Question

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Answer 1

Answer:

$\frac{-4}{5} and \frac{-2}{3} \\Lcm=15\\\frac{-4}{5} =\frac{-12}{15} \\\frac{-2}{3} =\frac{-10}{15}$

so now $\frac{-11}{15}$ is the middle number so now we will multiply by 10 to make it bigger...

$\frac{-10}{15} *10=\frac{-100}{150} \\\frac{-12}{15} *10=\frac{-120}{150}$

so the rational numbers between$\frac{-4}{5} and \frac{-2}{3} is \frac{-11}{15} ,\frac{-121}{150} ,\frac{-122}{150} ...$

Step-by-step explanation:

Answer 2

Given:

• Numbers $\sf-\frac{4}{5} \: and \: -\frac{2}{3}$

To Find:

• Any 3 rational numbers between the following given numbers

Solution:

Here, We have got 2 Rational numbers which are -4/5 and -2/3 now It is said that we have to find any 3 Rational numbers In between them.

So, when we find rational numbers between numbers we have to make sure that we convert their denominators to the same,So that we can find the numbers easily.

First Number:

$\tt - \dfrac{4}{5}$

where,

• - 4 is the numerator and 5 is the denominator

Second Number:

$\tt - \dfrac{2}{3}$

Where,

• -2 is the numerator and 3 is the denominator

Now, let's find the L.C.M of the numbers 3 and 5

$\begin{gathered}\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\begin{gathered} \begin{array}{c|c} \underline{\sf{ 5 }}& {\sf{ \underline{ \red{3,5} \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \underline{\sf{3}}&{\sf{ \underline{3 ,1\: \: \: }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\\underline{\sf{1}}&{\sf{ \underline{1,1 \: \: \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \sf{} & \sf{1 \: \: \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}\end{gathered}\end{gathered}\end{gathered}$

Now,

$\longrightarrow \tt \: l.c.m = 5 \times 3 \times 1 \\ \\ \longrightarrow \tt \: l.c.m = {\boxed{ \pink{15}}} \: \: \: \: \: \: \: \: \: \: \: \:$

As we know,

• 5 × 3 = 15
• 3 × 5 = 15

So, now let's multiply the numerator and the denominator with the same number.

$\longrightarrow \tt - \frac{2 \times 5}{3 \times 5} \\ \\ \\ \longrightarrow \tt \: - \frac{10}{15} \: \: \: \: \:$

Now, let's do the same with the other number:

$\longrightarrow \tt \: - \frac{4 \times 3}{5 \times 3} \\ \\ \\ \longrightarrow \tt \: - \frac{12}{15} \: \: \: \: \: \: \:$

As, Now only their is possibly Of two rational numbers between so, let's multiply the numerators and denominators with 2

$\longrightarrow \tt \: - \frac{10 \times 2}{15 \times 2} \\ \\ \\ \longrightarrow \tt \: \frac{ - 20}{ \: \: 30} \bigstar \: \: \: \\ \\ \\ \longrightarrow \tt \: - \frac{12 \times 2}{15 \times 2} \\ \\ \\ \longrightarrow \tt \: \frac{ - 24}{ \: \: 30} \bigstar \: \: \:$

${\longmapsto} \rm \: hence \: the \: numbers \: in \: between \: are :$

$\purple \rightarrow \tt - \dfrac{21}{30} \\ \\ \purple \rightarrow \tt \: - \frac{22}{30} \\ \\ \purple \rightarrow \tt - \frac{23}{30}$