Tech Prep/Mtag Curriculum

MTAG MODULARIZED CURRICULUM

APPLIED MATHEMATICS ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 2 TECH PREP/MTAG CURRICULUM Applied Mathematics

MODULE DESCRIPTION This module exposes students to common applications of mathematics within manufacturing and provides opportunities to develop proficiency in arithmetic calculations.

MODULE OUTCOME After completing this module, students should be able to convert between USCS, fractional, and metric measurements and consult tolerances to properly dimension parts.

PERFORMANCE CRITERIA  Given a drawing with USCS measurements and a copy of the same drawing with no measurements, the student will be able to dimension the second drawing with metric equivalents  Using a pencil and paper, the student will be able to convert ten different fractional measurements to decimal measurements to the thousandth decimal place.  The student with be able to perform basic addition, subtraction, multiplication, and division using decimals, fractions, ratios, and percentages.

SEQUENCING Introduction Working with Decimals Adding Fractions and Mixed Numbers Practice Adding & Subtracting Fractions Converting between Fractions and Decimals Practice Converting between Fractions and Decimals Application: Working with Fractions Skill Check 1: Working with Fractions Working with Tolerances Practice with Tolerances Application: Working with Tolerances Skill Check 2: Working with Tolerances The Metric System Practice with the Metric System Skill Check 3: Converting From English to Metric Units Final Skill Check Module Evaluation

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 3 ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 4 Student Assessment Rubric

Module: Applied Mathematics Student: Date: Location: Ratings: 1 =demonstrates poor 2 =demonstrates limited 3 =demonstrates good 4 = demonstrates excellent understanding of core concepts understanding of core concepts understanding of core concepts understanding of core concepts  Cannot complete tasks  can perform complete with supervision  can complete tasks without supervision  can teach tasks to others  Makes frequent errors  makes occasional errors  makes few errors  makes no errors  Offers no suggestions  offers suggestions  offers effective suggestions  offers creative & effective suggestions

Skill Check 1 1 2 3 4 Reason for Rating:

Final Skill Check 1 2 3 4 Reason for Rating:

TOTAL SCORE Summary Comments:

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 5 PUGET SOUND CONSORTIUM FOR MANUFACTURING EXCELLENCE (CME) MODULE EVALUATION SURVEY—STUDENT FORM

We would like to ask you questions about the CME module curriculum so we can make it better. You don’t have to fill out the survey or answer all the questions. Please don’t tell us your name. Circle one response for each question. 1. Which module did you work with? (circle one) Applied Mathematics Career Exploration Computer Applications Hazardous Materials Interpreting Technical Drawing Interpersonal Effectiveness Introduction to Manufacturing Job Readiness Labor in Industry Manufacturing Field Trip Manufacturing Planning Precision Measurement Safety in Manufacturing Shop Skills Statistical Process Control Total Quality Management

2. How challenging was the module? Very easy Easy Challenging Very Challenging 3. How effective were the exercises in helping you learn the material? Very ineffective Ineffective Effective Very Effective 4. How easy was it to stay focused on the module? Very Difficult Difficult Easy Very Easy 5. Were the objectives clear? Yes No 6. At the end of the module, did you feel that you met the objectives? Yes No

7. What did you like best about the module? (if you need more space, please use the back of the sheet)

8. What was the most important thing that you learned?

9. What would you suggest to make the module better?

We want to make sure the module works well for all students. 10. Please describe yourself: (circle all that apply) Black/African American Pacific Islander Latina/o American White/Caucasian American Asian American Native American/Alaskan Other (please specify):

11. Your gender: Male Female

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 6 Handout 1 Working with Decimals

Decimals in Drawings  Many dimensions in drawings are expressed in decimals.

 Students need to be comfortable in working to thousandths of an inch, and in many cases, to ten-thousandths.

Places in Decimals  In decimal notation, inches are written to the left of the decimal point and fractions are to the right: 100.000 = one hundred 10.000 = ten 1.000 = one 0.100 = one tenth 0.010 = one hundredth 0.001 = one thousandth

Reading Decimals

 To read decimals, work from the decimal point.

 For example, the decimal 137.295 is 100 + 30 + 7 inches. The fraction is 2 tenths + 9 hundredths + 5 thousandths

 You would express this as 137 inches, 295 thousandths.

