Question

Give five rational number between givem 5/6 and 2/8
(2) - 5/9 and 2/4​

Answer 1

Answer:

Answer :-

Two rational numbers between -5/6 and -2/8 are -7/24 and -8/24.

Given :-

Two rational numbers -5/6 and -2/8.

To find :-

Two rational numbers between them.

Step-by-step explanation :-

Here, we are asked to find three rational numbers between -5/6 and -2/8. So first we have to make their denominator same. For this, we have to find the LCM of their denominators [6, 8]

Finding the LCM of 6 and 8 :-

\begin{gathered} \\ \end{gathered}

\begin{gathered}\begin{array}{c | c} \underline2 & \underline{6, 8} \\ \underline2 & \underline{3, 4} \\ \underline2 & \underline{3, 2} \\ \underline3 & \underline{3, 1} \\ & 1, 1\end{array}\end{gathered}22236,83,43,23,11,1

\begin{gathered} \\ \end{gathered}

Hence :-

The LCM of 6 and 8 is 2 × 2 × 2 × 3 = 24.

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So, the given rational numbers can also be written as :-

\sf{\dfrac{-5}{6} = \dfrac{-5 \times 4}{6 \times 4} = \dfrac{-20}{24}}6−5=6×4−5×4=24−20

\sf{\dfrac{-2}{8} = \dfrac{-2 \times 3}{8 \times 3} = \dfrac{-6}{24}}8−2=8×3−2×3=24−6

Now,

\bf\dfrac{ - 20}{ \: \: \: 24} , \dfrac{ - 19}{ \: \: \: 20} , \dfrac{ - 18}{ \: \: \: 20} \: ... \: \dfrac{ - 6}{24}24−20,20−19,20−18...24−6

We can choose any two rational numbers from here.

\begin{gathered} \\ \end{gathered}

Hence :-

Two rational numbers between -5/6 and -2/8 are -7/24 and -8/24.