Transcript Dimensional Analysis #3

Dimensional Analysis
Lecture 3
Chapter 3
Solving common fraction equations

Whole number equations
2
7
X 5 =
6
First reduce with common denominator and
eliminating the zeros
Second multiple across
1X5=5
7 X 3 = 21
Third divide the two products
5 ÷ 21 = 0.238
Solving common fraction equations
 Whole number equations
2
7
X 5 =
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 zeros
Second multiple across
4 x 3 = 12
1X5=5
Third – divide the two products
12 ÷ 5 = 2.4
Solving common fraction equations
 Whole number equations
200
50
X
75 =
125
Calculator
200 x 75 ÷ 50 ÷ 125 =
2.4
Solving common fraction equations
 Whole number equations: Express to the nearest
hundredth
7
3
X
25
21
X
120
50
=
First: reduce with common denominator and eliminating zeros
Second: multiple across
1 x 1 x 40 = 40
1x3x2=6
Third: divide the two products
40 ÷ 6 =
6.666666666
 6.67
Solving common fraction equations
 Whole number equations: Express to the
nearest hundredth
7
3
X
25
21
X
120 =
50
Calculator
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
1
X
10,000
60,000
X
1200 X
40
4000 =
600
First: reduce with common denominator and eliminating zeros
Second: multiple across
1 x 1 x 2 x 1000 = 2000
Third: divide the two products
2000 ÷ 3 =
666.6666666
 666.7
1x3x1x1=3
Solving common fraction equations
 Whole number equations: Express to the
nearest tenth
20
1
X
10,000
60,000
X
1200 X
40
4000 =
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
175
10
 Divide
3÷7 =
0.428 
0.43
=
3
7
x
1
1
=
3
7
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

0.7 / 5.6
tenth = 0.1 hundredth = 0.06
2. 0.4 / 1.2

x
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
10
45
Is the same as
30 X
90 x
10
45
6
=
6
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