Math Fundamentals for Operators in Training
Transcript of Math Fundamentals for Operators in Training
State of Tennessee
Math Fundamentals for Operators in Training August 10-12, 2021 Course #1009 or 1009-V
Instructor: Amanda Carter Fleming Training Center [email protected]
Wednesday
8:30 Registration and Welcome 8:45 Order of Operations 11:00 Lunch 12:00 Solving Equations
Thursday
8:30 Review Day 1 8:45 Ratios 10:00 Proportions 1100 Lunch 12:00 Dimensional Analysis
Friday
8:30 Exam Review & Practice 11:15 Lunch 12:30 Exam
Phone: 615-898-6507 Fax: 615-898-8064 E-mail: [email protected]
Fleming Training Center 2022 Blanton Dr.
Murfreesboro, TN 37129
Table of Contents
Section 1 Order of Operations 3
Section 2 Solving Equations 19
Section 3 Ratios 47
Section 4 Proportions 61
Section 5 Dimensional Analysis 79
Section 6 Solutions 103
ORDER OF OPERATIONSBasic Math for Operators-in-Training
WHAT IS ORDER OF OPERATIONS?
• A set way to solve an calculation8 16 4
• Which way is the correct way?
8 16 424 4
6
8 16 48 4
12
Section 1 TDEC - Fleming Training Center
Order of Operations4
PEMDAS
• Parenthesis• Exponents• Multiplication/Division• Addition/Subtraction
8 16 424 4
6
8 16 48 4
12
EXAMPLE7 3 4 2 5 6
7 3 4 2 5 6
21 4 2 5 6
84 2 5 6
42 5 6
42 30
12
ParenthesisExponentsMultiplication/DivisionAddition/Subtraction
Since Multiplication and Division are on the same “level,” work left to right
Skip the subtraction because it is on the next “level”
TDEC - Fleming Training Center Section 1
Order of Operations 5
Math Fundamentals
Order of Operations (1)
1. 3(6 + 7)
2. 5 × 3 × 2
3. 72 ÷ 9 + 7
4. 2 + 7 × 5
5. 20 ÷ [4 − (10 − 8)]
6. 40 ÷ 4 − (5 − 3)
7. 9 + 9 + 6 – 5
Section 1 TDEC - Fleming Training Center
Order of Operations6
8. (5 + 16) ÷ 7 – 2
9. 3
10. 2 7
11. 8 5 9
Answers
1. 39 7. 19
2. 30 8. 1
3. 15 9. 6
4. 37 10. 12
5. 10 11. 10
6. 8
TDEC - Fleming Training Center Section 1
Order of Operations 7
Math Fundamentals
Order of Operations (2)
Order of Operations
1. 8 + 96 ÷ 2
2. 42 ÷ 6 – 3
3. 42 – 15 ÷ 5
4. 8 × 6 + 5
5. 45 + 6 × 15
6. 91 ÷ 7 – 9
Section 1 TDEC - Fleming Training Center
Order of Operations8
7. 848 ‐ 2 × 67
8. 8 + 9 – 2 × 3
9. 36 ÷ 3 – 4 × 3 + 24 ÷ 2
10. 55 + 8 × 2 ÷ 2 + 34 – 17 + 19
11. 44 – (18 ÷ 9)
12. (73 + 4) + 14 × 6
13. (9 + 5) x (9 + 5)
TDEC - Fleming Training Center Section 1
Order of Operations 9
14. [(15 + 18) – 33] × 6
15. (10 + 2) + 15 x 3
16. [16 – (14 ÷ 7)] + 82
17. (10 x 7 ‐ 82) + 10
18. (69 – 32) – (0 + 5)
19. 4 x (13 – 3) + 42
20. (10 – 5)2 + [(12 + 6) x 52]
Section 1 TDEC - Fleming Training Center
Order of Operations10
Order of Operations (2) Answers
1. 56
2. 4
3. 39
4. 53
5. 135
6. 4
7. 714
8. 11
9. 12
10. 99
11. 42
12. 161
13. 196
14. 0
15. 57
16. 96
17. 16
18. 55
19. 56
20. 475
TDEC - Fleming Training Center Section 1
Order of Operations 11
Math Fundamentals Order of Operations (3)
1. (14 + 2) x 8 – 4
2. 4 x 3 + (3 + 6)
3. (11 + 5) + 10 x 5
4. (8 + 27 – 5) x 6
5. (10 + 3) x (7 – 5)
6. (12 + 7) x 9 + 2
Section 1 TDEC - Fleming Training Center
Order of Operations12
7. 2 x 3 + (9 + 6)
8. (9 + 3) + 15 x 5
9. (10 + 20 – 6) x 6
10. (14 + 3) x (12 + 5)
11. (14 + (15 - 3)) x 7
12. 12 + ((17 + 4) + 2)
TDEC - Fleming Training Center Section 1
Order of Operations 13
13. (7 + (18 – 3 + 2))
14. ((11 + 4) + 4) + 8
15. (10 + (18 – 3)) x 7
16. 2 + ((13 + 5) + 6)
17. ((10 – 2) x 5) – 10
18. 13 + (10 + (11 – 5))
Section 1 TDEC - Fleming Training Center
Order of Operations14
19. 15 + (5 x (17 – 6))
20. 8 + (14 – 7 – 6))
21. 18 + (5 x (11 – 4)²)
22. ((14 – 2) +14 – 2)²)
23. 14 + (5 x (4 + 3)²)
24. 18 + ((10 + 3) + 2²)
TDEC - Fleming Training Center Section 1
Order of Operations 15
25. (4² + (10 - 2 + 4²))
26. (6² + (20 – 5 + 3²))
27. 18 + ((11 + 7) + 3²)
28. ((5 + 4) ² x 2) + 2²
29. ((18 + 2) + (20 – 4)²)
30. ((10 – 4)² + 6) - 4²
Section 1 TDEC - Fleming Training Center
Order of Operations16
Order of Operations (3) Answers:
1) 124
2) 21
3) 66
4) 180
5) 26
6) 173
7) 21
8) 87
9) 144
10) 289
11) 182
12) 35
13) 24
14) 27
15) 175
16) 26
17) 30
18) 29
19) 70
20) 9
21) 263
22) 576
23) 259
24) 35
25) 40
26) 60
27) 45
28) 166
29) 276
30) 26
TDEC - Fleming Training Center Section 1
Order of Operations 17
Introduction to Equations
Basic Algebra for Operators‐in‐Training
Evaluating Expressions• An expression is a statement of value
– A statement of some type of quantity
10 + 5 370 ‐ x
• The expression gives the area of a
triangle where b is the base of the triangle and h is the height
– If b is 7 cm and h is 4 cm, then we can evaluate the expression
𝑏 ℎ 14 𝑐𝑚
Section 2 TDEC - Fleming Training Center
Solving Equations20
Introduction to Equations
• An equation is when expressions are set to be equal to each other
235
28
2 7=143 4 = 0.75
Introduction to Equations
• Equations are “balanced”
– The quantity on one side of the equal sign is equivalent to the quantity on the other side of the equal sign
25 4 20 5100 100
TDEC - Fleming Training Center Section 2
Solving Equations 21
Introduction to Equations
• Equations are “balanced”
– It is vital to maintain that balance. 25 4 20 5
100 115– To maintain that balance, we whatever we do to
one side of the equation, we must do the same to the other side
25 4 20 5115 115
15
1515
Variables
• So far, we have known all the numbers that we are working with
• In algebra, we start to see and work with variables
– A variable is a symbol that represents different varying values
𝑥 5𝐼𝑓 𝑥 1,
𝑡ℎ𝑒𝑛 𝑥 5 6
Section 2 TDEC - Fleming Training Center
Solving Equations22
Introduction to Equations
• But what if we didn’t know what one of those were
25 𝑦 20 5
• We would have to solve the equation to find the value of the unknown (y)
– This is accomplished by getting the unknown by itself on one side of the equal sign.
