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Contextualized Learning Packet

Welding Technology

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Contextualized Learning Packet

Applied Mathematics

Welding Technology

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What the WorkKeys Applied Mathematics Test MeasuresThere are five levels of difficulty. Level 3 is the least complex, and Level 7 is the most complex. The levels build on each other, each incorporating the skills assessed at the previous levels.

Level Characteristics of Items Skills

3 Translate easily from a word problem to a math equation

All needed information is presented in logical order

No extra information

Solve problems that require a single type of mathematics operation (addition, subtraction, multiplication, and division) using whole numbers

Add or subtract negative numbers Change numbers from one form to

another using whole numbers, fractions, decimals, or percentages

Convert simple money and time units (e.g., hours to minutes)


4 Information may be presented out of order

May include extra, unnecessary information

May include a simple chart, diagram, or graph

Solve problems that require one or two operations

Multiply negative numbers Calculate averages, simple ratios,

simple proportions, or rates using whole numbers and decimals

Add commonly known fractions, decimals, or percentages (e.g., 1/2, .75, 25%)

Add up to three fractions that share a common denominator

Multiply a mixed number by a whole number or decimal

Put the information in the right order before performing calculations


5 Problems require several steps of logic and calculation (e.g., problem may involve completing an order form by totaling the order and then computing tax)

Decide what information, calculations, or unit conversions to use to solve the problem

Look up a formula and perform single-step conversions within or between systems of measurement

Calculate using mixed units (e.g., 3.5 hours and 4 hours 30 minutes)

Divide negative numbers Find the best deal using one- and

two-step calculations and then

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compare results Calculate perimeters and areas of

basic shapes (rectangles and circles)

Calculate percent discounts or markups


6 May require considerable translation from verbal form to mathematical expression

Generally require considerable setup and involve multiple-step calculations

Use fractions, negative numbers, ratios, percentages, or mixed numbers

Rearrange a formula before solving a problem

Use two formulas to change from one unit to another within the same system of measurement

Use two formulas to change from one unit in one system of measurement to a unit in another system of measurement

Find mistakes in questions that belong at Levels 3, 4, and 5

Find the best deal and use the result for another calculation

Find areas of basic shapes when it may be necessary to rearrange the formula, convert units of measurement in the calculations, or use the result in further calculations

Find the volume of rectangular solids

Calculate multiple rates


7 Content or format may be unusual

Information may be incomplete or implicit

Problems often involve multiple steps of logic and calculation

Solve problems that include nonlinear functions and/or that involve more than one unknown

Find mistakes in Level 6 questions Convert between systems of measurement

that involve fractions, mixed numbers, decimals, and/or percentages

Calculate multiple areas and volumes of spheres, cylinders, or cones

Set up and manipulate complex ratios or proportions

Find the best deal when there are several choices

Apply basic statistical concepts

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1. Bob added up the hours on his timecard. He got a total of 37 6/8 hrs.

Reduce his hours to lowest terms.

2. You need to drill a hole in a piece of metal for an 11/16 inch bolt to pass thru

Will a ¾ inch hole be a little too big or little too small?

3. Arrange these four drill bits in order from smallest (left) to largest ( right) 3/8

11/32 7/16 13/32

4. Which steel bar is longer?

Bar 1 25 1/8 inches or Bar 2 25 3/32 inches

5. Eleven 2 and1/2 inch pieces are cut from a bar of round stock.

How much material is used? (Ignore any loss due to cutting.)

6. A rectangular plate which is 36" wide and 49" long is to be cut into strips that are 36" long and 7/8 in. wide.

How many strips can be cut from the plate?

7. 4 7/8 in long pieces are to be cut from a 120" long bar.

How many complete pieces can be cut from the bar?

