6. Health Option
6.2 Ratio, Rate, and Percent; Health Applications
Learning Objectives
By the end of this section it is expected that you will be able to:
- Write a ratio as a fraction
- Application of ratio
- Write ratio as a fraction
- Find unit rate
- Use the definition of percent
- Convert percents to fractions and decimals
- Convert decimals and fractions to percents
Write a Ratio as a Fraction
Ratios
A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of to is written
In this section, we will use the fraction notation. When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number. Because a ratio compares two quantities, we would leave a ratio as instead of simplifying it to so that we can see the two parts of the ratio.
EXAMPLE 1
Write each ratio as a fraction: a) b) .
| Write as a fraction with the first number in the numerator and the second in the denominator. | |
| Simplify the fraction. |
We leave the ratio in b) as an improper fraction.
| Write as a fraction with the first number in the numerator and the second in the denominator. | |
| Simplify. |
TRY IT 1
Write each ratio as a fraction: a) b) .
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Applications of Ratios
One real-world application of ratios that affects many people involves measuring cholesterol in blood. The ratio of total cholesterol to HDL cholesterol is one way doctors assess a person’s overall health. A ratio of less than to 1 is considered good.
EXAMPLE 2
Hector’s total cholesterol is mg/dl and his HDL cholesterol is mg/dl. a) Find the ratio of his total cholesterol to his HDL cholesterol. b) Assuming that a ratio less than to is considered good, what would you suggest to Hector?
a) First, write the words that express the ratio. We want to know the ratio of Hector’s total cholesterol to his HDL cholesterol.
| Write as a fraction. | |
| Substitute the values. | |
| Simplify. |
b) Is Hector’s cholesterol ratio ok? If we divide by we obtain approximately , so . Hector’s cholesterol ratio is high! Hector should either lower his total cholesterol or raise his HDL cholesterol.
TRY IT 2
Find the patient’s ratio of total cholesterol to HDL cholesterol using the given information.
Total cholesterol is mg/dL and HDL cholesterol is mg/dL.
Show answer
Write a Rate as a Fraction
Frequently, using rate, we compare two different types of measurements. Examples of rates are kilometres in hours, words in minutes, and dollars per ounces.
Rate
A rate compares two quantities of different units. A rate is usually written as a fraction.
When writing a fraction as a rate, we put the first given amount with its units in the numerator and the second amount with its units in the denominator. When rates are simplified, the units remain in the numerator and denominator.
EXAMPLE 3
A healthy heart has a rate around 72 beats per 60 seconds. Write this rate as a fraction.
| Write as a fraction, 72 beats in t