Final answer:
To find the rational number lying at half of the way between -4 3/7 and 8 1/3, first convert the mixed numbers into improper fractions. Then find the average of the two fractions to get the final answer.
Step-by-step explanation:
To find the rational number lying at half of the way between -4 3/7 and 8 1/3, we can first convert the mixed numbers into improper fractions. -4 3/7 is equal to -31/7 and 8 1/3 is equal to 25/3.
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Next, we find the average of the two fractions by adding them together and dividing the sum by 2. (-31/7 + 25/3) / 2 = -43/21 + 25/6 = -753/126 + 525/126 = -228/126 = -38/21.
Therefore, the rational number lying at half of the way between -4 3/7 and 8 1/3 is -38/21.