list six rational number less than -2 and greater than-3??
plz its urgent
Answers
Question:
List 6 Rational numbers less than -2 and more than -3 .
Answer:
-20/7 , -19/7 , -18/7 , -17/7 , -16/7 , -15/7
Working rule:
★ Let the smaller number be x and greater number be y .
★ Find out d , using the formula given below ↓
d = (y - x) / (n + 1) , where n is the number of Rational numbers which are to be found between x and y .
★ Then the required rational numbers will be given as follow ↓
• 1st Rational no. = x + d
• 2nd Rational no. = x + 2d
• 3rd Rational no. = x + 3d
:
:
• nth Rational no. = x + nd
Solution:
Here,
We need to find 6 Rational numbers between -3 and -2 .
Thus , let
x = -3 (smaller number)
y = -2 (greater number)
n = 6 (no. of Rational numbers to be found between -3 and -2)
Now,
d will be given as ;
=> d = (y -x) / (n + 1)
=> d = [ - 2 - (-3) ] / (6 + 1)
=> d = ( - 2 + 3 ) / 7
=> d = 1/7
Now,
The required Rational numbers will be ;
• 1st Rational no. = x + d
= - 3 + 1/7
= ( - 21 + 1 ) / 7
= -20/7
• 2nd Rational no. = x + 2d
= - 3 + 2/7
= ( - 21 + 2 ) / 7
= -19/7
• 3rd Rational no. = x + 3d
= - 3 + 3/7
= ( - 21 + 3 ) / 7
= -18/7
• 4th Rational no. = x + 4d
= - 3 + 4/7
= ( - 21 + 4 ) / 7
= -17/7
• 5th Rational no. = x + 5d
= - 3 + 5/7
= ( - 21 + 5 ) / 7
= -16/7
• 6th Rational no. = x + 6d
= - 3 + 6/7
= ( - 21 + 6 ) / 7
= -15/7
Hence,
Required Rational numbers are ;
-20/7 , -19/7 , -18/7 , -17/7 , -16/7 , -15/7