Introduction to Equations
25 𝑦 20 5• 25 is on the same side of the equal sign as the
unknown
– To get rid of it, we have to perform the opposite function
25 𝑦25
1 𝑦 20 5𝑦 100
• Is this answer correct?
TDEC - Fleming Training Center Section 2
Solving Equations 23
Introduction to Equations
• If y=100, and 25 𝑦 20 5– Does the equation balance out with the new
information?
25 100 20 52500 100
• The equation is no longer balanced so it is untrue
Introduction to Equations
25 𝑦 20 5• How do we solve for the unknown without
losing the balance?
– What we do to one side of the equal sign, we must do to the other side
25 𝑦25
20 525
1 𝑦10025
𝑦 4
• Now, is the answer correct?
Section 2 TDEC - Fleming Training Center
Solving Equations24
Introduction to Equations
• If y=4, and 25 𝑦 20 5– Does the equation balance out with the new
information?
25 4 20 5100 100
• The equation is balanced
Solving for X
• Rules for solving for X:
– X on top
– X alone
• Questions to ask:
– Is X alone?
– What is keeping X from being alone?
– What is it doing to X?
– What do we have to do to get rid of it?
TDEC - Fleming Training Center Section 2
Solving Equations 25
Example
𝑥 7 107 7
𝑥 0 10 7
𝑥 17
Example 1
730𝑥
3847
730𝑥
3847
38471
38471
730𝑥
38473847
1
3847 730 𝑥
2,808,310 𝑥
What you do to one side of the equation, must be done to the other side.
Section 2 TDEC - Fleming Training Center
Solving Equations26
Example 20.5=
(165)(3)(8.34)
x
0.5 4128.3𝑥
0.54128.3𝑥
𝑥1
𝑥1
0.54128.3𝑥
𝑥1
𝑥 0.5 4128.3
𝑥 0.5
0.54128.3
0.5
𝑥4128.3
0.5
𝑥 8256.6
What you do to one side of the equation, must be done to the other side.
Simplify
Solving for X
• When solving for x involving addition and subtraction, the balance of the equation must still remain.
– What you do to one side you must do to the other
TDEC - Fleming Training Center Section 2
Solving Equations 27
Example 3
115 105 80 𝑥 386
300 𝑥 386
300 𝑥 300 386 300
𝑥 86
Example 4
17 23 7 𝑥 38
47 𝑥 38
47 𝑥 𝑥 38 𝑥
47 38 𝑥
47 38 38 𝑥 38
9 𝑥
Step 1. Simplify
Step 2. Make x positive
Section 2 TDEC - Fleming Training Center
Solving Equations28
Solving for X2
• Follow same procedure as solving for X
• Then take the square root
𝑥 15,625
𝑥 15,625
𝑥 125
Example 50.785 𝑥 2826
0.785 𝑥0.785
28260.785
𝑥28260.785
𝑥 3600
𝑥 3600
𝑥 60
TDEC - Fleming Training Center Section 2
Solving Equations 29
Math Fundamentals Solving for the Unknown (1)
1) Clarence has 8 small spoons and 7 big spoons. Write an expression that shows how many spoons Clarence has.
2) Oliver earned 115 extra credit points. Dustin earned 57 fewer extra credit points than Oliver. Write an expression that shows how many extra credit points Dustin earned.
3) Andy had 98 DVDs. His mother bought him X more DVDs. Write an expression that shows how many DVDs Andy has now.
4) Terrell bought 6 boxes of granola bars. There are X granola bars in each box. Write an expression that shows how many granola bars Terrell bought.
5) The jazz band has 5 members. To raise money for a tour, each member sold X raffle tickets. Choose the expression that shows the number of raffle tickets sold.
Section 2 TDEC - Fleming Training Center
Solving Equations30
Solve for the unknown value.
Addition
6) 3 + g = 10
7) x + 2 = 3
8) x + 15 = 19 + 22
9) 7 + 10 + x + 7 + 9 = 41
10) x + 93 = 165
Subtraction
11) 3 = k − 2
12) x – 2 = 9
13) x – 93 = 65
14) 9.5 – x = 8.7
15) 115 = x – 7.5
TDEC - Fleming Training Center Section 2
Solving Equations 31
Multiplication
16) 10 = (2)(w)
17) (5)(m) = 10
18) 48 = (6)(m)
19) 8.1 = (3)(x)(1.5)
20) (0.785)(0.33)(0.33)(x) = 0.49
Division
21) 12
22) 6
23) 50
24) 56.5 .
Section 2 TDEC - Fleming Training Center
Solving Equations32
25) 114 . .
.
