Kyle is thinking of a number greater than - 6 2/3 and less than - 6 1/2. which number could be kyle's number

-6 2/3 = - (6*3+2) / 3=-20/3=-6.666 ... ≈-6.67

-6 1/2 = - (6*2+1) / 2=-13/2=-6.5

Therefore:

-6.67
then:

We have infinites numbers:

x₁=-6.65

x₂=-6.61

x₃=-6.532

x₄=-6.584 ...

The number is greater than - 6 2/3 and less than - 6 1/2.

We focus on the 2/3 and 1/2

Since it is a negative number we think of a fraction less than 2/3 and greater than 1/2, because of the negatives.

2/3 is around 0.66, 1/2 is = 0.5, Example is 0.6 = 6/10 = 3/5

A number that fits is - 6 3/5.

Check:

- 6 2/3 ≈ - 6.66

-6 3/5 = - 6.60

-6 1/2 = - 6.50

-6.60 is greater than - 6.66, and less than - 6.50