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Problem Solving

Problem Solving.  Problem solving involves developing a plan, and mapping out a pathway through a problem before solving.  Any two measurements that are equal to one another but expressed in different units can be written as a ratio.

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Problem Solving

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  1. Problem Solving  Problem solving involves developing a plan, and mapping out a pathway through a problem before solving.  Any two measurements that are equal to one another but expressed in different units can be written as a ratio.  A ratio of equivalent measurements is called a conversion factor and is equal to unity.  Conversion factors are used in the problem solving technique of dimensional analysis.  A ratio of equivalent measurements has two forms. The correct conversion factor for solving a particular problem will have the known unit in the denominator and the unknown unit in the numerator.  Conversion problems in which you are asked to express a measurement in some other unit are easily solved using dimensional analysis.  In dimensional analysis, units are used to help write the solution to a problem.  More than one conversion factor may be required in some more complex conversion problems.  The given measurement in a rate problem has a ratio of units. Rate problems may be solved by converting the unit in the numerator followed by converting the unit in the denominator.

  2. Chapter Vocabulary • Conversion factor: how measurements are related to each other. • Dimensional anaylsis: • using units to figure out problems • unit • Grams, ounces, and other labels which tell you what type of quantity you are using. • density • How mass is related to volume. • Boling point • The temperature at which the vapor pressure equals atmospheric pressure • temperature • A measure of the hotness or coldness of a substance

  3. Dimensional Analysis • Step 1: copy the known • Step 2: identify and copy the conversion factor • Step 3: multiply the numerator, divide the denominator

  4. More vocabulary • Celsius • Metric measurement of temperature • volume • Length x width x height or area x height. How much space is occupied by an object. • mass • The quantity of matter • known • The thing given in the problem. • Unknown • The thing you are trying to find in the problem

  5. 5280 feet = 1 mile 16 oz = 1 pounds 12 inches = 1 foot 1 pint = 473 milliliters 1 ton = 2000 pounds 5 carats = 1 kilograms Step 1: copy the known Step 2: identify and copy the conversion factor Step 3: multiply the numerator, divide the denominator 32 miles = ? feet _5280 feet_ 1 mile 32 miles = 168960 feet = 170,000 feet 45 oz = ? pounds _1 pound_ 16 oz = 2.8125 pound = 2.8 pound 45 oz

  6. 5280 feet = 1 mile 16 oz = 1 pounds 12 inches = 1 foot 1 pint = 473 milliliters 1 ton = 2000 pounds 5 carats = 1 kilograms 3.4 pints = ? milliliters _473 mL_ 1 pint 3.4 pints = 1608.2 mL = 1600 mL 5.6 pounds = ? tons _1 ton_ 2000 pounds 5.6 pounds = 0.0028 tons

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