A woman spent 1/4 of her salary on drugs and 1/8 on rent, what fraction of her salary is left? b. Simplify 2-2/3 x 1 1/2 - 4 4/5

To do this, we add the fractions spent on drugs and rent.

$$\text{Total spent} = \frac{1}{4} + \frac{1}{8}$$

To add these fractions, find a common denominator, which is 8.

$$\text{Total spent} = \frac{1 \times 2}{4 \times 2} + \frac{1}{8} = \frac{2}{8} + \frac{1}{8} = \frac{2+1}{8} = \frac{3}{8}$$

The total salary can be represented as 1 (or $\frac{8}{8}$). To find the fraction left, subtract the total fraction spent from 1.

$$\text{Fraction left} = 1 - \frac{3}{8}$$ $$\text{Fraction left} = \frac{8}{8} - \frac{3}{8} = \frac{8-3}{8} = \frac{5}{8}$$

The fraction of her salary left is $\boxed{\frac{5}{8}}$.

Question 1b: Simplify $2 \frac{2}{3} \times 1 \frac{1}{2} - 4 \frac{4}{5}$

$$2 \frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6+2}{3} = \frac{8}{3}$$ $$1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2+1}{2} = \frac{3}{2}$$ $$4 \frac{4}{5} = \frac{(4 \times 5) + 4}{5} = \frac{20+4}{5} = \frac{24}{5}$$

$$\frac{8}{3} \times \frac{3}{2}$$

We can cancel out the 3s and simplify the 8 and 2.

$$\frac{8}{\cancel{3}} \times \frac{\cancel{3}}{2} = \frac{8}{2} = 4$$

Now we have $4 - \frac{24}{5}$.
To subtract, find a common denominator, which is 5.

$$4 - \frac{24}{5} = \frac{4 \times 5}{5} - \frac{24}{5} = \frac{20}{5} - \frac{24}{5}$$ $$= \frac{20 - 24}{5} = \frac{-4}{5}$$

The simplified expression is $\boxed{-\frac{4}{5}}$.