How do you divide -\frac { 5} { 2} \div \frac { 5} { 7} ?

2 Answers
May 18, 2018

-7/2

Explanation:

First, let's throw the negative out and just look at how the fractions are set up.

Isn't 5/2 ÷ 5/7 really the same as saying (5/2)/(5/7)?

If we go by that, then we can use a rather handy fractional algebraic rule which says:

color(red)((a/b)/(c/d) = (a*d)/(b*c)

So in reality...all we're doing is cross multiplying!

To set up your particular problem though (with the negative)...

color(green)(-(5/2)/(5/7)) =-(5*7)/(2*5)

(that negative is really in the numerator, so its the same as saying -5 * 7 divided by 2 * 5)

Doing this will get you an answer of -7/2

There is a slightly quicker way though...

=-(cancel(5)*7)/(2*cancel(5))

= -7/2

Anytime you have common terms on the top or bottom, you can cancel them out!

Hope this helps!

May 18, 2018

-5/2-:5/7=-7/2

Explanation:

Divide:

-5/2-:5/7

When dividing by a fraction, you invert it and multiply.

-5/2xx7/5

-(5xx7)/(2xx5)

Simplify.

-35/10

Simplify by dividing the numerator and denominator by 5.

-(35-:5)/(10-:5)=-7/2