Question 48 of 58beginner🔧 ApplyNumerical2 marks

Find 6 rational numbers between 3 and 4.

Correct Answer

25/8, 26/8, 27/8, 28/8, 29/8, 30/8

Exercise: END-OF-CHAPTER EXERCISES | Q: 5 | (Page 25)
For More Understanding

Explanation

The textbook context suggests expressing numbers in the form k1/m and k2/m where the difference between numerators is greater than n+1 (here, 6+1=7). By choosing a denominator of 8, we convert 3 and 4 to 24/8 and 32/8. The integers between 24 and 32 provide the numerators for the required rational numbers.

Solution Steps

  1. Step 1: Choose a denominator greater than 6+1=7. Let's choose 8.

  2. Step 2: Convert 3 and 4 to equivalent rational numbers with denominator 8: 3 = 24/8 and 4 = 32/8.

  3. Step 3: Identify integers between 24 and 32, which are 25, 26, 27, 28, 29, 30, 31.

  4. Step 4: Select any 6 integers to form the rational numbers: 25/8, 26/8, 27/8, 28/8, 29/8, 30/8.

PreviousNext