5 5 Customary Units Dimensional Analysis
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This document provides a review of customary units, fractions, and dimensional analysis. It includes examples of using conversion factors to find a common denominator between fractions and to convert between units. Dimensional analysis is described as the process of analyzing units to determine which conversion factors to use. Examples are provided of using conversion factors and fraction bars to solve conversion problems between units like inches, feet, quarts, gallons, and yards.
5 5 Customary Units Dimensional Analysis
- 1. Review of Customary Units, Fractions, and Dimensional Analysis. By Ms. Dewey-Hoffman February 23, 2020 Chapter 5, Section 5 (if you must know)
- 2. Example of Conversion Factors To find a COMMON DENOMINATOR between Two Fractions , you MULTIPLY one or both fractions by a Conversion Factor . A Conversion Factor is always equal to 1 .
- 3. This is the Same with Conversion Factors in Converting Units! Use Equivalent Units To Write A Conversion Factor. Like: 12 inches = 1 foot. They Are Equivalent! Also: 4 quarts = 1 gallon. They Are Equivalent! Also: 24 hours = 1 day. They Are Equivalent!
- 4. Turn The Conversions Into Fractions…They’re Equivalent Just Write These Equivalents to Make a Fraction that is Equal to 1. 12 inches = 1 1 foot 2 cups = 1 8 Fluid Ounces
- 5. Dimensional Analysis The process of analyzing units to decide which conversion factors to use. When you are looking at the Legend on your handout, that’s Dimensional Analysis!
- 6. This is a Fraction Bar These Bars mean Multipl-ication and separate fractions or Conversion Factors. 10 quarts = ? gallons 10 Quarts ? Gallons Conversion Factor Goes Here 4 Quarts 1 Gallon Now turn it into a Fraction/Multiplication Problem 10 ¼ = 2 ½ gallons 10 quarts = 2 ½ gallons
- 7. This is a Fraction Bar These Bars mean Multipl-ication and separate fractions or Conversion Factors. Dealing with Mixed Numbers and Conversions? 3 3/16 yards = ? inches 1) Change Mixed Number to an Improper Fraction, then Convert. 51 Yards 1 Yard 3 Feet 1 Foot 12 Inches 16 2) Take the answer and Change to a Mixed Number. Notice how the IMPROPER Fraction looks like a Fraction on the T graph. (51 3 12) (16 1 1) = 114.75 or 114 ¾
- 8. To Compare Different Units… Change ONE Unit into the other and see which is bigger, less, or equal. Inequalities Anyone? 10 Gallons ____ 42 Quarts 42 Quarts is how many gallons? 4 Quarts for every 1 Gallon. (42/4 = 10 ½ Gallons) Which is bigger? 42 Quarts or 10 Gallons? <