Simplify the following fractions: 1. 24/60 2. 33/153 3. 24/120 4. 30/21 5. 34/54 6. 22/176

Okay, let's simplify these fractions step by step.

1. $$\frac{24}{60}$$
Both 24 and 60 are divisible by 12. So, we divide both the numerator and denominator by 12:
$$\frac{24 \div 12}{60 \div 12} = \frac{2}{5}$$
So, $$\frac{24}{60} = \frac{2}{5}$$

2. $$\frac{33}{153}$$
Both 33 and 153 are divisible by 3. Let's divide by 3:
$$\frac{33 \div 3}{153 \div 3} = \frac{11}{51}$$
Now, let's see if we can simplify further. 51 = 3 * 17, and 11 is a prime number, so we cannot simplify further.
So, $$\frac{33}{153} = \frac{11}{51}$$

3. $$\frac{24}{120}$$
Both 24 and 120 are divisible by 24:
$$\frac{24 \div 24}{120 \div 24} = \frac{1}{5}$$
So, $$\frac{24}{120} = \frac{1}{5}$$

4. $$\frac{30}{21}$$
Both 30 and 21 are divisible by 3:
$$\frac{30 \div 3}{21 \div 3} = \frac{10}{7}$$
So, $$\frac{30}{21} = \frac{10}{7}$$

5. $$\frac{34}{54}$$
Both 34 and 54 are divisible by 2:
$$\frac{34 \div 2}{54 \div 2} = \frac{17}{27}$$
So, $$\frac{34}{54} = \frac{17}{27}$$

6. $$\frac{22}{176}$$
Both 22 and 176 are divisible by 22:
$$\frac{22 \div 22}{176 \div 22} = \frac{1}{8}$$
So, $$\frac{22}{176} = \frac{1}{8}$$

Here are the simplified fractions:

1. 2/5
2. 11/51
3. 1/5
4. 10/7
5. 17/27
6. 1/8