Ratios (1/3) -- College Mathematics Review for Nursing S...

Ratios Ratios are numbers that are used in nursing to compare two numbers that have a relationship to each other. In nursing practice, there are many numbers that are related to each other. For example, 50 milligrams are contained in each vial. Learning Objectives By the end of this section, you will be able to: Write a Ratio as a Fraction When you apply for a mortgage, the loan officer will compare your total debt to your total income to decide if you qualify for the loan. This comparison is called the debt-to-income ratio. A ratio compares two quantities that are measured with the same unit. If we compare 𝑎 and 𝑏, the ratio is written as to , , or . RATIOS A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of to is written to , , or .. 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 5.58: Write each ratio as a fraction. Write each ratio as a fraction of whole numbers: - ⓐ to - ⓑ to Solution: | ⓐ to | | | Write as a fraction with the first number in the numerator and the second number in the denominator. | | | Simplify the fraction. | | ⓑ to | | | Write as a fraction with the first number in the numerator and the second number in the denominator. | | | Simplify. | We leave the ratio in ⓑ as an improper fraction. Try It: Write each ratio as a fraction. 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 to is considered good. Example 5.6.1 Hector’s total cholesterol is mg/dl and his HDL cholesterol is mg/dl. - ⓐ Find the ratio of his total cholesterol to his HDL cholesterol. - ⓑ Assuming that a ratio less than to is considered good, what would you suggest to Hector? Solution: ⓐ 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 Hector’s values. | | | Simplify the fraction. | ⓑ Is Hector’s cholesterol ratio ok? If we divide by , we obtain approximately , so . Now compare Hector’s value to the ratio that is considered good: . Hector’s cholesterol ratio is high! Hector should either lower his total cholesterol or raise his HDL cholesterol. Try It: Ratio of Total cholesterol to HDL cholesterol Ratios of Two Measurements in Different Units To find the ratio of two measurements, we must make sure the quantities have been measured with the same unit. If the measurements are not in the same units, we must first convert them to the same units. We know that to simplify a fraction, we divide out common factors. Sim