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

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