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

May 18, 2018

$- \frac{7}{2}$

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 $\frac{\frac{5}{2}}{\frac{5}{7}}$?

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)...

$\textcolor{g r e e n}{- \frac{\frac{5}{2}}{\frac{5}{7}}} = - \frac{5 \cdot 7}{2 \cdot 5}$

(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 $- \frac{7}{2}$

There is a slightly quicker way though...

$= - \frac{\cancel{5} \cdot 7}{2 \cdot \cancel{5}}$

$= - \frac{7}{2}$

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

Hope this helps!

May 18, 2018

$- \frac{5}{2} \div \frac{5}{7} = - \frac{7}{2}$

Explanation:

Divide:

$- \frac{5}{2} \div \frac{5}{7}$

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

$- \frac{5}{2} \times \frac{7}{5}$

$- \frac{5 \times 7}{2 \times 5}$

Simplify.

$- \frac{35}{10}$

Simplify by dividing the numerator and denominator by $5$.

$- \frac{35 \div 5}{10 \div 5} = - \frac{7}{2}$