There's no particular reason why they SHOULD be equivalent. Let's examine their decimal values:
2/3 = 0.666
6/8 = 0.750
Can you see now that [6/8] is larger than [2/3] ?
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Six and two thirds divided by seven eighths = 713/21
You multiply the two fractions.
three eighths, two thirds, four fifths.
four eighths, which simplifies to one half.
31/48Thirty one forty eighths.