9514 1404 393
Answer:
-0.67, -0.68, -0.69, -0.70, -0.71
Step-by-step explanation:
There are an infinite number of ways to do this.
Perhaps the simplest is to do it in decimal.
-4/5 = -0.8
-2/3 = -0.666... (repeating 6)
Any negative decimal number between these values will do. For example, ...
-0.67, -0.68, -0.69, -0.70, -0.71
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If you want to choose fractions that are evenly spaced between the given values, you can find their difference, then divide that difference into 6 parts (1 more than the number of numbers you need).
-2/3 -(-4/5) = 4/5 -2/3 = (12 -10)/(5·3) = 2/15 . . . . length of interval
1/6 of this difference is ...
(1/6)(2/15) = 2/90 = 1/45
The interval end point nearest 0 is ...
-2/3 = -30/45
so the 5 intermediate values will be that value with -1/45 repeatedly added:
-31/45, -32/45, -33/45 = -11/15, -34/45, -35/45 = -7/9
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Additional comment
The fractions we came up with could be referred to as "5 arithmetic means between -2/3 and -4/5." There is nothing in the problem statement suggesting the values need to be evenly spaced.
When doing this in decimal, you can obtain a new value simply by adding more digits to the decimal fraction:
-0.68, -0.685, -0.6853, -0.68531, -0.799