Assorted
26) (5)(x) + 9 = 9
27) 7 + (6)(x) = 37
28) 4
29) 2
30) 7 𝑓 16 12
TDEC - Fleming Training Center Section 2
Solving Equations 33
Answers
1) 8+7
2) 115‐57
3) 98+x
4) (6)(x)
5) (5)(x)
6) g=7
7) x=1
8) x=26
9) x=8
10) x=72
11) 5=k
12) x=11
13) x=158
14) 0.8=x
15) 122.5=x
16) 5=w
17) m=2
18) 8=m
19) 1.8=x
20) x=5.73
21) 96=t
22) 0.33=e
23) 2=x
24) x=8.06
25) x=0.005
26) x=0
27) x=5
28) m=41
29) 13=x
30) f=4
Section 2 TDEC - Fleming Training Center
Solving Equations34
Solving for the Unknown (2)
Basics – finding x 1. 7 + 10 + x + 7 + 9 = 41 2. 16=(2)(x) 3. 142 = (3)(x)+13 4. 10.1 = 9.5 + x 5. x + 15 = 19 + 22 6. 16 = (2)(x)
7. 211 = (15)(x)(0.785) 8. (0.785)(2.5)(2.5)(x) = 5151.56 9. 100 = 50 x 10. 233 = 44 x
TDEC - Fleming Training Center Section 2
Solving Equations 35
11. 56.5 = 3800 (x)(8.34)
12. 10 = x 4 13. 940 = x (0.785)(90)(90)
14. x = (165)(3)(8.34) 0.5
15. 114 = (230)(1.15)(8.34) (0.785)(70)(70)(x)
16. 2 = x 180
17. 46 = (105)(x)(8.34) (0.785)(100)(100)(4)
18. 2.4 = (0.785)(5)(5)(4)(7.48) x
Section 2 TDEC - Fleming Training Center
Solving Equations36
19. 19,747 = (20)(12)(x)(7.48) 20. (15)(12)(1.25)(7.48) = 337 x
21. x = 213 (4.5)(8.34)
22. x = 2.4 246
23. 6 = (x)(0.18)(8.34) (65)(1.3)(8.34)
24. (3000)(3.6)(8.34) = 23.4 (0.785)(x)
25. 109 = x (0.785)(80)(80)
26. (x)(3.7)(8.34) = 3620
TDEC - Fleming Training Center Section 2
Solving Equations 37
27. 2.5 = 1,270,000 x 28. 0.59 = (170)(2.42)(8.34) (1980)(x)(8.34) 29. 142 = (2)(x) + 13 30. (3.5)(x) – 62 = 560
Finding x2
31. x2 = 100
32. (2)(x2) = 288 33. 942 = (0.785)(x2)(12) 34. 6358.5 = (0.785)(x2) 35. 835 = 4,200,000 (0.785)(x2) 36. 920 = 3,312,000 x2
Section 2 TDEC - Fleming Training Center
Solving Equations38
37. 23.9 = (3650)(3.95)(8.34) (0.785)(x2) 38. (0.785)(D2) = 5024 39. (x2)(10)(7.48) = 10,771.2 40. 51 = 64,000 (0.785)(D2)
41. (0.785)(D2) = 0.54 42. 2.1 = (0.785)(D2)(15)(7.48) (0.785)(80)(80)
TDEC - Fleming Training Center Section 2
Solving Equations 39
Answers 1) 8 2) 8 3) 43 4) 0.6 5) 26 6) 8 7) 17.92 8) 1050 9) 2 10) 5.3 11) 8.06 12) 40 13) 5,976,990 14) 8256.6 15) 0.005 16) 360 17) 1649.42 18) 244.66 19) 11.0 20) 4.99 21) 7993.89
22) 590.4 23) 2816.67 24) 4903.48 25) 547,616 26) 117.31 27) 508,000 28) 0.35 29) 64.5 30) 177.7149 31) 10 32) 12 33) 10 34) 90 35) 80.05 36) 60 37) 80.06 38) 80 39) 12 40) 39.98 41) 0.83 42) 10.94
Section 2 TDEC - Fleming Training Center
Solving Equations40
Math Fundamentals
Solving for a Variable
1. Solve for width. Area length width
2. Solve for height.
Area base height
2
3. Solve for diameter. Area 0.785 D
4. Solve for time in minutes.
lbday
grams 60 min hr⁄ 24 hr day⁄454 gram lb⁄ min
5. Solve for diameter. feet π Diameter
TDEC - Fleming Training Center Section 2
Solving Equations 41
6. Solve for flow.
feed rate dose flow 8.34 lb gal⁄
% purity
7. Solve for area. flow rate area velocity
8. Solve for width. flow rate length width velocity
9. Solve for distance.
flow rate 0.785 Diameterdistance
time
10. Solve for pressure. force pressure area
11. Solve for flow.
bhp flow head
3960 % pump
Section 2 TDEC - Fleming Training Center
Solving Equations42
12. Solve for % motor efficiency.
mhp flow head
3960 % pump % motor
13. Solve for head.
whp flow head
3960
14. Solve for dose.
mass dose concentration 8.34 lb gal⁄
15. Solve for substance weight.
specific gravity substance weight
water weight
16. Solve for volume2. concentration volume concentration volume
17. Solve for time.
velocity distance
time
TDEC - Fleming Training Center Section 2
Solving Equations 43
18. Solve for diameter. volume 1
3 0.785 D h
19. Solve for height. volume 0.785 D h
20. Solve for width. volume length width height
Section 2 TDEC - Fleming Training Center
Solving Equations44
Answers
1. width
2. height
3. .
D
4. min / /
/ ⁄
5. D
6. %
.flow
7. area
8. width
9. distance .
10. pressure
11. % flow
12. % motor%
13. head
14. . ⁄
dose
15. water weight specific gravity substance weight
16. volume
17. time
18. .
D
19. .
height
20. width
TDEC - Fleming Training Center Section 2
Solving Equations 45
Three bank robbers have a bag of money that they intend to split evenly in the morning. After they are all asleep one of the robbers wakes up and decides that he doesn’t trust the other two, so he takes his third cut and goes back to sleep. A little later, the second robber wakes up and decides that he doesn’t trust the other two, so he takes his third cut and goes back to sleep. A little later, the third robber wakes up and does the same. In the morning, they all wake up and notice that the bag looks smaller than they remember, but no one says anything. The split what’s there evenly three ways. What proportion/percentage of the money stolen did each robber walk away with?
Ratios
How much of the grids are shaded red? Write each in at least 2 ways.
Section 3 TDEC - Fleming Training Center
Ratios48
Ratios
How much of the grids are shaded red? Write each in at least 2 ways.
Ratios
How much of the grids are shaded red? Write each in at least 2 ways.
TDEC - Fleming Training Center Section 3
Ratios 49
Ratios
How much of the grids are shaded red? Write each in at least 2 ways.
Ratios
Shade 3/10 of this grid.
Section 3 TDEC - Fleming Training Center
Ratios50
Ratios
Shade 2/5 of this grid.
Ratios
Shade 3/4 of this grid.
TDEC - Fleming Training Center Section 3
Ratios 51
Ratios
What percent of the months start with a “J”?
