Question

Using the average method, find four rational numbers between -2/9 and 1/2​

Answer 1

Answer:

Answer in the attachment

Answer 2

Answer:

Here we have to find 4 rational numbers between 1 and 2.

As, we know, the rational number between a and b is given by, (a+b)2

Hence, the rational number between 1 and 2 is (1+2)2=32=1.5

Rational number between 1 and 3/2 is ⎡⎣⎢⎢⎢1+(32)2⎤⎦⎥⎥⎥=54=1.25

Rational number between 1 and 5/4 is ⎡⎣⎢⎢⎢1+(54)2⎤⎦⎥⎥⎥=98=1.125

Rational number between 3/2 and 2 is ⎡⎣⎢⎢⎢(32)+22⎤⎦⎥⎥⎥=74=1.75

Therefore, four rational numbers between 1 and 2 are 9/8, 5/4, 3/2, and 7/4.

Note: Whenever such a type of question appears, i.e., it is asked to find a rational number between any two rational numbers, suppose x and y, the simplest approach is to divide their sum by 2, as mentioned in the question. Proceed step by step, obtain the value of (sum of the two no.)/2, then find the next rational number by dividing the sum of the first rational no. obtained in step 1 with the first number in the range, repeat it till you get all the required rational numbers.

Step-by-step explanation: