Question

Ten rational numbers between -3/4 and 5/6

Answer 1

Find 10 rational numbers between -4/5 and 2/3? 

I would get a common denominator between these two fractions to make things easier... we'll achieve a common denominator of 15. 

We will multiply the -4/5 entirely by 3 to get a denominator of 15 and 2/3 entirely by 5 to get denominator of 15..

(-4/5)(3/3) = -12/20 

(2/3)(5/5) = 10/15 

So what are 10 rational numbers between -12/15 and 10/15? 

Well, -11/15, -8/15, -7/15, -2/15, -1/15, 0, 1/15, 2/15, 4/15, 7/15, 8/15...

Some other rational numbers: 

-10/15 => -2/3, -9/15 => -3/5, -6/15 => -2/5, -3/15 => -1/5 

3/15 => 1/5, 6/15 => 2/5, 9/15 => 3/5, -4/15

-5/15 => -1/3, 5/15 => 1/3...

Answer 2

Answer:

LCM (4,6)=12

$\frac{ - 3}{4} \times \frac{3}{3} = \frac{ - 9}{12} \times \frac{10}{10} = \frac{ - 90}{120} \\ \frac{5}{6} \times \frac{2}{2} = \frac{10}{12} \times \frac{10}{10} = \frac{100}{120}$

So, ten rational numbers are 80/120 , 99/120, 1/120 , -12/120 ,....