Question

Q2. Insert 5 rational numbers between:
(i)-3/11and-1/13. (ii)3/8and-1/2. (iii)2/3and3/13
Q3. Insert 3 rational numbers between:
(i)-5/11and-4/11 (ii)9/13and11/13
​

Answer 1

Answer:

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I hope it will help you.....

Answer 2

Answer:

Q2.

$(i) \frac{ - 3}{11} and \frac{ - 1}{13}$

We have,

LCM of 11 and 13= 11×13

= 143

Now,

$\frac{ - 3}{11} = \frac{ - 3 \times 13}{11 \times 13} = \frac{ - 39}{143}$

$\frac{ - 1}{13} = \frac{ - 1 \times 13}{13 \times 11} = \frac{ - 13}{143}$

.·. 5 rational numbers between

$\frac{ - 3}{11}$ and $\frac{ - 1}{13} = \frac{ - 38}{143}, \frac{ - 37}{143} , \frac{ - 36}{143} , \frac{ - 35}{143} and \: \frac{ - 34}{143}$

$(ii) \frac{ 3}{8} and \frac{ - 1}{2}$

We have,

LCM of 8 and 2= 8

Now,

$\frac{ 3}{8} = \frac{ 3 \times 1}{8 \times 1} = \frac{ 3}{8}$

$\frac{ - 1}{2} = \frac{ - 1 \times 4}{2 \times 4} = \frac{ - 4}{8}$

.·. 5 rational numbers between

$\frac{ 3}{8} and \frac{ - 1}{2} = \frac{ 2}{8}, \frac{ 1}{8} , \frac{ - 1}{8} , \frac{ - 2}{8} and \: \frac{ - 3}{8}$

$(iii) \frac{ 2}{3} and \frac{ 3}{13}$

We have,

LCM of 3 and 13= 3×13

= 39

Now,

$\frac{ 2}{3} = \frac{ 2 \times 13}{3 \times 13} = \frac{ 26}{39}$

$\frac{ 3}{13} = \frac{ 3 \times 3}{13 \times 3} = \frac{ 9}{39}$

.·. 5 rational numbers between

$\frac{ 2}{3}$ and $\frac{ 3}{13} = \frac{ 25}{13}, \frac{24}{13} , \frac{23}{13} , \frac{22}{13} and \: \frac{21}{13}$

Q3.

$(i) \frac{ - 5}{11} and \frac{ - 4}{11}$

We have,

$\frac{ - 5}{11} = \frac{ - 5 \times 4}{11 \times 4 } = \frac{ - 20}{44}$

$\frac{ -4}{11} = \frac{ - 4 \times 4}{11 \times 4} = \frac{ - 16}{44}$

.·. 3 rational numbers between $\frac{ -5}{11} and \frac{ - 4}{11} = \frac{ -19}{44}, \frac{ -18}{44} , and \: \frac{ -17 }{44}$

$(ii) \frac{ 9}{13} and \frac{ 11}{13}$

We have,

$\frac{ 9}{13} = \frac{ 9 \times 4}{13 \times 4 } = \frac{ 36}{52}$

$\frac{ 11}{13} = \frac{ 11 \times 4}{13 \times 4} = \frac{ 44}{52}$

.·. 3 rational numbers between $\frac{ 9}{13} and \frac{11}{13} = \frac{ 37}{52}, \frac{ 38}{52} , and \frac{ 39 }{52}$

I hope it helps u a lot.. ^_^