8. Seven weldments, each 1 ¾ in, long, are made. What is the total length of weldments?

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9. A support bracket as shown below has equally spaced uprights welded to it. If the

distance between the centers of the first and fourth uprights is 16 ½"

Find the distance between the centers of the first and second uprights. 16 112"

10. If one piece of angle iron weighs 24 ½ lbs., how much will three pieces weigh?

11. If three tanks of propane gas lasted 22 3/8 days, how long did each tank last?

12. A 7 ¼ in piece and a 9 3/8 in are cut from a 49" length of round stock. If 1/8 in. of waste is allowed for each cut how much of the round stock remains?

13. A steel frame is constructed in the welding shop. At one corner, three pieces of steel overlap.

If their thicknesses are 3/8”, 3/16”, 5/32” what will the total thickness be?

14. Given the following diagram, determine the distance "X".

Note: You may assume that the 3/8" dia. hole is centered on the width of the piece

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15. What is the total clearance when a 5/16" bolt is inserted into a 3/8" hole?

16. Convert each of the following drill bit sizes to decimal form then rearrange them in order from the smallest (left) to the largest (right).

3/8 5/16 7/16 11/32 13/32

17. A ¾ in. wrench is needed to loosen a hex-head bolt.

What would be the decimal size wrench that could be used?

18. A specification calls for the clearance between piston and cylinder in an engine to be 3/64 in.

What is its decimal equivalent? (Nearest ten thousandth)

19. Four sheets of sheet metal have the following thicknesses:3/16 in. 11/16 in. 7/32 in. 1/8 in.

Convert these to decimal form and then arrange them from thinnest to thickest.

20. You are to bore a hole which is 0.27 " in diameter.

If you have a drill bit set that is made in increments of 64ths of an inch, what size drill bit will give a hole of at least 0.27"?

21. Two pieces of metal overlap as shown.

If these are welded together, what is the total length of the welded piece?

22. Three rectangular sections of plate steel are connected by overlaps as shown below.

Using the dimensions given, find the total length of the welded section.

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23. A cross-section of steel channel as shown below has a width of 4.25 inches, with each flange having a thickness of 0.1875 inches.

Determine the inside width of the channel. (nearest thousandth)

24. Using the diagram below, determine the thickness of the main stem of the I-beam (dimension "X")

25. Two holes, 3.6cm and 3.2cm in diameter, are drilled into a 20cm long strip of steel bar as shown below.

Using the given dimensions, find the missing dimension, labeled "x” that separates the edges of the two holes.

26. What is the final cost for this stock order?

Quantity Description Unit Price

15 ¾" 8' stock $3.49 per 8' section10 112" 8' stock $2.75 per 8' section25 114" 8' stock $2.23 per 8' section

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27. Eleven 8 inch long sections of ½” inch diameter round stock is needed.

If 0.125" of material is lost from each cut, what will be the total length of material removed from a 120 inch bar? (Nearest thousandth)

28. Thirty-five L-shaped pieces are cut from sheet metal which is 0.310" thick. The pieces are then stacked as shown below.

What is the height of that stack of metal pieces? (Nearest thousandth)

29. A strip of metal 20" long has four rectangular slots each 2.5" long stamped from it.

If the spacing between the slots is 1.75", how far is it from the end of the metal strip to the edge of the first slot?

30. A 72" length of angle iron is subdivided into 7 pieces of equal length.

If 1/8" is allowed for each cut, what is the length of each piece? (Nearest hundredth)

31. Calculate the weight of a product if the parts before welding have the following weights:

5 lengths of angle iron, each 3.6Ibs

4 lengths of bar steel, each 1.1lbs

2 lengths of round stock, each 0.85 lbs.

32. A portable welding unit was purchased at a list price of $795 less a 10% discount plus a 5% sales tax.

What is the selling price?

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20”

33. A series of holes are drilled into a circular flange. The spec calls for diameters of 0.65 in. ± 0.05".

Restate the tolerance in terms of percentage. (i.e., 0.75 in.±?%)

34. The diameter of certain round stock is 112 in. ±0.3%.

What maximum diameter could a buyer expect from the stock?

