Transcript Chapter 3
Chapter 3 Solving Common Fraction Equations Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Common Fraction Equations • Solved by multiplying all numerators • Then divide numerators by denominators • Numbers in equation may initially be reduced using common denominators to simplify final multiplication and division Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Calculator Solution of Equations • Most safely done by concentrating only on entries being done – Not numbers that register and change throughout calculation Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Calculator Use • Double-check all calculator entries and answers, as well as all calculations performed manually Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Answers to Fraction Equations • Can be expressed as whole numbers or to the tenth or hundredth – Depends on calculation being done Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Two Options • Option 1 – Calculator use throughout • Option 2 – Initial fraction reduction – Followed by calculator use for final division Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Which Option To Use • Use option desired or option required by instructor Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Option 1 • In continuous entries, multiply numerators and divide by denominators 2 3 5 4 2 3 5 4 = 0.3 Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Option 2 • Divide numerator 2 and denominator 4 by 2 2 3 13 becomes 5 4 5 2 3 5 2 0.3 • Use calculator to divide remaining numerator by remaining denominators Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Decimal Fraction Equations • Most dosage errors occur with use of decimal fraction equations Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Simplify Before Calculating • As with whole numbers, simplify numbers in decimal fraction equations by eliminating decimal points and reducing numbers as optional first step Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Safety Point • Take particular care with calculator entry of decimal numbers to include decimal point • Routinely double-check each entry and answer Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Option 1 • Multiply numerators and divide by denominators 0.3 2.1 1.2 0.15 0.3 2.11.2 0.15 • Answer = 3.5 (tenth) or 3.5 (hundredth) Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Option 2 • Move decimal points one place 0.3 2.1 becomes 3 210 1.2 0.15 12 15 Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Option 2 • Divide 3 and 12 by 3 • Divide 210 and 15 by 5 3 210 becomes 1 42 4 3 12 15 Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Option 2 • Divide 42 and 4 by 2 1 42 becomes 1 21 2 3 4 3 • Use calculator to divide remaining numerator by remaining denominators 21 2 3 • Answer = 3.5 (tenth) or 3.5 (hundredth) Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Multiple Number Equations • Reduction of numbers may be of particular benefit here because calculations of this type sometimes have numbers that cancel and/or reduce dramatically Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Multiple Number Equations • Use same options previously practiced with common fraction equations and decimal fraction equations Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Example of Multiple Number Fractions: Option 1 • Multiply numerators and divide by denominators 60 1000 1 6 1 4 1000 1 60 1000 6 4 1000 • Answer = 90 Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Example of Multiple Number Fractions: Option 2 • Eliminate 1000 from numerator and denominator 60 1000 1 6 becomes 60 6 1 4 1 4 1000 1 • Divide 6 and 4 by 2 60 3 1 2 Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Example of Multiple Number Fractions: Option 2 • Use calculator to divide remaining numerators by remaining denominator 60 3 2 • Answer = 90 Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED. Safety Point • Measure twice; cut once • Double-check all calculator entries, calculator answers, and manual calculations Copyright © 2010 Delmar, Cengage Learning. ALL RIGHTS RESERVED.