3/12 = 0.25 = 25%
Ratios
What percent of the months start with a “J”?
3/12 = 0.25 = 25%
What is the ratio of months that start with “J” to all the months?
3/12 = 0.25
You might also see it written as3:12 = 1:4
Section 3 TDEC - Fleming Training Center
Ratios52
Ratios
Simplifying Ratios
Let’s think of percentages. If 25% of a group of people are married, then you might say that 25 out of every 100 are married.
You could say that 1 out of every 4 are married.
Ratios – with notation
Simplifying Ratios – What does that look like mathematically?
Or, 1:4
TDEC - Fleming Training Center Section 3
Ratios 53
Ratios
Some ratios are called something else.
For example, the ratio of miles to hours is called your speed.
MPH is miles per hour
Miles/Hour
Ratios
Ratio are not necessarily fractions. Fractions are a comparison of parts to whole. For example, in the grid below, 2/4 or ½ of the grid is red. That is a comparison of red to white (ratio), but it is also a fraction, because it is comparison of red to whole grid.
MPH is not a fraction. It’s a ratio.
Section 3 TDEC - Fleming Training Center
Ratios54
Ratios
If you went 500 miles in 10 hours, what is the ratio of miles to hours?
What’s another way to write that?
Ratios
If a 10 pound bag of potatoes is $5.49, what is the ratio of cost to pounds?
What is the ratio of pounds to cost?
What if I wanted to know the cost per one pound?
TDEC - Fleming Training Center Section 3
Ratios 55
Math Fundamentals
Reducing Ratios (1)
1. 14 : 12 ___________
2. 35 : 14 ___________
3. 36 : 81 ___________
4. 6 : 36 ___________
5. 45 : 72 ___________
6. 25 : 15 ___________
7. 28 : 35 ___________
8. 6 : 12 ___________
9. 9 : 27 ___________
10. 70 : 21 __________
11. 10 : 15 ___________
12. 30 : 42 ___________
13. 24 : 42 ___________
14. 15 : 27 ___________
15. 28 : 36 ___________
16. 80 : 70 ___________
Section 3 TDEC - Fleming Training Center
Ratios56
17. 15 : 3 ___________
18. 8 : 6 ___________
19. 16 : 6 ___________
20. 20 : 2 ___________
Answers:
1) 7 : 6
2) 5 : 2
3) 4 : 9
4) 1 : 6
5) 5 : 8
6) 5 : 3
7) 4 : 5
8) 1 : 2
9) 1 : 3
10) 10 : 3
11) 2 : 3
12) 5 : 7
13) 4 : 7
14) 5 : 9
15) 7 : 9
16) 8 : 7
17) 5 : 1
18) 4 : 3
19) 8 : 3
20) 10 : 1
TDEC - Fleming Training Center Section 3
Ratios 57
Math Fundamentals
Ratios (2)
Ratios ‐ Answer in the reduced form.
1. For every 7 hamburgers sold at the malt shop there are 3 hotdogs
sold. What is the ratio of hotdogs sold to hamburgers sold?
2. A group of preschoolers has 15 boys and 4 girls. What is the ratio
of boys to all children?
3. A herd of 36 horses has 12 white and the rest are black horses.
What is the ratio of black horses to white horses?
4. Brayden drew 27 hearts, 1 star, and 5 circles. What is the ratio of
stars to all shapes?
5. A herd of 31 horses has 2 white and the rest are black horses.
What is the ratio of black horses to white horses?
6. A jar contains 36 marbles, of which 10 are blue, 17 are red, and
the rest are green. What is the ratio of blue marbles to green
marbles?
Section 3 TDEC - Fleming Training Center
Ratios58
7. A herd of 16 horses has 3 white and the rest are black horses.
What is the ratio of black horses to white horses?
8. A herd of 52 horses has 12 white and the rest are black horses.
What is the ratio of white to black horses?
9. A pattern has 5 blue triangles to every 80 yellow triangles. What is
the ratio of blue triangles to all triangles?
10. Noah drew 22 hearts and 76 circles. What is the ratio of
circles to all shapes?
11. A pattern has 14 blue triangles to every 18 yellow triangles.
What is the ratio of yellow triangles to blue triangles?
12. A pattern has 6 blue triangles to every 42 yellow triangles.
What is the ratio of yellow triangles to blue triangles?
13. A group of preschoolers has 63 boys and 27 girls. What is the
ratio of boys to all children?
TDEC - Fleming Training Center Section 3
Ratios 59
Answers
Ratios
1) 3:7
2) 15:19
3) 2:1
4) 1:33
5) 29:2
6) 10:9
7) 13:3
8) 3:10
9) 1:17
10) 38:49
11) 9:7
12) 7:1
13) 7:10
Section 3 TDEC - Fleming Training Center
Ratios60
Proportions
1009 Math Fundamentals forOperators‐in‐Training
Proportions
• A proportion is two ratios that have been set equal to each other
– a proportion is an equation that can be solved
25100
14
Section 4 TDEC - Fleming Training Center
Proportions62
Solving Proportions
• Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross‐multiplying, and solving the resulting equation
𝑥100
14
Solving Proportions
𝑥100
14
𝑥 4 100 1
𝑥 44
100 14
𝑥100
4
𝑥 25
Cross multiply
Solve for x
TDEC - Fleming Training Center Section 4
Proportions 63
Example
• There are 16 ducks and 9 geese in a certain park. Suppose that there are 192 ducks. How many geese are there?
We can determine the ratio of ducks to geese:
16 ducks to 9 geese
We need to turn the question into an equation or proportion
16 𝑑𝑢𝑐𝑘𝑠9 𝑔𝑒𝑒𝑠𝑒
192 𝑑𝑢𝑐𝑘𝑠𝑥 𝑔𝑒𝑒𝑠𝑒
Example
• Be sure to set up equation so that the units match on both sides of the equal sign
𝑑𝑢𝑐𝑘𝑠𝑔𝑒𝑒𝑠𝑒
𝑑𝑢𝑐𝑘𝑠𝑔𝑒𝑒𝑠𝑒
Section 4 TDEC - Fleming Training Center
Proportions64
Example
16 𝑑𝑢𝑐𝑘𝑠9 𝑔𝑒𝑒𝑠𝑒
192 𝑑𝑢𝑐𝑘𝑠𝑥 𝑔𝑒𝑒𝑠𝑒
16 𝑥 9 192
16 𝑥16
9 19216
𝑥9 192
16
𝑥1728
16
𝑥 108
Cross multiply
There are 16 ducks and 9 geese in a park. If there are 192 ducks, how many geese are there?