35. The supply of metal stock in a shop weighs about 3 tons.

If 0.2 ton of this is used, what percentage remains? (Nearest percent)

36. A motor is rated at 85% efficiency.

If it has an input power of 1/2 HP, what would be its output power? (Nearest hundredth)

37. A shop does $1300 worth of business one month and $1700 worth of business the next.

What is the rate of increase? (Nearest whole percent)

38. A welder receives a $0.24/hour raise.

If he used to get $7.50 for 1hr, what is the percent increase in his salary? (Nearest tenth of a percent)

39. A frame is made up of five l-ft sections of solid round stock steel that is 0.5" in diameter each steel bar weighs 0.67 lbs. A solid aluminum rod with the same dimensions weighs 0.23 lbs.

If the aluminum rods replaced the steel bars mentioned above, what will be the percent decrease in weight of the frame?

Find the measurements for the questions 40 to 45:

40..

41.

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42.

43.

44.

45.

46. Find the weight of a 1 ft. long piece of steel round stock if the diameter is 2".

Use the formula: lbs. per linear ft. = 3.67 X D2

47. Using the information found in problem #46, what's the weight of a 65 ft. piece of round stock?

48. Find the weight of a 1 ft. piece of aluminum tubing that has dimensions W=.125", and OD=2.375":

Use the formula: lbs. per linear ft. = 2.69 x (OD - W) x W

49. How much would a 23.5 ft. piece of the above tubing weigh?

50. A rectangular frame measures 9 6 " by 48".

Find the length of the diagonal, dimension C, using this formula:

C = . J a2 + b

51. Determine the volume of an oxygen cylinder with a height of 24" and a diameter of 6", by using this formula:

V= 3.14 x H x D 2 divided by 4

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52. Identify the type of angle and give its measurement.



55. Find the total length of stock needed to make this table frame?

56. Find the total area of these plates that are welded together?

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57. Find the area and perimeter of this flame-cut steel plate.

s

58. Compare the areas of these two figures. Since the sides are the same length, are the areas the same?

59. Calculate the perimeter and the area of the following.


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62. Calculate the perimeter:

63. Calculate the perimeter.

64. Find the missing dimension. (Round to the nearest tenth.)

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65. Find the missing dimension.

66. Find the missing dimension. (Round to the nearest tenth)

67. Find the missing dimension.

68. Find the Area.

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69. Find the area. (Round to the nearest tenth)

70. Find the area. (Round to the nearest whole number)

71. Find the circumference. (Round to the nearest tenth)

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74. Find the area of the ring. (Round to the nearest tenth)

75. A welder is required to sheer-cut a piece of sheet steel as shown in the illustration.

After the cut piece is removed, how much sheet, in inches, remains from the original piece?

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76. Welded support is illustrated.

A customer orders 34 supports:

A. What, in inches, is the total length of weld needed?

B. The support plate is 13 inches long and 9 inches wide. How much 9-inch-wide bar stock, in inches, is used for the completed order?

C. Each support weighs 14 pounds. What is the weight in pounds of the total order?

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Make fractions out of the following information:

(Reduce, if possible)

77. An inch into 8ths

78. Read the distances from the start of the steel tape measure to the letters. Record the answers in the proper blanks.

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79. Find the total combined length of these 2 pieces of bar stock

80. Find the total combined weight of these 3 pieces of steel.

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81. To make shims for leveling a shear, three pieces of material are welded together.

What is the total thickness of the welded material, in inches?

82. Determine the missing dimension on this welded bracket.

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83. A frame-cut wheel is to have the shape shown. Find the missing dimension.

84. Three of these welded brackets are needed.

What is the total length, in inches, of the bar stock needed for all of the brackets?

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85. This piece of angle is to be used for an anchor bracket.

If the holes are equally spaced, what is the measurement between hole 1 and hole 2?

