No. The easiest way to see this is to multiply 4/5 by 9/9 (i.e. 1) to get 36/45, and to multiply 8/9 by 5/5 (also 1) to get 40/45. 40 > 36, so 40/45 > 36/45, so 8/9 is larger than 4/5.
Or you could just use a calculator and actually do the division; 4/5 is 0.8 (exactly) and 8/9 is 0.888... (repeating) which is obviously larger.
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8/9 ÷ 4/5 = 11/9
They are equivalent.
four fifths
One is bigger than the other,
It is: 4/9 times 4/5 = 16/4516/45