TDEC - Fleming Training Center Section 4
Proportions 65
Math Fundamentals
Solving Proportions (1)
1) _____ : 15 = 36 : 45
2) 8 : 12 = _____ : 3
3) 27 : _____ = 9 : 18
4) 24 : 4 = 6 : _____
5) _____ : 6 = 3 : 2
6) 5 : _____ = 20 : 8
7) 25 : 35 = 40 : _____
8) 4 : 12 = 6 : _____
9) 14 : 42 = 2 : _____
10) 10 : _____ = 2 : 8
11) 8 : _____ = 4 : 5
12) _____ : 28 = 6 : 12
13) 3 : 4 = 18 : _____
14) 1 : 2 = _____ : 4
15) 72 : 54 = _____ : 6
16) _____ : 64 = 2 : 8
17) _____ : 2 = 27 : 18
18) 21 : 35 = _____ : 10
19) 8 : 3 = _____ : 21
20) 6 : 3 = _____ : 6
Section 4 TDEC - Fleming Training Center
Proportions66
Answers
1) 12 2) 2 3) 54 4) 1 5) 9 6) 2 7) 56 8) 18 9) 6 10) 40
11) 10 12) 14 13) 24 14) 2 15) 8 16) 16 17) 3 18) 6 19) 56 20) 12
TDEC - Fleming Training Center Section 4
Proportions 67
Math Fundamentals
Proportions (2)
1. In a certain class, the ratio of passing grades to failing grades is 7 to 5. How
many of the 36 students failed the course?
2. Shares of stock represent how much of a company a person owns. Puff
incorporated is owned by Peter, Paul and Mary. Peter owns 4,050 shares. Paul
owns 2,510 shares and Mary owns 4,200 shares. Suppose the company made a
profit this year of $1,500,000. If each shareholder gets a proportion of the
total profit that is equal to the proportion of the shares that they own, how
much money does Mary receive? (round to the nearest penny)
3. Ben the camel drinks tea (so classy!). He drinks 350 liters of tea every 2 days.
How many liters of tea does Ben drink every 6 days?
4. According to Greg, perfect cherry pies have a ratio of 240 cherries to 3 pies.
How many cherries does Greg need to make 9 perfect cherry pies?
Section 4 TDEC - Fleming Training Center
Proportions68
5. You are throwing a party and you need 5 liters of soda for every 12 guests. If
you have 36 guests, how many liters of soda do you need?
6. You can buy 3 apples at the Quick Market for $1.14. You can buy 5 of the same
apples at Stop and Save for $2.35. Which place is the better buy?
7. A jet travels 410 miles in 5 hours. At this rate, how far could the jet fly in 14
hours? What is the rate of speed of the jet in miles per hour?
8. An ice cream factory makes 350 quarts of ice cream in 5 hours. How many
quarts could be made in 12 hours?
9. A test of a new car results in 580 miles on 20 gallons of gas. How far could you
drive on 40 gallons of gas?
TDEC - Fleming Training Center Section 4
Proportions 69
Answers
1) 15 failed
2) $585,501.86
3) 1050 liters
4) 720 cherries
5) 15 liters
6) Quick Mkt
7) 1148 miles; 82 mph
8) 840 qts
9) 1160 miles
Section 4 TDEC - Fleming Training Center
Proportions70
Math Fundamentals
Proportions (3)
1. There are a total of 63 bikes. If the ratio of blue bikes to black bikes is 4 to 5, how many of the bikes are blue?
2. Paul can walk 15 steps in 5 minutes. How long does it take Paul to walk 75 steps at the same speed?
3. Candy is at the balloon shop and sees that 10 balloons cost $0.15. He needs 50 balloons to decorate his room. How much will 50 balloons cost?
4. It takes 8 people to pull a 16 ton truck. How many people would it take to pull a 60 ton truck?
5. If a globe rotates through 150 degrees in 5 seconds, how many degrees does it turn in 30 seconds?
6. If the ratio of white pens to green pens is 2 to 8 and there are a total of 30 pens, how many pens are white?
7. Giles is searching for a sock and discovers that he has 10 socks for every 5 pairs of shoes. If he has 20 socks, how many pairs of shoes does he have?
8. The sum of two numbers is 150. The ratio of the same two numbers is 3:2. Find the bigger number.
9. If the ratio of pink flower to blue flower is 3 to 6 and there are total 72 flowers, how many of them are pink?
TDEC - Fleming Training Center Section 4
Proportions 71
10. There are a total of 18 chairs. If the ratio of the red chairs to brown chairs is 2 to 4, how many of them are red?
11. Rock can read 10 books in 30 minutes. How long does it take Rock to read 15 books, if the speed is consistent?
12. Ricky is at the bakery shop when he sees that 8 pastries cost $160. He needs 16 pastries. How much will 16 pastries cost?
13. It takes 10 people to pull a 50 ton bus. How many people would it take to pull a 100 ton bus?
14. If a ball rotates 110 degrees in 8 seconds, how many degrees does it rotate in 32 seconds?
15. If the ratio of red roses to yellow roses is 4 to 6 and there are a total of 50 roses, how many of them are yellow?
16. Freddy is searching for a shirt and discovers that he has 12 shirts for every 6 pair of jeans. If he has 18 shirts, how many pairs of jeans does he have?
17. The sum of two numbers is 200 and the two numbers are in a ratio of 4:6. Find the larger number.
18. If the ratio of the purple flowers to black flowers is 4 to 8 and there are a total of 108 flowers, how many of the flowers are purple?
Section 4 TDEC - Fleming Training Center
Proportions72
19. There is a total of 25 bicycles. If the ratio of gray bicycles to black bicycles is 6 to 9, how many of them are black?
20. Ritz can eat 8 apples in 15 minutes. How long does it take Ritz to eat 16 apples at the same rate?
21. Tom is at McDonalds and he sees that 2 burgers cost $40. He needs 12 burgers. How much will 12 burgers cost?
22. It takes 12 people to pull 30 tons of goods. How many people would it take to pull 60 tons of goods?
23. If a tire rotates through 250 degrees in 15 seconds, how many degrees does it rotate in 45 seconds?
24. If the ratio of purple bikes to red bikes is 8 to 12 and there are a total of 100 bikes, how many of them are purple?
25. Andrew is searching for a cup and discovers that he has 20 plates for every 5 pairs of cups. If he has 40 plates, how many pairs of cups does he have?
26. The sum of two numbers is 80. The ratio of those two numbers is 3:5. Find the larger number.
TDEC - Fleming Training Center Section 4
Proportions 73
27. If the ratio of red hair bands to green hair bands is 5 to 9 with a total of 70 hair bands, how many of them are green?