86. Nine sections of steel bar, each 12 ¼” long, are welded together. The finished piece is cut into 4 equal parts.

What is the length of each new piece? Disregard cut waste.

87. Round off to the nearest whole number.

a. 7.7 _________________

b. 12.1 _________________

c. 9.7 _________________

d. 17.398 _________________

88. A welder uses 4.18 cubic feet of acetylene gas to cut one flange.

How much acetylene gas is used to cut 19 flanges?

89. A welder shears key stock into pieces 3.75” long.

How many whole pieces are sheared from a length of key stock 74.15” long?

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90. Express each decimal dimension as a fractional number.

91. A piece of steel channel and a piece of I beam are needed. Express each dimension as a decimal number.

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92. Find the length of slot 2.

93. The fillet weld shown has 2’, plus 18” of weld on the other side of the joint.

Express the total amount of weld in feet.

94. Six welding jobs are completed using 33 pounds, 13 pounds, 48 pounds, 14 pounds, 31 pounds, and 95 pounds of electrodes.

What is the average poundage of electrodes used for each job?

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95. This I Beam is 180 cm long and 14.5 cm high. (Round each answer to two decimal places)

96. How many square inches are in 2 square foot?

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97. These two triangular shapes are cut from sheet metal.

What is the area of each piece in square inches?

1. Triangle A ________________ ii) Triangle C ___________

98. Two pieces of square stock are welded together. Find, in cubic feet, the total volume of the pieces. (Round the answer to three decimal places)

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99. Circles A and B are cut from 3/8 steel plate. What is the circumference of both circles in inches and in feet?

A. __________Inches B. _____________Inches

__________Feet _____________Feet

100. How many degrees are in each of these parts of a circle?

i) 1/3 Circle _______________

ii) 5/6 Circle _______________

101. Find the size of ¼” plate needed to construct this semicircular ventilation section. The average diameter is 19 3/16.

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102. A weld shop supplies 104 shaft blanks, each 4” wide and 5” long. How many can be cut from the piece of plate shown?

103. The circular bland is used to make sprocket drives.

How many sprocket drive blanks can be cut from a plate of steel having the dimensions of 44” x 44”?

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ANSWER SHEETQ # ANSWER1 37 ¾ 2 TO BIG3 11/32, 3/8,

13/32, 7/12

4 BAR 15 27.56 56 STRIPS7 24 WHOLE PIECES8 12 ¼ 9 5 ½ 10 73 ½ LBS.11 7.5 DAYS

ROUNDED12 32 1/8

13 23/32

14 3/16

15 1/16

16 0.31250.343750.3750.406250.4375

17 0.7518 0.0469 ROUNDED19 0.125

0.18750.218750.6875

20 18/64

21 13.922 44.5 CM.23 3.87524 1.525 5.2 CM.26 $135.60 27 89.37528 10.8529 2.37530 10.231 23 LBS.32 $751.27 33 6.7

34 0.502535 96.7 ROUNDED36 0.45 HP.37 30.80%38 2.90%39 65.70%40 2 5/16 41 1 7/16

42 4 11/16

43 5 3/16

44 9 1/2

45 9 ¾ 46 14.68 LBS.47 95.42 LBS.48 1.03 LBS.49 24.2 LBS.50 16.7351 678.24 CU.IN.52 OBTUSE 112 DEG.53 ACUTE 49 DEG.54 RIGHT 90 DEG.55 249.556 28.25 SQ. IN.57 69 CM.58 NOT THE SAME59 P=36IN.

A=54SQ. IN.60 P=91YDS.

A=390SQ. YD.61 P=32FT.

A=45SQ. FT.62 P=16CM.63 P=44FT.64 18.3IN..65 20 IN.66 13.7 FT.67 86.6 MTRS.68 4.5SQ. FT.69 210.4SQ. FT.70 65 SQ. FT.71 100.5 in.