Adding and Subtracting Decimals

 Line up the decimals so that the decimal points are above each other, the tenths are above each other, the hundredths are above each other.

 Then add or subtract normally

Examples:

132.525 436.295 276.524 373.325 +245.237 +385.378 -132.316 -198.436 ______377.762 821.673 144.208 174.889

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 7 Handout 2

Practice Reading, Adding and Subtracting Decimals

Answer the following questions and provide the results to the instructor when you are done.

1. 245.898 = ___ hundreds, ___ tens, ___ units, ___ tenths, ___ hundredths, ___ thousandths

6. 234.575 7. 413.527 +165.424 +367.462

8. 621.354 9. 466.487 +176.597 +287.735

10. 323.768 11. 464.757 +269.577 -176.364

12. 789.237 13. 895.362 -395.388 -309.487

14. 547.573 15. 462.361 -253.682 -189.693

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 8 Overhead 3 Answer Key: Practice Reading, Adding and Subtracting Decimals

1. 245.898 = _2_ hundreds, _4_ tens, _5_ units, _8_ tenths, _9_ hundredths, _8_ thousandths

6. 234.575 7. 413.527 +165.424 +367.462 399.999 780.989

8. 621.354 9. 466.487 +176.597 +287.735 797.941 854.222

10. 323.768 11. 464.757 +269.577 -176.364 583.345 288.393

12. 789.237 13. 895.362 -395.388 -309.487 383.849 585.875

14. 547.573 15. 462.361 -253.682 -189.693 293.891 272.668

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 9 Handout 4 Working with Fractions Rule of the Lowest Common Denominator  The number at the top of a fraction is called the numerator. The number at the bottom is called the denominator. See below: ½ 1 is the numerator, 2 is the denominator 5/32 5 is the numerator, 32 is the denominator  If you are adding or subtracting fractions, the denominators have to be the same. You can’t add the two numbers above as they are, instead you need to multiply the fractions by some other number such that the denominators of the fractions are equal.  You do not have to multiply both fractions by the same number.  The only rule is that the number by which you multiply must be a fraction equal to 1. For example we could multiply by 2/2, 5/5, or even 1348/1348. Remember that saying 5/5 is equivalent to saying 55, and a number divided by itself is equal to 1.  The goal is to keep the denominators as small as possible and have them equal. SPEED LESSON – Multiplying Fractions To multiply two fractions a/b and c/d, simply multiply the numerators together and multiply the denominators together to get a new numerator and denominator. In mathematical terms: a c ac b  d  bd For example 4/5 multiplied by 2/3 is equal to 8/15.  Continuing with the example, if we multiply ½ by 16/16 we get 16/32, which has the same denominator as 5/32. Adding the Fractions  Having done the conversion above, we can now add the two fractions. This is done by adding the numerators and keeping the same denominator:

16 5 165 21 32  32  32  32

Subtracting the Fractions  To subtract the fractions, first do exactly the same conversion to get the denominators the same, and then subtract the numerators as follows:

16 5 165 11 32  32  32  32

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 10 Handout 5a Working with Mixed Fractions

Numbers such as 2 1/2 are called “Mixed Fractions” because they are a mix of a whole number part, the 2, and a fractional part, the 1/2. Mathematically mixed fractions are equivalent to adding the whole number to the fractional part. For example, 3 15/16 is mathematically equivalent to 3 + 15/16. Below we will discuss two methods by which to add and subtract mixed fractions.

METHOD 1 Assume you wanted to add 2 1/2 + 5/8.

STEP 1 – Convert 2 ½ to a fraction. To do this start by multiplying the whole number by the denominator, 2 x 2 = 4, and add that product to the numerator, 4 + 1 = 5. This number, in this case 5, is the new numerator, and the denominator stays the same, 2. Thus the mixed fraction 2 1/2 converted to a standard fraction is 5/2.

STEP 2 – Add the fractions. Now you can add the fractions as was done in the last section: 5/2 + 5/8 = 20/8 + 5/8 = 25/8

 If you end up with a fraction whose numerator is larger than its denominator, then that fraction needs to be converted back into a mixed fraction. In our running example, 25 is larger than 8, therefore we need to convert 25/8 to a mixed fraction.

