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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 - PowerPoint PPT Presentation
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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
5 ÷ 21 = 0.238
Solving common fraction equations
Whole number equations
2 X 5 =
7 6
Calculator: 2 X 5 ÷ 7 ÷ 6 =
0.238
Solving common fraction equations
Whole number equations
200 X 75 = 50 125
First – reduce with common denominator and eliminating zerosSecond multiple across 4 x 3 = 12 1 X 5 = 5Third – divide the two products12 ÷ 5 = 2.4
Solving common fraction equations
Whole number equations
200 X 75 =
50 125
Calculator
200 x 75 ÷ 50 ÷ 125 =
2.4
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 = 6Third: divide the two products
40 ÷ 6 = 6.666666666 6.67
Solving common fraction equations
Whole number equations: Express to the nearest hundredth
7 X 25 X 120 =
3 21 50Calculator
7 x 25 x 120 ÷ 3 ÷ 21 ÷ 50 =
6.6666666 nearest hundredth
6.67
Solving common fraction equations
Whole number equations: Express to the nearest tenth
20 X 10,000 X 1200 X 4000 =
1 60,000 40 600First: 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 = 3Third: divide the two products
2000 ÷ 3 = 666.6666666 666.7
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 =
Your Turn: Express to the nearest tenth
1. 3 / 7 x 11 / 2 =
2. 3 / 7 x 500 / 60 x 1000 / 200 =
3. 2000 / 2700 x 1100 / 900 x 60 / 90 =
Your Turn: Express to the nearest tenth
1. 3 / 7 x 11 / 2 = 1. 2.1428 2.1
2. 3 / 7 x 500 / 60 x 1000 / 200 = 1. 17.857 17.9
3. 2000 / 2700 x 1100 / 900 x 60 / 90 = 1. 0.77 0.8
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.
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
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
Your Turn
Solve the equations. Express your answer to the nearest tenth and hundredth. A calculator may be used for the final division.
1. 2.1 / 4.08 x 0.7 / 5.6
2. 0.4 / 1.2 x 4 / 2.1
3. 1.75 / 0.85 x 2.5 / 4
Your Turn
Solve the equations. Express your answer to the nearest tenth and hundredth. A calculator may be used for the final division.
1. 2.1 / 4.08 x 0.7 / 5.6 tenth = 0.1 hundredth = 0.06
2. 0.4 / 1.2 x 4 / 2.1 tenth = 0.6 hundredth = 0.63
3. 1.75 / 0.85 x 2.5 / 4 tenth = 1.3 hundredth = 1.29
More problems page 28
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
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
Mixed equations
Example
30 X 90 x 6 =
10 45
Is the same as
30 X 90 x 6 =
10 45 1
Sample Quiz #2 questions
Solve the equation. Express your answers to the nearest tenths and hundredths. A calculator may be used for final division.
1. 0.7/0.65 x 1.2/1
2. 100,000/90,000 x 1.3
3. 20/24 x 250/5 x 0.375/7.5
4. 1/30 x 1/50 x 100/1 x 1000/1
5. 240/90 x 1000/10 x 100/700 x 30/80 x 3150/1
