Unit 21 Proportion.

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Presentation transcript:

Unit 21 Proportion

Basic Principles of Proportion Problems A proportion is an equation that states that two ratios are equal. Proportions are written with an equal sign between two ratios. For example: 1:2 = 3:6.

Basic Principles of Proportion Problems The first and last numbers of the proportion are called the extremes, and the two middle numbers are called the means. For a proportion to be a true proportion, the product of the means must equal the product of the extremes. If one factor in a true proportion is unknown, the missing factor can be found because the product of the means must equal the product of the extremes.

Basic Principles of Proportion Problems Cross-multiplication can be used to solve proportions. Proportions can be used while preparing solutions. Any percent can be converted to a ratio.

Proportion Example: How many grams (g) of boric acid crystals are needed to prepare 500 milliliters (mL) of a 5% boric acid solution? First calculate that a 5% boric acid solution equals 0.05 or 5/100 or 5:100 or 1:20. This means there is 1 g of boric acid crystals in every 20 mL of solution.

Proportion Set up a proportion: Multiply the means: 20 x X = 20X Multiply the extremes: 1 x 500 = 500

Proportion Write as means equals extremes: 20X = 500 Divide both sides by 20 to find X: Write the answer: X = 25 g (Use 25 g of boric acid.)

Practical Problem A public health nurse calculates that it costs $1.30 for every 2.5 miles he drives his car. If he travels 382 miles in 1 week, how much does it cost him to drive his car?

Practical Problem Set up the proportion and cross-multiply: It costs the nurse $198.64 to drive his car for 1 week.