28. There are a total of 100 balloons. If the ratio of yellow balloons to blue balloons is 8 to 12, how many of them are yellow?
29. Furry can eat 10 mangoes in 5 minutes. How long does it take Furry to eat 18 mangoes at the same speed?
30. Harry is at the Pizza Hut and he sees that 5 pizzas cost $300. He needs 15 pizzas. How much do 15 pizzas cost?
31. It takes 24 people to pull a 50 ton iron rod. How many people would it take to pull a 150 ton iron rod?
32. If a coin rotates through 160 degrees in 6 seconds, how many degrees does it rotate in 60 seconds?
33. If the ratio of blue shirts to green shirts is 5 to 12 with a total of 340 shirts, how many of the shirts are blue?
Section 4 TDEC - Fleming Training Center
Proportions74
34. Rex is searching for bread and discovers that he has 40 buns for every 10 cubes of cheese. If he has 80 buns, how many cubes of cheese does he have?
35. The sum of two numbers is 500 with a ratio of 15:10. Find the larger number.
36. If the ratio of silver nail paints to golden nail paints is 4 to 2 and there are total 60 nail paints, how many of them are golden?
37. There are a total of 18 frocks. If the ratio of purple frocks to white frocks is 2 to 4, how many of them are white?
38. Johnny can eat 5 chocolates in 2 minutes. How long does it take Johnny to eat 10 chocolates at the same rate?
39. Gerry is at Dominos and sees that 2 choco‐lava cakes cost $50. He needs 6 choco‐lava cakes. How much will those 6 choco‐lava cakes cost?
40. It takes 16 people to pull a 30 ton cable wire. How many people would it take to pull a 60 ton cable wire?
TDEC - Fleming Training Center Section 4
Proportions 75
41. If a marble rotates through 180 degrees in 9 seconds, how many degrees does it rotate in 18 seconds?
42. If the ratio of black jeans to blue jeans is 6 to 18 with a total of 240 jeans, how many of them are blue?
43. Rex is searching for shoes and discovers that he has 25 pairs of shoes for every 15 pairs of socks. If he has 50 pairs of shoes, how many socks does he have?
44. The sum of two numbers is 300 and the two numbers have a ratio of 20:10. Find the larger number.
45. If the ratio of red roses to pink roses is 5 to 4 and there are a total of 45 roses, how many of them are red?
Section 4 TDEC - Fleming Training Center
Proportions76
Answers
1) 28 19) 15 37) 12
2) 25 20) 30 38) 4
3) 0.75 21) 240 39) 150
4) 30 22) 24 40) 32
5) 900 23) 750 41) 360
6) 6 24) 40 42) 180
7) 10 25) 10 43) 30
8) 90 26) 50 44) 200
9) 24 27) 45 45) 25
10) 6 28) 40
11) 45 29) 9
12) 320 30) 900
13) 20 31) 72
14) 440 32) 1600
15) 30 33) 100
16) 9 34) 20
17) 120 35) 300
18) 36 36) 20
TDEC - Fleming Training Center Section 4
Proportions 77
DIMENSIONAL ANALYSIS
MATHEMATICS MANUAL FOR WATER AND WASTEWATER TREATMENT PLANT OPERATORS
BY FRANK R. SPELLMAN
DIMENSIONAL ANALYSIS
• Used to check if a problem is set up correctly
• Work with the units of measure, not the numbers
• Step 1:
• Express fraction in a vertical format
𝑔𝑎𝑙 𝑓𝑡⁄ to
• Step 2:
• Be able to divide a fraction
becomes
Section 5 TDEC - Fleming Training Center
Dimensional Analysis80
DIMENSIONAL ANALYSIS
• Step 3:
• Know how to divide terms in the numerator and denominator
• Like terms can cancel each other out
• For every term that is canceled in the numerator, a similar term must be canceled in the denominator
𝑙𝑏𝑑𝑎𝑦
𝑑𝑎𝑦𝑚𝑖𝑛
𝑙𝑏𝑚𝑖𝑛
• Units with exponents should be written in expanded form
𝑓𝑡 𝑓𝑡 𝑓𝑡 𝑓𝑡
EXAMPLE 1
• Convert 1800 ft3 into gallons.
• We need the conversion factor that connects the two units
1 cubic foot of water = 7.48 gal
• This is a ratio, so it can be written two different ways
1 𝑓𝑡7.48 𝑔𝑎𝑙
OR 7.48 𝑔𝑎𝑙
1 𝑓𝑡
• We want to use the version that allows us to cancel out units
TDEC - Fleming Training Center Section 5
Dimensional Analysis 81
EXAMPLE 1
1800 𝑓𝑡1
1 𝑓𝑡7.48 𝑔𝑎𝑙
1800 𝑓𝑡7.48 𝑔𝑎𝑙
• Will anything cancel out?
NO
• Let’s try the other version
1800 𝑓𝑡1
7.48 𝑔𝑎𝑙1 𝑓𝑡
1800 7.481 1
• Will anything cancel out?
YES
13,464 𝑔𝑎𝑙
1 𝑓𝑡7.48 𝑔𝑎𝑙
OR 7.48 𝑔𝑎𝑙
1 𝑓𝑡
EXAMPLE 2
• Determine the square feet given 70𝑓𝑡 𝑠𝑒𝑐⁄ and 4.5𝑓𝑡 𝑠𝑒𝑐⁄
• Use units to determine set up
• Two ways to write the number
4.5 𝑓𝑡𝑠𝑒𝑐
𝑂𝑅 𝑠𝑒𝑐
4.5 𝑓𝑡• Which way is the right way?
70 𝑓𝑡𝑠𝑒𝑐
𝑠𝑒𝑐4.5 𝑓𝑡
• Will anything cancel?
Section 5 TDEC - Fleming Training Center
Dimensional Analysis82
EXAMPLE 2 CONT’D
• Remember, units function the same as numbers.
𝑓𝑡 𝑓𝑡 𝑓𝑡 𝑓𝑡
• Therefore
70 𝑓𝑡𝑠𝑒𝑐
𝑏𝑒𝑐𝑜𝑚𝑒𝑠 70 𝑓𝑡 𝑓𝑡 𝑓𝑡
𝑠𝑒𝑐
70 𝑓𝑡 𝑓𝑡 𝑓𝑡𝑠𝑒𝑐
𝑠𝑒𝑐4.5 𝑓𝑡
• Will anything cancel out?
