Final answer:
The complex ratio 2/5 : 1/10 : 2/5 simplifies to the number 10, by first dividing 2/5 by 1/10 to get 4, and then dividing 4 by 2/5 to reach the final answer.
Step-by-step explanation:
The question asks to simplify the complex ratio 2/5 : 1/10 : 2/5. This can be interpreted as (2/5) divided by (1/10), and then divided by (2/5) again. To solve this, we convert the division of fractions into multiplication by the reciprocal. The reciprocal of 1/10 is 10/1, so (2/5) divided by (1/10) becomes (2/5) × (10/1). When we multiply these two fractions, we get (2 × 10) / (5 × 1), which simplifies to 20/5. The value 20/5 is equal to 4. Now, we need to divide this result by the third fraction, which is again, 2/5. Using the same method of reciprocals, we get 4 × (5/2). When you multiply 4 by 5/2, you get a result of (4 × 5) / 2 which is 20/2, which simplifies to 10; hence the final answer to the complex ratio is 10.