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

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Answer 1 · 2018-05-18T22:09:39

#-7/2#

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!

Answer 2 · 2018-05-18T22:14:16

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

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#