Question

Write as a fraction and reduce, if possible:

Answer 1

Answer:

$\frac{d-5c}{5d^2}$

$\frac{2}{y}$

21nk

Step-by-step explanation:

$\frac{1}{5d}- \frac{c}{d^2}$

We need to get the denominators to be the sameso what can you do to 5d and d^2 to be the same?  If you multiply 5d by d you get 5d^2 and if you multiply d^2 by 5 you get 5d^2.  And whatever you have to do to the denominator you do to the numerator.

$\frac{d}{d}*\frac{1}{5d}-\frac{5}{5}*\frac{c}{d^2}\\\frac{d}{5d^2}-\frac{5c}{5d^2}\\ \frac{d-5c}{5d^2}$

Once you have the same denominator you can just add or subtract the numerators as needed.  You don't need to do this for multiplication or division

Multiplying is super easy, just multiply the denominators and the numerators.

$\frac{3x}{y^2}*5y\frac{2}{15x} \\\frac{3x}{y^2}*\frac{5y*2}{15x}\\\frac{3x}{y^2}*\frac{10y}{15x}\\\frac{3x*10y}{y^2*15x}\\\frac{30xy}{15xy^2}\\\frac{2}{y}$

Let me know if you don't get how things canceled out.

Division is almost as simple  as multiplication.  The second fraction gets flipped and you multiply them.

$\frac{\frac{12mn^2}{k} }{\frac{4mn}{7k^2} }\\\frac{12mn^2}{k}*\frac{7k^2}{4mn}\\ \frac{12mn^2*7k^2}{k*4mn}\\ \frac{84mn^2k^2}{4mnk}\\ 21nk$

Again, let me know if you don't understand how things cancel out or got multiplied or something else.