Overview: Why Proportions?
Solving proportions is an important math skill, both on tests and in everyday life. In addition, understanding proportions is critical in the sciences, as elements exist in varying quantities in compounds and mixtures. Understanding proportions within populations and how they work can also be essential as part of statistical analysis in social sciences.
Proportions as Ratios
Proportions are used most simply in problems like ” If c cans of soup can make x cups, how many cans will make y cups?” This can be represented simply as c/x = n/y. It can be solved by cross-multiplication, or xn =cy, so n =cy/x. If the x, y, c, n don’t make much sense, try substitution on the practice problem. If 2 cans of soup can make 6 cups, how many cans will make 9 cups? Then, 2/6 = n/9, or 6n = 2(9) or 6n/6 = 18/6, or 3. Granted, the problems on the SAT or ACT won’t be that easy, but those that use proportions are extensions of problems like that.
Proportions as Fractions
Most proportion problems are fractions in plain sight. (This includes percentage problems, which are fractions of 100 and can be converted easily to decimals). The numerator can be one expression and the denominator can be another expression. As long as the numerators and denominators match on both sides, they can be cross multiplied and solved like the cans and cups in the ratio problem.
Proportions in Science Reading Passages
Math proportions can also be tested during reading comprehension and on science questions. For example, a reading passage may be presented about the process of photosynthesis. According to the chemical equations for photosynthesis, free oxygen molecules are produced from water and chlorophyll after the action of sunlight. Understanding that the amount of oxygen that is produced is in proportion to the elements before photosynthesis will help with comprehension questions.
Proportions in Statistics
Statistical analysis is used as a tool in most social science research. The essential question in any experiment or collection of data is “Does the data deviate significantly from the expected proportions on some measure?” For example, suppose teachers in high school Algebra II classes in a particular school want to know how their classes this year perform as compared with the previous year. They can record data on students taking a test last year, and compare the proportion of student scores above a certain cutoff on the same test given this year.
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