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72 16.6 sq. mtrs73 19.6 sq. in.74 141.4 sq. ft.75 1776 272. IN

442 IN476 LBS

77 1/8 IN3/8 IN½ IN¾ IN

78 ¼ in5/8 IN1 AND 1/8

2 AND 1/8

79 8 AND 5/8

80 29 AND 3/8

81 1 AND 5/8

82 6 AND 1/8

83 2 AND 9/16

84 53 AND 7/16

85 3 AND 9/74

86 27 AND 9/16

87 8121017

88 79.42CUFT89 19 PIECES90 9 AND ½

2 AND ¾ 91 2.25 IN

0.1875 IN6.5625 IN

92 7.037593 3 AND ½ FT94 39 LBS95 70.87 IN

5.71 IN96 288 SQ IN97 32 SQ IN

72 SQ IN98 2.949 CU FT99 A=30.35 FT

364.24 IN

B=13.345 FT160.14 IN

100 120 DEG300 DEG

101 ¾ X63 AND ¾ IN

102 72 PIECES103 9 PIECES

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Mathematical Points to Remember and

Problem Solving TipsAdditionUse addition in order to find the total when combining two or more amounts.SubtractionUse subtraction in order to:

Determine how much remains when taking a particular amount away from a larger amount

Determine the difference between two numbers

MultiplicationUse multiplication to find a total when there are a number of equally sized groups.DivisionUse division to:

Split a larger amount into equal parts Share a larger amount equally amount a certain number of people or groups

Calculating Time

When solving problems that involve time, using a visual aid such as an analog clock can be very helpful.

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TimeWhen adding time, be careful to distinguish between A.M. and P.M times. If you begin at a P.M. time and the elapsed time takes you past midnight the ending time will likely be in A.M. If you start from an A.M. time and the elapsed time takes you past noon, the ending time will likely be in P.M. time. For instance, if you start sleeping at 10 P.M. and you sleep for 8 hours, the time you will wake up is going to be in the A.M. To calculate, add the hours, and then subtract 12 from

the total – 10 + 8 = 18 hours; 18 hours – 12 hours = 6 hours past midnight or 6 A.M.Fraction/Decimal/Percent

Fraction – identifies the number of parts (top number) divided by the total number of pars in the whole (bottom number)

Decimal – place values to identify part of 1, written in tenths, hundredths, thousandths, etc.

Percent – part of 100.

Remember!A decimal number reads the same as its fractional equivalent. For example, 0.4 = four tenths = 4/10; 0.15 = fifteen hundredths = 15/100

When working with fraction and decimal quantities that are greater than 1, remember that these numbers can be written as the number of wholes plus the

number of parts. For example, 2.5 can be written as 2 + 0.5 (two wholes plus five-tenths of another whole). The mixed number 2 ½ can be written as 2 + ½ (2 wholes plus half of another whole). When converting these numbers, the

whole number stays the same. Always remember to add the whole number back to the fraction or decimal after you have completed converting.Multiplying fractions by fractionsDecimals are named by their ending place value – tenth’s, hundredths, thousandth’s, etc. This makes it easy to convert to fractions.

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0.3 “3 tenths” 3/10

0.76 “76 hundredths” 76/100

0.923 “923 thousandths” 923/1000

1.7 “1 and 7 tenths” 1 7/10

When you multiply a fraction by another fraction, the result is the product of the numerators over the product of the denominators.

