Yes, that is correct.
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negative one ninth
No. One third is 1/3 and one ninth is 1/9. A ninth is much smaller, three thirds is equal to one ninth - 3/9=1/3. Another way to look at it is like a pie. If you cut one pie into three pieces and one pie into nine and took a piece from each. The piece that you took from the pie cut into three would be much bigger, and equal to three pieces of the pie you cut into nine.
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-1/9 x 1/9 = -1/81