STEP 3 – Convert back to a mixed fraction. You do this by dividing 8 into 25. It goes 3 times with a remainder of 1. The 3 is the whole number, the 1 is the new numerator, and the denominator stays as an 8.

 So the final answer is: 2 ½ + 7/8 = 3 3/8

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 11 Handout 5b Working with Mixed Fractions (p. 2 of 2) METHOD 2 This time we’ll add the same two fractions, 2 1/2 + 5/8, but use a slightly different method. This method utilizes the fact that a mixed fraction is mathematically equivalent to the whole number added to the fractional part (i.e. 2 1/2 = 2 + 1/2).

STEP 1 – Add like parts of the fractions. Utilizing the fact that 2 1/2 = 2 + 1/2 then 2 1/2 + 5/8 is the same as 2+1/2+5/8. Since addition can be done in any order, add the whole number parts of each mixed fraction together and the fractional parts of each mixed fraction together. In our example, 2 is the whole number part of 2 1/2 and 0 is the whole number part of 5/8. So, adding the whole numbers gives us 2 + 0 = 2. Similarly, the fractional part of 2 1/2 is 1/2 and the fractional part of 5/8 is 5/8, therefore adding the fractional parts 1/2 +5/8 = 4/8 + 5/8 = 9/8.

 Now a slight analysis is required. If the new fractional part has a bigger numerator than a denominator, similarly to method 1, that fraction needs to be converted to a mixed fraction. In our example, since the numerator, 9, is bigger than the denominator, 8, we need to make the conversion to a mixed fraction.

STEP 2 – Convert the fractional part to a mixed fraction To do this divide 8 into 9. It goes 1 time with a remainder of 1. The first 1 is the whole number, the remainder 1 is the new numerator, and the denominator stays as an 8.

 So far, from step 1 we have a whole number of 2, and from step 2 we have a whole number of 1 and a fraction of 1/8.

STEP 3 – Add the remaining parts together. In our example this is 2+1+1/8, which is the same as 3+1/8, and is thus the mixed fraction 3 1/8.

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 12 Handout 6 Practice Adding & Subtracting Fractions

Add or subtract the following mixed fractions without a calculator. Show how you did it.

1. 3/8 + 7/8 =

2. 3/4 – 5/8 =

3. 3/8 + 13/16 =

4. 15/16 – 3/4 =

5. 9/16 + 3/32 =

6. 3 3/4 + 1 7/8 =

7. 2 5/16 – 3/4 =

8. 2 7/8 + 1 15/16 =

9. 3 3/16 – 1 1/2 =

10. 9 3/32 + 4 1/8 =

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 13 Overhead 7 Answer Key: Practice Adding & Subtracting Fractions

1. 3/8 + 7/8 = 10/8 = 1 2/8 = 1 1/4

2. 3/4 – 5/8 = 6/8 – 5/8 = 1/8

3. 3/8 + 13/16 = 6/16 + 13/16 = 19/16 = 1 3/16

4. 15/16 – 3/4 = 15/16 – 12/16= 3/16

5. 9/16 + 3/32 = 18/32 + 3/32 = 21/32

6. 3 3/4 + 1 7/8 = 15/4 + 15/8 = 30/8 + 15/8 = 45/8 = 5 5/8

7. 2 5/16 – 3/4 = 37/16 – 12/16 = 25/16 = 1 9/16

8. 2 7/8 + 1 15/16 = 23/8 + 31/16 = 46/16 + 31/16 = 77/16 = 4 13/16

9. 3 3/16 – 1 1/2 = 51/16 – 3/2 = 51/16 – 24/16 = 27/16 = 1 11/16

10. 3/32 + 4 1/8 = 291/32 + 33/8 = 291/32 + 132/32 = 423/32 = 13 7/32

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 14 Handout 8 Converting Fractions into Decimals

To convert a fraction into a decimal remember that the fraction a/b actually means that ‘a’ is divided by ‘b’. In other words, the numerator is divided by the denominator.

Take the fraction 1/8 for example. If we wanted to convert it into a decimal we divide 8 into 1 as follows: 0.125 8 1.000 Therefore 1/8 = 0.125 0.125 is the “decimal equivalent” of 1/8.

