Final answer:
The simplest form of the ratio for 24 messages to 10 messages is 12/5, and for 5 meters to 20 meters, it is 1/4. When setting the ratio of x meters to 11 kilometers as a proportion, it should be written as x/11000 after converting kilometers to meters using the known conversion that 1 km equals 1000 m.
Step-by-step explanation:
To write the ratio as a fraction in simplest form for the two sets of values provided:
For 24 messages to 10 messages, you divide both numbers by their greatest common divisor (GCD), which is 2. Therefore, the ratio in simplest form is 24/2 : 10/2, which simplifies to 12/5.
For 5 meters to 20 meters, the GCD is 5. The ratio in simplest form is 5/5 : 20/5, which simplifies to 1/4.
To write the proportion by setting the two ratios equal to one another using meters:
x meters / 11 kilometers
Since 1 kilometer equals 1000 meters, this proportion can be simplified by converting kilometers to meters, making the ratio x/11000.