1.15 Ratios & Percentages

### Ratios

A ratio is a proportional relationship of one value to another, e.g., the ratio of gas to oil in chain saw mix. Ratios can be written either as a fraction, 1/2, or in ratio notation, 1:2. The value of a ratio is the division of the first number by the second number. For example, consider the ratio 1:40 . This ratio is read as "1 to 40". Any fraction, for instance, 1/20, can also be written as a ratio: 1:20

Example 1 - The Mara Bella District has 6 engines. The Baldy District has 5 engines. What is the ratio of engines in the Mara Bella versus the Baldy districts?

The ratio of engines in the Mara Bella versus Baldy districts is 6:5 or 6/5.

### Percentages

A percentage is another way of describing a ratio with respect to 100. Percent (%) is a value corresponding to how many out of a hundred (per hundred). For instance, if 92 out of 100 firefighters have completed the FireFighter Math course, the ratio of firefighters completing the course is 92:100, and the percentage is written as 92%.

Example 2 - Write four notations for 56.8%.

56.8% = 56.8 out of 100
56.8% = 56.8/100
56.8% = 56.8:100
56.8% = 0.568 (Note that performing this calculation results in moving the decimal two places to the left because there are two zeros in 100.)

### Percentages and Live Fuel Moistures

Percentages are useful for a number of fire science applications. One of these applications is estimating live fuel moisture. Live fuel moisture can be measured using oven drying and weighing procedures. Because this process is time-consuming and cannot be completed in the field, fire considerations are usually satisfied with a good estimate. Live fuel moisture can be estimated using the values in the figure below, which provides moisture percentages for fuels at different stages of vegetative development. For instance, from the figure, we observe that completely cured fuels have a live fuel moisture of less than 30%. This value is the result of subtracting the dry weight of the fuel from the total (wet) weight and dividing by the dry weight.

Example 3 - A fuel sample collected in the field weighs 377 grams. After the sample is dried in an oven, it weighs 198 grams. What is the live fuel moisture content?

Step 1. Subtract the dry weight from the wet weight. 377 - 198 = 179.

Step 2.Divide the difference by the dry weight and multiply by 100 to find the value as a percent. 179 / 198 × 100 = 0.904 × 100 = 90.4%.

The live fuel moisture of your sample is 90.4%.

### Problem Solving with Ratios

When solving a more complex percentage or ratio problem, write the problem down in words and numbers and work through one step at a time.

Example 4 - Sabrina has a 2-1/2 gallon container. She is going to fill it with a 40:1 gas-to-oil mixture. How much of each does she need to put into the container? Proceed through the questions below to see the steps involved in answering this question.

First, determine the number of parts needed to produce the mixture. How many parts are present in a 40:1 mixture?

The correct answer is d, 41.

A 40:1 mixture contains 40 + 1 = 41 parts.

For these 41 parts to fill the 2-1/2 gallon container, what is the volume of each part?

The correct answer is c, 0.06 gallons.

2-1/2 gallons = 2.5 gallons. 2.5 gallons/41 parts = 0.06 gallons/part.

How much gasoline and how much oil should Sabrina pour into the container? Please enter your answer in the space below in the format ?? gallons gasoline, ?? gallons oil

The correct answer is 2.44 gallons gasoline, 0.06 gallons oil. 40 parts gasoline × 0.06 gallons/part = 2.44 gallons of gasoline. 1 part oil × 0.06 gallons/part = 0.06 gallons of oil.

### Practice

Exercise 1. A commonly used ratio for relating 20-foot, eye-level, and litter-level wind speeds is 4:3:1. That is, the eye-level winds are 3/4 the 20-foot wind speed, and the litter-level winds are 1/3 the eye-level wind speed. Use this 4:3:1 ratio to answer the following questions.

1. You receive a RAWS report of 20-foot winds blowing at 24 mph. What are the winds at eye-level?

2. What are the litter level winds?

Exercise 2. When the crew leaves for a fire, they have a full tank of foam agent. This tank holds a total of 4.80 gallons. When they return to the station, they find only 0.91 gallons. Answer the questions below to assess foam amounts.

1. What percentage of the total foam is left?

2. What percentage of the foam was used?