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Dimensional Analysis

Dimensional Analysis. Lecture 3 Chapter 3. Solving common fraction equations. Whole number equations 2 X 5 = 7 6 First reduce with common denominator and eliminating the zeros Second multiple across 1 X 5 = 5 7 X 3 = 21 Third divide the two products

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Dimensional Analysis

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  1. Dimensional Analysis Lecture 3 Chapter 3

  2. Solving common fraction equations • Whole number equations 2 X 5 = 7 6 First reduce with common denominator and eliminating the zeros Second multiple across 1 X 5 = 5 7 X 3 = 21 Third divide the two products 5 ÷ 21 = 0.238

  3. Solving common fraction equations • Whole number equations 2 X 5 = 7 6 Calculator: 2 X 5 ÷ 7 ÷ 6 = 0.238

  4. Solving common fraction equations • Whole number equations 200 X 75 = 50 125 First – reduce with common denominator and eliminating zeros Second multiple across 4 x 3 = 12 1 X 5 = 5 Third – divide the two products 12 ÷ 5 = 2.4

  5. Solving common fraction equations • Whole number equations 200 X 75 = 50 125 Calculator 200 x 75 ÷ 50 ÷ 125 = 2.4

  6. Solving common fraction equations • Whole number equations: Express to the nearest hundredth 7 X 25 X 120 = 3 21 50 First: reduce with common denominator and eliminating zeros Second: multiple across 1 x 1 x 40 = 40 1 x 3 x 2 = 6 Third: divide the two products 40 ÷ 6 = 6.666666666  6.67

  7. Solving common fraction equations • Whole number equations: Express to the nearest hundredth 7 X 25 X 120 = 3 21 50 Calculator 7 x 25 x 120 ÷ 3 ÷ 21 ÷ 50= 6.6666666 nearest hundredth 6.67

  8. Solving common fraction equations • Whole number equations: Express to the nearest tenth 20 X 10,000 X 1200 X 4000 = 1 60,000 40 600 First: reduce with common denominator and eliminating zeros Second: multiple across 1 x 1 x 2 x 1000 = 2000 1 x 3 x 1 x 1 = 3 Third: divide the two products 2000 ÷ 3 = 666.6666666  666.7

  9. Solving common fraction equations • Whole number equations: Express to the nearest tenth 20 X 10,000 X 1200 X 4000 = 1 60,000 40 600 Calculator 20 x 10,000 x 1200 x 4000 ÷ 1 ÷ 60,000 ÷40 ÷ 600 =

  10. Your Turn: Express to the nearest tenth • 3 / 7 x 11 / 2 = • 3 / 7 x 500 / 60 x 1000 / 200 = • 2000 / 2700 x 1100 / 900 x 60 / 90 =

  11. Your Turn: Express to the nearest tenth • 3 / 7 x 11 / 2 = • 2.1428  2.1 • 3 / 7 x 500 / 60 x 1000 / 200 = • 17.857  17.9 • 2000 / 2700 x 1100 / 900 x 60 / 90 = • 0.77  0.8

  12. Decimal Fraction Equations • Extreme care must be taken with calculator entry of decimal numbers, to include the decimal point, and entries and answers must always be double checked.

  13. Example Solve the equation to the nearest hundredth 0.3 x 2.5 1.75 1 • Eliminate the decimal point, eliminate zeros & reduce 30 X 25 = 3 x 1 = 3 175 10 7 1 7 • Divide 3 ÷ 7 = 0.428  0.43

  14. Example Solve the equation to the nearest hundredth 0.3 x 2.5 1.75 1 • Calculator 0.3 x 2.5 ÷ 1.75 ÷ 1 = 0.428  0.43

  15. Your Turn • Solve the equations. Express your answer to the nearest tenth and hundredth. A calculator may be used for the final division. • 2.1 / 4.08 x 0.7 / 5.6 • 0.4 / 1.2 x 4 / 2.1 • 1.75 / 0.85 x 2.5 / 4

  16. Your Turn • Solve the equations. Express your answer to the nearest tenth and hundredth. A calculator may be used for the final division. • 2.1 / 4.08 x 0.7 / 5.6 • tenth = 0.1 hundredth = 0.06 • 0.4 / 1.2 x 4 / 2.1 • tenth = 0.6 hundredth = 0.63 • 1.75 / 0.85 x 2.5 / 4 • tenth = 1.3 hundredth = 1.29 More problems page 28

  17. Multiple number equations • Eliminate the decimals, eliminate zero’s, reduce then solve • (don’t panic!) 60 X 1000 x 1 x 6 = 1 4 1000 1 • Calculator 60 x 1000 x 1 x 6 ÷ 1 ÷ 4 ÷ 1000 ÷ 1 = 90

  18. Whole numbers into fractions A whole number can be made into a fraction by simply placing it over one (1) • Example • 13  13 1 • 5.1  5.1 1

  19. Mixed equations • Example 30 X 90 x 6 = 10 45 Is the same as 30 X 90 x 6 = 10 45 1

  20. Sample Quiz #2 questions Solve the equation. Express your answers to the nearest tenths and hundredths. A calculator may be used for final division. • 0.7/0.65 x 1.2/1 • 100,000/90,000 x 1.3 • 20/24 x 250/5 x 0.375/7.5 • 1/30 x 1/50 x 100/1 x 1000/1 • 240/90 x 1000/10 x 100/700 x 30/80 x 3150/1

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