$-\frac76=-\frac {4n}{3}$ struggling on solving this equation

Question

I was wondering how to do this equation step by step. I forgot how to but it would be awesome if someone could help me out $$-\frac76=-\frac {4n}{3}$$

Answer 1

$$-\frac76=-\frac {4n}{3} $$

$$\frac{-7}{6} \times \frac{-3}4 = \frac{-4n}{3} \times \frac{-3}4$$

$$\frac{21 }{24} = n$$

$$ n = \frac{7}{8} $$

Answer 2

Consider $$ \frac{a}{b}=\frac{c}{d}n $$ where $b,d\neq 0$. Then $$ n=\frac{ad}{bc}. $$ Now if you have, $$ \frac{a}{b}=\frac{c}{dn} $$ Then $$ n=\frac{cb}{da} $$ Both results were obtained by cross multiplying in order to isolate the unknown variable $n$

Answer 3

$$\frac{-7}{6}=\frac{-4}{3}n\\3\times\frac{-7}{6}=-4\times n\\3\times -7=-4\times6\times n\\\frac{3\times -7}{-4\times 6}=n\\n=\frac{21}{24}=\frac{7}{8}$$

Answer 4

It's the same sort of question as "How many dimes are ther in seven nickels?". To answer it, just convert everything to a common denomination--or, in this case, make the fractions being compared have the same denominator.

$$-\frac 76 =-\frac{4n}{3}$$ $$\frac {-7}6 = \frac{-4n}{3}$$ $$\frac {-7}6 = \frac{-4n\cdot 2}{3\cdot 2}$$ $$\frac {-7}6 = \frac{-8n}{6}$$

So it must be that $-7$ and $-8n$ are the same thing: $$-7=-8n$$ $$n=\frac{-7}{-8}$$ $$n=\boxed{\dfrac 78}$$

Answer 5

All other answers are way too complicated. You have: $$-\frac76=-\frac {4n}{3}$$ Therefore: $$\frac76=\frac {4n}{3}$$ Equivalently: $$\frac76=\frac {8n}{6}$$ So: $$7=8n$$ Thus: $$n = \frac 7 8$$