Can you show me how to multiply these fractions: 8/12 14/22 and 22/45 4/18?

For $\frac{8}{12}$, the greatest common factor of 8 and 12 is 4.

$$\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$$

For $\frac{14}{22}$, the greatest common factor of 14 and 22 is 2.

$$\frac{14 \div 2}{22 \div 2} = \frac{7}{11}$$

$$\frac{2}{3} \times \frac{7}{11} = \frac{2 \times 7}{3 \times 11} = \frac{14}{33}$$

The result for the first problem is $\boxed{\frac{14}{33}}$.

:

$$\frac{22}{45} \times \frac{4}{18}$$

Find common factors between a numerator and a denominator across the multiplication sign.
We can simplify 22 (numerator of the first fraction) and 18 (denominator of the second fraction) by dividing both by their common factor, 2.

$$22 \div 2 = 11$$ $$18 \div 2 = 9$$

The expression now becomes:

$$\frac{11}{45} \times \frac{4}{9}$$

There are no further common factors between the numerators (11, 4) and the denominators (45, 9).

$$\frac{11 \times 4}{45 \times 9} = \frac{44}{405}$$

The result for the second problem is $\boxed{\frac{44}{405}}$.