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Math: Basic Tutorials : Proportions
Proportions
A proportion is formed when two rates or ratios are equal to one another. For example, the scale on a map can be used to find the real distance using proportions. In this module, you will review how to use proportions to solve for unknown variables, and you will explore common applications of proportions, including unit conversions and dosage calculations.
Examples & Activity
Examples
Click on the titles below to view each example.
You have to write a 15-page paper. If it takes you 2 hours to write 4 pages, how long will it take you to finish the paper?
Line 1: Set up the problem as equivalent fractions and let x represent the unknown number of hours. 1.5 hours over 4 pages equals x hours over 15 pages.
Line 2: Cross multiply, which means to multiply the numerator of the fraction on the left by the denominator of the fraction on the right, and multiply the numerator of the fraction on the right by the denominator of the fraction on the left. 4x equals 2 times 15.
Line 3: Solve for x by dividing both sides by 4. 4x over 4 equals 30 over 4.
Line 4: x equals 7.5
Line 5: It will take 7.5 hours to finish a 15-page paper.
If there are 3.28 feet in a meter, convert 23 feet to meters. Round to the nearest tenth of a meter.
Line 1: Set up the problem as a proportion with equivalent fractions and let x represent the unknown number of meters. 3.28 feet over 1 meter equals 23 feet over x meters.
Line 2: Cross multiply which means to multiply the numerator of the fraction on the left by the denominator of the fraction on the right, and multiply the numerator of the fraction on the right by the denominator of the fraction on the left. 3.28 times x equals 23 times 1.
Line 3: Solve for x by dividing both sides of the equation by 3.28. 3.28x over 3.28 equals 23 over 3.28.
Line 4. Round the final answers to the nearest tenth of a meter. X equals 7.0 meters.
Line 5: 23 feet is equivalent to 7.0 meters.
Line 1: First, find how many milligrams of the drug the patient needs. Set up the problem as a proportion with equivalent fractions, and let x represent the unknown number of milligrams. 1.5 milligrams over 1 kilogram equals x milligrams over 90.5 kilograms.
Line 2: Cross multiply and solve for x. 1 times x equals 1.5 times 90.5.
Line 3: Solve for x. x equals 135.75.
Line 4: Therefore, the patient needs 135.75 milligrams of medication.
Line 5. Next, find the number of mL of the drug that needs to be administered. Set up another proportion using the concentration on hand, and let x represent the required number of mL needed for the patient. 20 milligrams over 1 milliliter equals 135.75 over x milliliters.
Line 6. Cross multiply. 20 times x equals 1 times 135.75.
Line 7. Solve for x. 20 x over 20 equals 135.75 over 20.
Line 8: Simplify and round your answer to the nearest tenth. X equals 6.8 milliliters.
Line 9: Therefore, the patient will require 6.8 mL of the prescribed medication.
Summary and Worksheet
- Summary: Proportions - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Proportions - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
Attribution
Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window