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find any ten rational numbers between -5/6 and 5/8​

Answer 1

Answer

$we \: first \: convert \: \frac{ - 5}{6} and \: \frac{5}{8} to \: the \: rational \: numbers \: with \: same \: denomination$

$\frac{-5}{6} \times \frac{4}{4} = \frac{}{}\frac{15}{24}$

$\frac{5}{8} \times \frac{3}{3} = \frac{15}{24}$

$thus \: we \: \: have \: \frac{ - 19}{24} \frac{ - 18}{24} \frac{ - 17}{24} as \: the \: rational \: numbers \: between \:$

$\frac{ - 20}{24} and \: \frac{15}{24 \:} \: we \: can \: take \: ten \: of \: these$

$another \: method$

let us find the rational numbers between 1 and 2.one of them is 1.5

$1 \times \frac{1}{2} \: or \: \frac{3}{2}.this \: means \: of \: 1 \: and \: 2.$

We have to find that between any two given numbers we need not necessary to get an integer but there will always lie a national numbers.

We can use the idea of mean also to find rational numbers between any two given rational numbers.

Answer 2

We have been given 2 unlike rational numbers and are supposed to find 10 rational numbers between these 2 numbers.

So, we should first convert the unlike rational numbers into like rational numbers.

Let's find the L.C.M of the denominators of the 2 numbers:

6 = 2 * 3.

8 = 2 * 2 * 2.

L.C.M = 2 * 2 * 2 * 3 = 24.

Converting unlike rational numbers into like rational numbers:

$- \frac{ 5}{6} = - \frac{5 \times 4}{6 \times 4} = - \frac{20}{24} \\ \\ \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}$

$Now, \: let's \: \: list \: \: out \: \: 10 \: \: rational \: \\ numbers \: \: between \: - \frac{5}{6} \: \: and \: \: \frac{5}{8}$

$\\ - \frac{19}{24} , - \frac{18}{24} = - \frac{3}{4} ,- \frac{17}{24} , \\ \\ - \frac{16}{24} = - \frac{2}{3} , - \frac{15}{24} = - \frac{5}{8} , \\ \\ - \frac{14}{24} = - \frac{7}{12} , - \frac{13}{24} , - \frac{12}{24} = - \frac{1}{2} , \\ \\ \frac{0}{24} = 0 \: \: and \: \: \frac{1}{24}$