Final answer:
The ratio 3.20 to 1.20, when simplified and written as a fraction in simplest form, is 8/3. To achieve this, both terms of the ratio are multiplied by 100 and then simplified by dividing by the greatest common divisor. Ratios can form proportions that are used to find unknown quantities, such as distances on a map scale.
Step-by-step explanation:
Converting a Ratio to a Fraction
To write the ratio 3.20 to 1.20 as a fraction in simplest form with whole numbers, you can start by eliminating the decimal points by multiplying both terms of the ratio by 100. Doing so, you get 320 to 120, which can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 40 in this case. This gives you 8 to 3, or written as a fraction, it's 8/3.
When working with ratios and proportions, remember that you can set two ratios equal to one another to form a proportion. For example, if you have a scale where the ratio is 1 inch to 2000 miles and you want to find the actual distance for a 3 inch length on the scale, you would write the proportion 1 inch/2000 miles = 3 inches/x miles and solve for x.
Ratios and proportions are useful in various contexts, such as converting scales in maps or models. The key is to ensure the units are consistent across the ratios. Whenever you're given a single unit like meters or feet, make sure to maintain that unit throughout your calculation.