4/5 x 2/3 = 8/15

To multiply a fraction by a decimal, convert the fraction to a decimal:½ x .25 = .5 x .25 = .125

Basic AlgebraBasic algebra involves solving equations for which there is a missing value. This value is often represented as a letter; such as the letter x or n. Solving equations for a missing value requires you to understand opposite operations. Addition and subtraction are opposite operations as well as multiplication and division. You use opposite operations so that an equation can remain “balanced” when solving the missing value.ProportionsMultiple operations are using when solving proportions. After the proportion statement is set up, multiply in order to find cross products. Then divide each side of the equation by the factor being multiplied by the unknown variable to solve for the unknown variable.

n8=16

4040 x n = 16 x 8

40n = 128

n = 12840 = 3

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Order of OperationsWhen calculations require you to more than one operation, you must follow the order of operations. Any operation containing a parenthesis must be calculated first. Exponents come next in the order of operations, followed by multiplication and division, addition and subtraction come last. An easy way to remember the order of operation is: PEMDAS or Please Excuse My Dear Aunt Sally – Parenthesis/Exponents/Multiplication/Division/Addition/SubtractionExponentsAn exponent is an expression that shows a number is multiplied by itself. The base is the number to be multiplied. The exponent tells how many times the base is multiplied by itself.

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The base is 2. The exponent is 3.2 x 2 x 2 = 8

Multiplying Negative Numbers

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Multiplying negative numbers is similar to multiplying positive numbers except for two rules:

When multiplying a positive number and a negative number, the answer is always negative

8 x (-6) = -48

When multiplying two negative numbers, the answer is always positive.

-2 x (-7) = 14By knowing the rules of multiplying positive and negative numbers, you can rule out incorrect answers before performing any calculations.

Perimeter MeasuresPerimeter measures the length of the outer edge of a shape. The space enclosed within this edge is measured by area. Area is a two-dimensional measurement that measures the number of square units of a surface.

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Formulas for Perimeter and Area of RectanglesTo understand the formulas for finding perimeters and area, consider the figure on the next page, which is 3 units wide by 5 units long.

Perimeter: by counting the number of units on each side of the rectangle, you find that the perimeter is 16 units.

Area: Area is a 2 dimensional (2D) measurement that measures a surface. By counting the total number of squares that make up the rectangle, you find that its area is 15 square units. So the formula is:

area = length x width

Volume is a 3 dimensional (3D) measurement that measures the amount of space taken up by an object. Like area, you need to know the length and width of an object in order to calculate volume. In addition to this, you need to know the object’s height. Volume is measured in cubic units. Use the formula V = 1 x W x hConvert Measurements

In the United States, there are two systems of measurements; the traditional (standard) system and the metric system. Gasoline is usually sold by the gallon (standard), and large bottles of soda are sold by the liter (metric).The Metric SystemThe metric system of measurement is used by most of the world. Units of length are measured in centimeters, meters, and kilometers. Units of

volume (capacity) include liters and milliliters. Units of weight include milligrams, grams, and kilograms. The metric system follows the base -10 system of numeration. This system is commonly used in sciences and medicine.

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The Customary/Standard SystemThe customary or standard system of measurement is the system most commonly used in everyday life in the United States. Units of length include inches, feet, and miles. Units of volume include cups, quarts, and gallons. Units of weight include ounces, pounds and tons. Unlike the metric system, the standard system of measurement does not follow the base -10 system.If you are unsure of whether to multiply or divide to convert from one unit of measurement to another, you can set up the problem as a proportion. Here is an example:

1 liter0.264 gallons =

x liters21 gallons

By finding the cross products, you see that:0.264x = 21

The final step needed to solve is to divide both sides of the equation by 0.264, which gives you the answer of x = 79.5 liters.

What’s the best deal? Use Ratios and Proportions to find the outcomeA rate is a kind of ratio. Rates compare two quantities that have different units of measure, such as miles and hours.

Unit RatesUnit rates have 1 as their second term. An example of unit rate is $32 per hour.

$32

1hourAnother example of a unit rate is $6 per page

$ 61 page

ProportionsProportions show equivalent ratios. You may find it helpful to use proportions to solve problems involving rates. Calculate the total cost based on the hourly rate. To find the total cost based on an hourly rate, multiply the number of hours worked by the hourly rate.

