7. $$ 6 \frac{25}{27}-4 \frac{4}{9}-1 \frac{1}{3} $$

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UpStudy AI · Accepted Answer

Convert each mixed number to an improper fraction:

- $$6 \frac{25}{27} = \frac{6 \times 27 + 25}{27} = \frac{162 + 25}{27} = \frac{187}{27}$$
- $$4 \frac{4}{9} = \frac{4 \times 9 + 4}{9} = \frac{36 + 4}{9} = \frac{40}{9}$$
- $$1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3}$$

Find a common denominator for $$27$$, $$9$$, and $$3$$. The common denominator is $$27$$:

- For $$\frac{40}{9}$$:
  $$
  \frac{40}{9} = \frac{40 \times 3}{9 \times 3} = \frac{120}{27}
  $$
- For $$\frac{4}{3}$$:
  $$
  \frac{4}{3} = \frac{4 \times 9}{3 \times 9} = \frac{36}{27}
  $$

Now perform the subtraction:
$$
\frac{187}{27} - \frac{120}{27} - \frac{36}{27} = \frac{187 - 120 - 36}{27} = \frac{31}{27}
$$

Write $$\frac{31}{27}$$ as a mixed number:
$$
\frac{31}{27} = 1 \frac{4}{27}
$$

Thus, the final answer is $$1 \frac{4}{27}$$.
The final answer is $$1 \frac{4}{27}$$.

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