70 1 1 4.5
15.56 𝑓𝑡
Metric System & TemperatureFor Water and Wastewater Plant Operators by Joanne Kirkpatrick Price
TDEC - Fleming Training Center Section 5
Dimensional Analysis 83
Metric Units
King Henry Died By Drinking Chocolate Milk
Metric Units
Kilo Hecto DecaBasic Unit Deci Centi Milli
King Henry Died By Drinking Chocolate Milk
1000Xlarger
100Xlarger
10X larger
MeterLiter
Gram1 unit
10X smaller 100X smaller 1000X smaller
MULTIPLY numbers by 10 if you are getting smaller
DIVIDE number by 10 if you are getting bigger
Section 5 TDEC - Fleming Training Center
Dimensional Analysis84
Problem 1 Convert 2500 milliliters to liters
Converting milliliters to liters requires a move of three place values to the left
Therefore, move the decimal point 3 places to the left
2 5 0 0. = 2.5 Liters3 2 1
Problem 2 Convert 0.75 km into cm
From kilometers to centimeters there is a move of 5 value places to the right
0. 7 5 = 75,000 cm1 2 3 4 5
TDEC - Fleming Training Center Section 5
Dimensional Analysis 85
Examples Convert 1.34 Liters to mL.
1.34 L = 1,340 mL
Convert 76,897 m into km.76897 m = 76.897 km
Convert 34,597 cg into kg.34597 cg = 0.34597 kg
1 2 3
3 2 1
5 4 3 2 1
Metric Conversion
When converting any type of measures •To convert from a larger to smaller metric unit you always multiply•To convert from a smaller to larger unit you always divide
Section 5 TDEC - Fleming Training Center
Dimensional Analysis86
Linear Measure
1 cen meter = 0.3937 inches
1 meter = 3.281 feet
1 meter = 1.0936 yards
1 kilometer = 0.6214 miles
Square Measure
1 cm2 = 0.155 in2
1 m2 = 10.76 2
1 m2 = 1.196 yd2
Cubic Measure
1cm3 = 0.061 in3
1 m3 = 35.3 3
1 m3 = 1.308 yd3
Capacity
1 Liter = 61.025 in3
1 Liter = 0.0353 3
1 Liter = 0.2642 gal
1 gram (g) = 15.43 grains
Weight
1 gram = 0.0353 ounces
1 kilogram = 2.205 pounds
1 inch = 2.540 cm
1 foot = 0.3048 m
1 yard = 0.9144 m
1 mile = 1.609 km
1 in2 = 6.4516 cm2
1 2 = 0.0929 m2
1 yd2 = 0.8361 m2
1 in3 = 16.39 cm3
1 3 = 0.0283 m3
1 yd3 = 0.7645 m3
1 in3 = 0.0164 L
1 3 = 28.32 L
1 gal = 3.79 L
1 grain = 0.0648 g
1 ounce = 28.35 g
1 pound = 454 g
Metric Conversion Equa ons
TDEC - Fleming Training Center Section 5
Dimensional Analysis 87
Math Fundamentals General Conversions (1)
1.) 325 ft3 = gal
2.) 2512 kg = lb
3.) 2.5 miles = ft
4.) 1500 hp = kW
5.) 2.2 ac-ft = gal
6.) 2100 ft2 = ac
7.) 92.6 ft3 = lb
8.) 17,260 ft3 = MG
9.) 0.6% = mg/L
10.) 30 gal = ft3
11.) A screening pit must have a capacity of 400 ft3. How many lbs is this?
12.) A reservoir contains 50 ac-ft of water. How many million gallons of water does it contain?
Section 5 TDEC - Fleming Training Center
Dimensional Analysis88
mg/L & % 13.) 340 mg/L = %
14.) 0.6% = mg/L
15.) 120 mg/L = %
16.) 0.025% = mg/L
17.) 1.5% = mg/L
18.) 5000 mg/L = %
19.) The suspended solids concentration of the return activated sludge is 6800 mg/L. What is the concentration expressed as a percent?
20.) A concentration of 195 mg/L is equivalent to a concentration of what percent?
Metric/English Conversions
21.) 20 feet = meters
22.) 50 L = gal
23.) 70 cm = in
TDEC - Fleming Training Center Section 5
Dimensional Analysis 89
24.) 35 m = feet
25.) 600 mL = gal
26.) 1 lb = mg
27.) 1000 mL = L
28.) 2.7 gal = mL
Linear Measurement
29.) ¼ mile = feet
30.) 4200 feet = miles
31.) 17 feet = meters
32.) 122 inches = feet
33.) 30 meters = inches
34.) 0.6 feet = inches
35.) 492 inches = feet
36.) The total weir length for a sedimentation tank is 142 feet 7 inches. Express this length in terms of feet only.
Section 5 TDEC - Fleming Training Center
Dimensional Analysis90
37.) A one-eighth mile section of pipeline is to be replaced. How many feet of pipeline is this?
38.) 2.7 miles of pipe is how many inches? Flow Conversions
39.) 3.6 cfs = gpm
40.) 1820 gpm = gpd
41.) 45 gps = cfs
42.) 8.6 MGD= gpm
43.) 2.92 MGD = gpm
44.) 385 cfm = gpd
45.) 1,662,000 gpd = gpm
46.) 3.77 cfs = MGD
47.) The flow through a pipeline is 8.4 cfs. What is the flow in gpd?
48.) A treatment plant receives a flow of 6.31 MGD. What is the flow in gpm?