$ 321hour =

$ 48015 hours

Convert Between Systems of MeasurementWhen solving problems that involve converting from one unit of measurement to another, you typically should first determine to which unit of measurement you should be converting. For example:You are the service manager for a corporation and are responsible for a fleet of vehicles. You need to determine which brand of engine oil to use with your fleet. There are two brands that you are deciding between. So, you

decided to run a test between the two brands. On average, a vehicle burned 5 milliliters of the more expensive synthetic blend. The average consumption of regular engine oil was 64 milliliters. Each vehicle holds 5.8 quarts of engine oil. What percentage of the regular oil was lost during the test?

A. 0.5% B. 1.2% C. 3.2% D. 5.6% E. 9.1%

Plan for Successful Solving

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What am I asked to do?

What are the facts?

How do I find the answer?

Is there any unnecessary information?

What prior knowledge will help me?

Find the percent of regular engine oil that was used

The engine holds 5.8 quarts, 64 ml of oil was lost

Convert one measurement to the same system as the other. Calculate the percentage that was lost.

5 milliliters of the synthetic oil was consumed

1 gallon = 4 qts.4 quarts = 1 liter1 liter = 0.264 gal.1 liter = 1,000 milliliters

Confirm your understanding of the problem and revise your plan as needed. Based on your plan, determine your solution approach: I am going to convert the quarts

to milliliters and then find the percent of the total that was lost.

5.8 quarts ÷ 4 = 1.45 gallons Divide to convert quarts to gallons1.45 gallons ÷ 0.264 ≈ 5.492 liters Divide to convert gallons to liters5.492 liters x 1,000 = 5,492 milliliters Multiply to convert liters to milliliters

64 milliliters5,492milliliters = 0.012 x 100% = 1.2% Divide the amount of oil that was lost by the initial

total to calculate the percent of lubricant that was consumed.

Check your answer. You can solve the problem another way by converting the milliliters to quarts and finding the percent.

Select the correct answer: B. 1.2% By converting the units of measure to the same system, you can calculate the percent of

oil lost in the test by dividing the amount consumed by the total capacity and multiplying by 100%

The symbol ≈ means “approximately equal to” and is used because the conversion formula between gallons and liters is not exact. When calculating conversions between measurements for which the conversions are not exact, you must take into account the fact that the numbers are often rounded at some point during the calculation

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BASIC ALGEBRA RULES

1. DO BRACKETS FIRST Example: ( ) [ ]

2. WHEN YOU ARE ADDING OR SUBTRACTING NUMBERS:IF YOU HAVE MORE POSITIVES THAN NEGATIVES NUMBERS YOUR ANSWER WILL BE A PLUS ANSWER.

Example: -4 + 7 equals +3

3. WHEN YOU ARE ADDING OR SUBTRACTING NUMBERS:IF YOU HAVE MORE NEGATIVES THAN POSITIVES NUMBERS YOUR

ANSWER WILL BE A MINUS ANSWERExample: -7 + 4 equals -3

4. WHEN YOU ARE MULTIPLYING OR DIVIDING NUMBERS LIKE SIGNS ARE POSITIVE AND UNLIKE SIGNS ARE MINUS

Example: (+ and + or -+- +) equal a plus sign (- and +) equals minus

5. WHEN ADDING OR SUBTRACTING EXPONENTS LIKE EXPONENTS CAN ONLY BE ADDED TOGETHER

Example: x to the second power can be combined With another x to the second power only

6. WHEN YOU ARE MULTIPLYING WHOLE NUMBERS 7. THEY ARE MULTIPLIED, AND EXPONENTS ARE ADDED TOGETHER

Example: 3x to the third power times 2x to the second power equals 6x to the fifth power

8. WHEN YOU DIVIDE NUMBERS THEY ARE DIVIDED AS USUAL AND EXPONENTS ARE SUBTRACTED FROM EACH OTHER

Example: 16m to the third power divided by 4m equals 4m to the second power

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Formulas 1Gear Ratio = Number of Teeth on the Driving

