Question

Write four rational numbers between 3/4 and 2/3 ​

Answer 1

SOLUTION

TO DETERMINE

The four rational number between

$\displaystyle \sf{ \frac{3}{4} \: \: \: \: and \: \: \: \frac{2}{3} }$

EVALUATION

Here the given two rational numbers are

$\displaystyle \sf{ \frac{3}{4} \: \: \: \: and \: \: \: \frac{2}{3} }$

Here the LCM of the denominators

= LCM of 4 & 3

= 12

Now

$\displaystyle \sf{ \frac{3}{4} \: = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} = \frac{9 \times 10}{12 \times 10} = \frac{90}{120} }$

$\displaystyle \sf{ \frac{2}{3} \: = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} = \frac{8 \times 10}{12 \times 10} = \frac{80}{120} }$

Hence the required four rational numbers are

$\displaystyle \sf{ \frac{81}{120} \: ,\: \frac{82}{120} \: , \: \frac{83}{120} \: , \: \frac{84}{120} }$

On simplification we get

$\displaystyle \sf{ \frac{27}{40} \: ,\: \frac{41}{60} \: , \: \frac{83}{120} \: , \: \frac{7}{10} }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If 2x/3y=3y/4z then show that 4x square -9y square+16z square=(2x -3y+4z) (2x+3y+4z)

https://brainly.in/question/17124386

2. If 1/2 is a root of the quadratic equation x²-mx-5/4=0 , then the value of m is

https://brainly.in/question/21062028

Answer 2

Answer:

To find a rational number first we have to make denominators same.

To make denominators same take LCM of 3/4&2/3.

LCM will be 12..

Now denominators are same so we can easily find the rational number.

3/4=3x3/4x3=9/12=9/10 /12/10=90/120

2/3=2x4/3x4=8/12=8/10/12/10=80/120

So the 4 rational numbers between 80/120&90/120 are..

81/120, 82/120,83/120,84/120...

Step-by-step explanation:

☃️Hope it's help you dear