Question

What is the ratio of the two values?

1. 5 pages in 60 min
2. 105 miles in 2 hours
3. $33 for 5 lb
4. 50 pages in 2 hours
a) 1:12
b) 105:2
c) $33:5 lb
d) 25:1

Answer 1

A ratio compares two quantities and can be written in various forms. The ratios for the given examples are 1:12 for reading speed, 105:2 for driving speed, $33:5 lb for cost per pound, and 25:1 for reading speed over hours.

Step-by-step explanation:

The ratio is a comparison of two quantities. It can be expressed in several ways, such as fractions, with a colon, or with the word "to". For example, 2/3, 2:3, or "2 to 3" all represent the same ratio. A proportion is a statement that two ratios are equivalent. For instance, 1/2 = 3/6 is a proportion because both sides reduce to the same value when simplified.

A unit rate is a ratio where one of the quantities compared is 1. An example of a unit rate is 55 miles per hour, which can also be written as 55 miles/1 hour. Similarly, a unit scale is a ratio that compares the dimensions of a real object to a model or drawing representation. The unit scale does not necessarily include a value of 1. For example, a map scale might be 1/2 inch = 100 feet, written as the ratio 0.5 inches/100 feet.

Applying the concept of ratio to the question at hand, we need to express each statement as a ratio:

1. 5 pages in 60 minutes would be 1:12, since dividing both quantities by their greatest common divisor results in 1 page every 12 minutes.
2. 105 miles in 2 hours is simply 105:2 as a ratio, representing 105 miles for every 2 hours of travel.
3. $33 for 5 lb can be expressed as the ratio $33:5 lb, indicating the cost per pound.
4. 50 pages in 2 hours reduces to a ratio of 25:1 when simplified, meaning 25 pages per hour.