Question 1023129
in general, a/b is the same as a * 1/b.


in other words, when you divide by something, it's the same thing as multiplying by the reciprocal of that something.


likewise, (a/b) / (c/d) is the same as (a/b) * (d/c).


same reason.


d/c is the reciprocal of c/d.


consequently, .....


(-48/90) / (-32/72) is the same as (-48/90) * (72/-32).


now a/-b is the same as -a/b is the same as -(a/b).


consequently, (-48/90) * (72/-32) is the same as -(48/90) * -(72/32).


now you know that a minus times a minus is equal to a plus, so .....


-(48/90) * -(72/32) is the same as (48/90) * (72/32).


now you also know that (48/90) * (72/32) is the same as (48 * 72) / (90 * 32) which is the same as (48/32) * (72/90).


48/32 can be reduced to 3/2, so the expression becomes (3 * 72) / (90 * 2).


3/90 can be reduced to 1/30, so the expression becomes (72) / (30 * 2).


72/2 can be reduced to 36/1, so the expression becomes 36 / 30.


36/30 can be reduced to 6/5.


since 6/5 can't be reduced any further, that's your solution.


you can confirm this solution is correct by doing the following in your scientific calculator that can handle parentheses.


enter exactly as shown:  (-48/90) / (-32/72) 


your calculator will tell you that the solution is 1.2.


enter 6/5 in your calculator and your calculator will tell you that the solution is 1.2.


since they both equal 1.2, they're equivalent, and so (-48/90) / (-32/72)  = 6/5.


this confirms your solution is correct.


some calculators use a different - symbol to indicate a negative number.


if you use the - symbol for operations, when you wanted to indicate a negative number, you might get an incorrect response.


you might have to be a little bit careful about that.


my ti-84 plus is such a calculator.