Solving proportions
Solving Proportions
MATT222 Intermediate Algebra
A comparison of two numbers is referred to as a ratio, similar to fractions that can be reduced to lowest terms and then converted into a ratio of integers. Ratios allow one to compare sizes of two quantities and unit measurements. Any statement expressing the equality of two ratios is known as a proportion, which is used in numerous formulas in today’s real world settings and applications. Using proportions is an effective way to find solutions by using the extreme means property or cross-multiplying. Extreme means property is simply the end result of the product of the extremes equaling the products of the means. Cross-multiplying is a short cut in proportions providing it is a faster way to solutions rather than multiplying each side of the rational expression equation by the LCD. Applications of rational expressions involving formulas include finding the equation of a line, distance, rate, time, uniform motion, and work problems. Proportions are used on a daily basis without even one realizing it by comparing measurements, unit pricing, driving distances, and calculating populations and wildlife on a daily basis to find a solution. For example, I will be using the extreme means property to estimate bear population in Keweenaw Peninsula. I was asked to solve problem #56, on page 437 of Elementary and intermediate algebra, (Dugopolski, M., 2012) which states, that conservationists captured, tagged, and released 50 bears. Over a one-year period, a random sample of 100 bears included only 2 tagged bears in Keweenaw Peninsula. To calculate the proportion, it will allow me to expect the ratio of bears that were originally tagged to the whole population is equal to the ratio of the returning bears totaling 100 but only 2 tagged bears to the size of the sample. The variable “b” for bears is applied, then followed by cross-multiplying the extremes and means to the proper set
MATT222 Intermediate Algebra
A comparison of two numbers is referred to as a ratio, similar to fractions that can be reduced to lowest terms and then converted into a ratio of integers. Ratios allow one to compare sizes of two quantities and unit measurements. Any statement expressing the equality of two ratios is known as a proportion, which is used in numerous formulas in today’s real world settings and applications. Using proportions is an effective way to find solutions by using the extreme means property or cross-multiplying. Extreme means property is simply the end result of the product of the extremes equaling the products of the means. Cross-multiplying is a short cut in proportions providing it is a faster way to solutions rather than multiplying each side of the rational expression equation by the LCD. Applications of rational expressions involving formulas include finding the equation of a line, distance, rate, time, uniform motion, and work problems. Proportions are used on a daily basis without even one realizing it by comparing measurements, unit pricing, driving distances, and calculating populations and wildlife on a daily basis to find a solution. For example, I will be using the extreme means property to estimate bear population in Keweenaw Peninsula. I was asked to solve problem #56, on page 437 of Elementary and intermediate algebra, (Dugopolski, M., 2012) which states, that conservationists captured, tagged, and released 50 bears. Over a one-year period, a random sample of 100 bears included only 2 tagged bears in Keweenaw Peninsula. To calculate the proportion, it will allow me to expect the ratio of bears that were originally tagged to the whole population is equal to the ratio of the returning bears totaling 100 but only 2 tagged bears to the size of the sample. The variable “b” for bears is applied, then followed by cross-multiplying the extremes and means to the proper set
References: ] Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing. Retrieved from http:// ashford.ebooks.edu (2009). Word problems involving proportions [Video]. Retrieved from http://www.youtube.com/watch