Question

Question 1 - 3 Marks
Insert five rational numbers between -3 and - 2.​

Answer 1

$\huge{ \red{\underline{{ \bf Solution} }}}$

We have to write 5 rational numbers between -3 and - 2

We can simply write in decimal places :-

• $\purple {\tt -2.1}$
• $\purple {\tt -2.2}$
• $\purple {\tt -2.3}$
• $\purple {\tt -2.4}$
• $\purple {\tt -2.5}$

Alternative Method :-

We have to find 5 rational number between -2 and -3

Firstly, we convert them into fraction

Then, we multiply one more than the number to be found, here we have to find five, therefore, we multiply numberator & denominator by six

After that, we simply write the numbers between those fraction

$\green{\sf \implies \dfrac{ - 2 \times 6}{1 \times 6} \: and \: \dfrac{ - 3 \times 6}{1 \times 6}}$

$\green{\sf \implies \dfrac{-12}{6} \: and \: \dfrac{-18}{6} }$

Thus, we can write the five rational numbers between them :-

• $\gray{\bf \dfrac{-13}{6}}$

• $\gray{\bf \dfrac{-14}{6}}$

• $\gray{\bf \dfrac{-15}{6}}$

• $\gray{\bf \dfrac{-16}{6}}$

• $\gray{\bf \dfrac{-17}{6}}$

${\green{ \underbrace{\boxed{\underline{\underline{\purple{ \tt Thus, Solved }}}}}}}$

Answer 2

For finding the rationals between the given numbers ; we need to follow up the given steps :

1. Take the LCM and make the denominators same of they aren't .
2. If the denominator are already equal ; multiply them with same number with both denominator and numerator or both numbers .

Solution :

-3 and -2 can be written as -3/1 and -2/1 .

As the denominators are already same ; we will multiply a single number with both numberator and denominator of both numbers .

Let's take 10 .

-3/1 × 10/10 = -30/10

-2/1 × 10/10 = -20/10

Here the denominator are same and we can take any numbers between them .

➜ -21/10 , -22/10 , -23/10 , -24/10 , -25/10 , -26/10 , -27/10 , -28/10 , -29/10 .

There is another method in which we consider the number of rationals to be found between as (n) and add (n+1) and consider it as the multiple that is to be multiplied by both the terms .

Here :

• n = 5
• n+1 = 6

-3/1 × 6/6 = -18/6

-2/1 ×6/6 = -12/6

Then ; we can take :

➜ -13/6 , -14/6 , -15/6 ,-16/6 , -17/6

They are exactly 5 .