868 WordsDec 23, 20134 Pages

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*…show more content…*

x - 3 4 (x – 3) Cancel out common factors which eliminates denominator on left.
y – 1 + 1 = -3x – 3 +1 To isolate y, 1 is added to both sides. Cancel common factors. y = -3 x -1 4 Equation complete and simplified.
For this equation, I could have multiplied the LCD to both sides, but I found the extreme means property was an efficient shortcut. Cross- multiplying allowed me to eliminate the fractions and have the same ending result. We can now consider this an extraneous solution because the number showing as the solution but causes zero (0) in the denominator. As rational expressions can be tricky when there is a variable involved in the denominator so caution must be adhered.
The use of proportions is everyday life and real world settings and applications are used without one even realizing it. While proportions can determine a solution whether it be driving distance, estimated population count, unit measuring, gas mileage, or to estimate an average time for a job to be completed, it is a necessary tool that is used in many ways. The ratios that build the proportion can be easily solved by cross- multiplying the extremes and means in a fast and effective way. The wildlife can be assured that their tags will be calculated with an accurate solution for any conservationist inquiring about a certain species. So the next time you find

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