Question

List five rational numbers betwwen: -2 and -1, -1/2 and 2/3​

Answer 1

$\huge\mathbb{\underline{SOLUTION:-}}$

$\bold{To\: Find}\begin{cases}\sf{Rational\: number between}\\ \sf{(-2)\:and\:(-1)}\\ \sf{\frac{(-1)}{2}\:and\:\frac{2}{3}}\end{cases}$

$\sf\underline{\red{According\:to\: Question:-}}$

$\sf Formula\: will\:be\:used\\ \\ \sf\implies d=\frac{(y-x)}{n+1}\: \: \: \: \: \: \: n=5\: \: \: \:\: y>x$

Let's find the d

where x=(-2) y=(-1)

n=5

$\sf d=\frac{(-2-(-1)}{5+1}\\ \\ \sf \implies d=\frac{(2+(-1)}{6}\\ \\ \sf\implies d=\frac{1}{6}$

The value of d is $\sf\frac{1}{6}$

So, rational number $\sf \implies x+d,\:x+2d\:x+3d,\:x+4d,\:x+5d$

$\bf\implies x+d\\ \\ \sf (-2)+\frac{1}{6}=\frac{-12+1}{6}=\frac{11}{6}$

$\bf \implies x+2d\\ \\ \sf (-2)+\frac{2}{6}=\frac{-12+2}{6}=\frac{(-10)}{6}$

$\bf\implies x+3d\\ \\ \sf (-2)+\frac{3}{6}=\frac{(-12+3)}{6}=\frac{(-9)}{6}$

$\bf \implies x+4d\\ \\ \sf (-2)+\frac{4}{6}=\frac{(-12+4)}{6}=\frac{(-8)}{6}$

$\bf\implies x+5d\\ \\ \sf (-2)+\frac{5}{6}=\frac{(-12+5)}{6}=\frac{(-7)}{6}$

$\boxed{\sf{\blue{The\: rational\:number\:between (-2)\:and\:(-1)}}}$

$\sf\underline{\red{\mathfrak{\frac{(-11)}{6}\:,\frac{(-10)}{6}\:,\frac{-9}{6}\:,\frac{-8}{6}\:,\frac{-7}{6}}}}$

• Now 2

$\sf x=\frac{-1}{2}\: \: \: \: \: y=\frac{2}{3}\: \: \: \: \: n=5$

Then to find d

$\bf\implies d=\frac{y-x}{n+1}$

$\sf\implies d=\frac{\frac{2}{3}-\frac{-1}{2}}{5+1}\\ \\ \sf d=\frac{\frac{4+3}{6}}{6}\\ \\ \sf\implies d=\frac{7}{6}\times \frac{1}{6}=\frac{7}{36}$

The value of d is=$\sf\implies \frac{7}{36}$

$\bf \implies x+d\\ \\ \sf \frac{-1}{2}+\frac{7}{36}=\frac{-18+7}{36}=\frac{-11}{36}$

$\bf\implies x+2d\\ \\ \sf \frac{-1}{2}+\frac{14}{36}=\frac{-18+14}{36}=\frac{-4}{36}$

$\bf\implies x+3d\\ \\ \sf \frac{-1}{2}+\frac{21}{36}=\frac{-18+21}{36}=\frac{3}{36}$

$\bf\implies x+4d\\ \\ \sf \frac{-1}{2}+\frac{28}{36}=\frac{-18+28}{36}=\frac{10}{36}$

$\bf\implies x+5d\\ \\ \sf \frac{-1}{2}+\frac{7}{36}=\frac{-18+35}{36}=\frac{17}{36}$

$\boxed{\sf{\purple{The\: rational\:number\:between \: \frac{(-1)}{2}\:and\:\frac{2}{3}}}}$

$\sf\underline{\red{\mathfrak{\frac{(-11)}{36}\:,\frac{(-4)}{36}\:,\frac{3}{36}\:,\frac{10}{36}\:,\frac{17}{36}}}}$

#BAL

#answerwithquality