How do you write these fractions in simplest form: 1/2 * 5/8 * 4/5 - 3/8 / 3/4 - 16/9 / 8?

To write these fractions in simplest form, we need to simplify each fraction individually and then perform the operations in order. Let's break it down step by step:

1. Multiply the fractions: 1/2 * 5/8 * 4/5

- Multiply the numerators (top numbers) together: 1 * 5 * 4 = 20

- Multiply the denominators (bottom numbers) together: 2 * 8 * 5 = 80

- The resulting fraction is 20/80

2. Divide the fractions: 3/8 / 3/4

- To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

- Flip the second fraction to get its reciprocal: 3/4 becomes 4/3

- Multiply the fractions: 3/8 * 4/3

- Multiply the numerators: 3 * 4 = 12

- Multiply the denominators: 8 * 3 = 24

- The resulting fraction is 12/24, which can be simplified further.

3. Divide the fractions: 16/9 / 8

- To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

- Flip 8 to get its reciprocal: 8 becomes 1/8

- Multiply the fractions: 16/9 * 1/8

- Multiply the numerators: 16 * 1 = 16

- Multiply the denominators: 9 * 8 = 72

- The resulting fraction is 16/72, which can also be simplified further.

Now, let's simplify the resulting fractions:

1. Simplify 20/80:

- Both the numerator and denominator can be divided by 20.

- Divide 20 by 20: 20/20 = 1

- Divide 80 by 20: 80/20 = 4

- The simplified fraction is 1/4

2. Simplify 12/24:

- Both the numerator and denominator can be divided by 12.

- Divide 12 by 12: 12/12 = 1

- Divide 24 by 12: 24/12 = 2

- The simplified fraction is 1/2

3. Simplify 16/72:

- Both the numerator and denominator can be divided by 8.

- Divide 16 by 8: 16/8 = 2

- Divide 72 by 8: 72/8 = 9

- The simplified fraction is 2/9

Now, let's substitute the simplified fractions back into the original expression:

1/2 * 5/8 * 4/5 - 3/8 / 3/4 - 16/9 / 8

= 1/4 * 1/2 * 2/9 - 1/2 / 3/4 - 2/9 / 8