TDEC - Fleming Training Center Section 5
Dimensional Analysis 91
Answers
1.) 2,431 gal 2.) 5,533.04 lb 3.) 13,200 ft 4.) 1,119 kW 5.) 717,200 gal 6.) 0.05 ac 7.) 5,778.24 lb 8.) 0.13 MG 9.) 6,000 mg/L 10.) 4.01 ft3 11.) 24,960 lb 12.) 16.3 MG 13.) 0.034% 14.) 6,000 mg/L 15.) 0.012% 16.) 250 mg/L 17.) 15.000 mg/L 18.) 0.5 % 19.) 0.68% 20.) 0.02 mg/L 21.) 6.1 m 22.) 13.2 gal 23.) 27.56 in 24.) 114.75 ft
25.) 0.16 gal 26.) 454,000 mg 27.) 1 L 28.) 10,219.5 mL 29.) 1,320 ft 30.) 0.8 mi 31.) 5.19 m 32.) 10.17 ft 33.) 1,180.33 in 34.) 7.2 in 35.) 41 36.) 142.58 ft 37.) 660 ft 38.) 171,072 in 39.) 1,615.68 gpm 40.) 2,620,800 gpd 41.) 6.02 cfs 42.) 5964.09 gpm 43.) 2,025.02 gpm 44.) 4,146,912 gpd 45.) 1,154.17 gpm 46.) 2.44 MGD 47.) 5,428,684.8 gpd 48.) 4,381.94 gpm
Section 5 TDEC - Fleming Training Center
Dimensional Analysis92
Math Fundamentals
Converting English to Metric (2)
1. 17 yds2 = ________ m2
2. ________ pounds = 7 kilograms
3. ________ mph = 5 kmph
4. 4.5 gallons = ________ liters
5. 3 miles = ________ km
6. ________ yd2 = 10 m2
7. 16 feet = ________ meters
8. ________ in = 16.5 cm
9. 25 gallons = ________ mL
10. 20.5 mph = ________ kmph
11. ________ ft3 = 3.5 m3
12. ________ yd2 = 9 m2
TDEC - Fleming Training Center Section 5
Dimensional Analysis 93
13. ________ lbs = 17.5 kg
14. 11.5 in = ________ cm
15. ________ ft3 = 1.5 m3
16. ________ ft3 = 12,000 mL
17. 18.5 ft3 = ________ mL
18. ________ yds2 = 14.5 m2
19. 8.5 in = ________ cm
20. 20 yd2 = ________ acres
21. 5 gallons = ______ mL
22. 30 psi = ______ ft of head
23. 41.7 lbs = ______ gallons of water
24. 3628.8 g = ______ lbs
25. 15,840 feet = ______ miles
Section 5 TDEC - Fleming Training Center
Dimensional Analysis94
26. 35 ft³ = ______ gal
27. 2244 gpm = ______ ft³/sec of water
28. 8 MGD = ______ gpm
29. 312 gallons of water = ______ ft³ of water
30. 161.7 ft of head = ______ psi
31. 5,000 gpm = ______ MGD
32. 7 ft³/sec = ______ gpm
33. 5000 gallons of water = ______ ft³
34. 6 miles = ______ feet
35. 1 day = ______ minutes
TDEC - Fleming Training Center Section 5
Dimensional Analysis 95
Answers:
1. 14.29 m2
2. 15.42 lb
3. 3.11 mph
4. 17.03 L
5. 4.83 Km
6. 11.92
7. 4.88 m
8. 6.5 in
9. 94,625 mL
10. 33.0 km
11. 123.53 ft2
12. 10.71 yd2
13. 38.58 lb
14. 29.21 cm
15. 52.94 ft3
16. 0.42 ft3
17. 523.77 L
18. 17.26 yd2
19. 21.59 cm
20. 0.004 ac
21. 18,925 mL
22. 69.28 ft
23. 5 gal
24. 7.99 lb
25. 3 mi
26. 261.8 gal
27. 5 cfs
28. 5,552 gpm
29. 41.71 ft3
30. 70 psi
31. 7.2 MGD
32. 3,141.6 gal/min
33. 668.45 ft3
34. 31,680 ft
35. 1440 min
Section 5 TDEC - Fleming Training Center
Dimensional Analysis96
Math Fundamentals
Conversions (3)
1.) Convert 723 gallons to liters
2.) Convert 17oC to degrees Fahrenheit.
3.) How many feet are in 2.5 miles?
4.) Convert 56 grains per gallon to mg/L.
5.) Convert 56 ft3/s to gallons per minute.
6.) Convert 34oC to degrees Fahrenheit.
7.) Calculate 42.0% of 7,310.
8.) Convert 72 ppm to percent.
9.) A solution was found to be 7.6% hypochlorite. How many milligrams per
liter of hypochlorite are in the solution?
10.) Convert 8.77 acre-ft to gallons.
11.) Convert 1.98 acres to square feet.
TDEC - Fleming Training Center Section 5
Dimensional Analysis 97
12.) Convert 81 ft3 to gallons and liters.
13.) Convert 212oF to degrees Celsius.
14.) Convert 1472 L to gallons.
15.) Convert 0.25 miles to meters.
16.) Convert a chlorine solution of 2.5 ppm to percent.
17.) Convert 2,367 g to pounds.
18.) Convert 3.45 MGD to cubic feet per second.
19.) Convert 63.5% to ppm.
20.) What percent is 12,887 of 475, 258?
Convert the following:
21.) 451oF to degrees Celsius
22.) 8,711,400 gal to acre-feet.
Section 5 TDEC - Fleming Training Center
Dimensional Analysis98
23.) 35 cfs to gpm
24.) 8 lb/sec to lb/day
25.) 45 gal/min to ft3/day
26.) 927 cfm to gps
27.) 0.3 MGD to gal/hr
28.) 89 cfd to cfs
29.) 93 gal/sec to MGD
30.) 2 ft3/min to gal/day
31.) 17 gal/day to lb/min
32.) 1.7 acre-foot to gal
33.) 7800 mg/L to lbs/gal
34.) 890 lb/day to cfm
TDEC - Fleming Training Center Section 5
Dimensional Analysis 99
35.) 10,600 gpd to ft3/sec
36.) 900 grams to lbs
37.) 29.78 lb/hr to gpd
38.) 790 mL to gal
39.) 830 m/min to ft/day
40.) 379 km/day to mph
Section 5 TDEC - Fleming Training Center
Dimensional Analysis100
Conversion Answers:
1.) 2736.6 L
2.) 62.6oF
3.) 13,200 ft
4.) 957.6 mg/L
5.) 25,132.8 gpm
6.) 93.2oF
7.) 3,070.2
8.) 0.0072%
9.) 76,000 mg/L
10.) 2,859,020 gal
11.) 86,248.8 ft2
12.) 2,293.3 L
13.) 100oC
14.) 388.9 gal
15.) 402.6 m
16.) 0.00025%
17.) 5.2 lb
18.) 5.3 cfs
19.) 635,000 mg/L
20.) 2.7%
21.) 232.8oC
22.) 26.7 ac-ft
23.) 15,708 gpm
24.) 691,200 lb/day
25.) 8,663.1 cfd
26.) 115.6 gps
27.) 12,500 gal/hr
28.) 0.001 cfs
29.) 8.04 MGD
30.) 21,542.4 gpd
31.) 0.1 lb/min
32.) 554,200 gal
33.) 0.07 lb/gal
34.) 0.01 cfm
35.) 0.02 cfs
36.) 2.0 lb
37.) 85.7 gpd
38.) 0.2 gal
39.) 3,918,688.5 ft/day
40.) 9.8 mi/hr
TDEC - Fleming Training Center Section 5
Dimensional Analysis 101