Gear

Number of Teeth on the DrivenGear

Reduce to Lowest Terms

Pulley Ratio = Diameter of Pulley A Diameter of Pulley B


Compression Ratio = Expanded Volume Compressed Volume


A Proportion is 2 Ratios that are = Example 1/3 = 4/12

Cross Product Rule A/B = C/D or A x D = B x C

Pitch = Rise Run

Changing a Decimal to a % Multiply by 100

Changing a Fraction to a % Divide the Numerator by the Denominator and Multiply by 100

Changing a % to a Decimal Divide by 100

P/B = R/100

When P is unknown

When R is unknown

When B is unknown

Changing a decimal to a fraction .375 hit 2nd hit prb hit enter

Sales Tax Sales Tax = Tax Rate Cost 100

Interest Annual Interest = Annual Interest Rate

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Principal 100

Commission Commission Sales = Rate Sales 100

Efficiency Output = Efficiency Input 100

Tolerance Tolerance = % of ToleranceMeasurement 100

% of Change Amount of Increase = % of Increase Original Amount 100

Discounts Sales Price = List Price –

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Discount

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PERCENT PROBLEMSThe Percent (%)The Whole (OF)The Part (IS)

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Trig Formulas

1. Change an angle to radians = angle times pie divided by 1802. Change an angle to degrees = radians times 180 divided by pie3. 30 deg., 60 deg., 90 deg., triangle; the short end is equal to ½ the hypotenuse or the

hypotenuse = 2 times the short end4. 45 deg., 45 deg., 90 deg., triangle – the 2 shorter sides are the same length and the

hypotenuse is 1.4114 times the leg5. Find trig value – put in SIN, COS, or TAN followed by degrees and hit enter6. Find acute angle X – hit 2nd button, then SIN, COS, or TAN; enter number and hit equals. Hit

RP move arrow to DMS hit enter twiceYou would use this when you need an answer in degrees, minutes, and or seconds

7. Find acute angle X – hit 2nd button, then SIN, COS, or TAN; enter number and hit equals. You would use this when you need an answer in degrees.

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Applied Mathematics Formula Sheet

Distance1 foot = 12 inches1 yard = 3 feet1 mile = 5,280 feet1 mile ≈ 1.61 kilometers1 inch = 2.54 centimeters1 foot = 0.3048 meters1 meter = 1,000 millimeters1 meter = 100 centimeters1 kilometer = 1,000 meters1 kilometer ≈ 0.62 miles

Area1 square foot = 144 inches1 square yard = 9 square feet1 acre = 43,560

Volume1 cup = 8 fluid ounces1 quart = 4 cups1 gallon = 4 quarts1 gallon = 231 cubic inches1 liter ≈ 0.264 gallons1 cubic foot = 1,728 cubic inches1 cubic yard = 27 cubic feet1 board = 1 inch by 12 inches by 12 inch

Weight1 ounce ≈ 28.3501 pound = 16 ounces1 pound ≈ 453.592 grams1 milligram = 0.0001 grams1 kilogram = 1,000 grams1 kilogram ≈ 2.2 pounds1 ton = 2,000 pounds

Rectangleperimeter = 2(length + width)area = length x width

Rectangle Solid (Box)volume = length x width x height

Cubevolume = (length of side)3

Trianglesum of angles = 180o

area = ½(base x height)

Circlenumber of degrees in a circle = 360o

circumference ≈ 3.14 x diameterarea ≈ 3.14 x (radius)2

Cylindervolume ≈ 3.14 x (radius)2 x height

Conevolume ≈ 3.14 × (radius)2 × height

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Sphere (Ball)volume ≈ 4/3 x 3.14 x (radius)3

Electricity1 kilowatt-hour = 1,000 watt-hoursAmps = watts ÷ volts

TemperatureoC = 0.56(oF-32) or 5/9(oF-32)oF = 1.8(oC) + 32 or (9/5 x oC) + 32

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