recombine the expression a bit to make it easier to see how it is that we can simplify the equation:

#(5*7)/(7*35) = 5/35 * 7/7#

Let's deal with the #7/7# fraction first. That works out to be 1.

The other fraction, the #5/35# fraction, can be reduced by using the factors of 35:

#5/35 = 5/(5*7) = 5/5 * 1/7#

Again, we can take #5/5#, do the division, and get 1.

Let's recap. We had:

#(-5/7)/-(35/-7)#, inverted the denominator and changed the operation to multiplication, #(-5/7)*-((-7)/35)#, found the fraction will be negative, and found that the "number part" of the fraction started at #(5*7)/(7*35)# and reduced to #5/35 * 7/7 = 5/35*1 = 5/5 * 1/7*1 = 1/7#.

So the answer is a negative 1/7, or #-1/7#