MIXED FRACTIONS  For a mixed fraction like 5 3/8, the procedure is similar with the exception of an added step.  First, we must change 5 3/8 into an improper fraction (remember that an improper fraction is one in which the numerator is bigger than the denominator).  To change 5 3/8 into an improper fraction it is important to note that 5 3/8 is equivalent to writing 5+3/8. Also 5 is the same as the fraction 5/1, because dividing a number by 1 just gives the number. This leads us to the fact that 5 3/8 = 5+3/8 = 5/1+3/8.  Now we just have the addition of two fractions, just like we did in Handout 4.  Adding the two fractions we see that 5/1+3/8 = 40/8+3/8 = 43/8. From here the procedure is just as above, that is we divided the denominator into the numerator: 43  8 43.000  5.375 8  5.375 is the decimal equivalent of 5 3/8: 5 3  5.375 8 EXAMPLE  Assume we wanted to know the decimal equivalent of 9 7/16 o First 7 9 7 144 7 151 9      16 1 16 16 16 16 o Second 9.4375 16 151.0000 o Finally 7 9  9.4375 16

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 15 Handout 9 Converting Decimals into Fractions

To convert from a decimal into a fraction, mathematically you do the opposite of what you did to convert from a fraction to a decimal.

 First, write the decimal in the form of a fraction (we’ll use 9.75 as our example): 9.75 9.75  1  Multiply the numerator and denominator, both, by the multiple of ten that will eliminate the decimal in the numerator. In our example, there are two numbers (the 7 and the 5) to the right of the decimal place, therefore multiplying the numerator and denominator by 100 will eliminate the decimal in the numerator: 9.75 100 975   1 100 100  Since we have an improper fraction (numerator bigger than the denominator) we need to convert it into a mixed fraction by dividing the denominator into the numerator. This time, instead of running out the decimal, we’ll keep the remainder. The remainder will be our new numerator: 9 R75 75 100 975  9 100  Now we reduce the fractional part of the mixed fraction: 75 3 25   100 4 25  Finally, reassemble your number: 3 9.75  9 4 EXAMPLE PROBLEM  Assume we wanted to convert 1.0625 into a fraction. o First 1.0625 10625 1.0625   1 10000 o Second 1 R625 625 10000 10625  1 10000 o Third 625 125 5 25 5 5 1 25 5 5 1           10000 2000 5 400 5 5 16 25 5 5 16 o Reassembling the answer 1 1.0625  1 16

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 16 Handout 10 Practice Converting Fractions & Decimals

Convert the following fractions into decimals:

1. 1/4 =

2. 7/8 =

3. 3/8 =

4. 1/16 =

5. 3/16 =

6. 3/32 =

Convert the following decimals into fractions:

7. 0.4375 =

8. 1.75 =

9. 2.5625 =

10. 3.125 =

11. 5.625 =

12. 12.40625 =

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 17 Overhead 11 Answer Key: Practice Converting Fractions & Decimals

Convert the following fractions into decimals:

1. ¼ = 0.25

2. 7/8 = 0.875

3. 3/8 = 0.375

4. 1/16 = 0.0625

5. 3/16 = 0.1875

6. 3/32 = 0.09375

Convert the following decimals into fractions:

7. 0.4375 = 7/16

8. 1.75 = 1 3/4

9. 2.5625 = 2 9/16

10. 3.125 = 3 1/8

11. 5.625 = 5 5/8

12. 12.40625 = 12 13/32

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 18 Handout 12

Application: Working with Fractions

The drawing below shows a piece of flat bar with rebar attached to it at various spacings to each other. In this case, a purchaser would have to determine from the drawing how long the piece of flat bar is in order to purchase the correct amount for the job. Using the drawing below, add the given dimensions together, and fill in the blank box with the appropriate overall length dimension.

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 19 Overhead 13 Application Answer Key: Working with Fractions

The drawing below shows a piece of flat bar with rebar attached to it at various spacings to each other. In this case, a purchaser would have to determine from the drawing how long the piece of flat bar is in order to purchase the correct amount for the job. Using the drawing below, add the given dimensions together, and fill in the blank box with the appropriate overall length dimension.

STEP 1

10 1 5 "1" " 8 16 8 4 1 " 4" " 2 16 5 3 5 " 3" " 16 16 12 4 3 " 4" " 4 16 6 4 3 " 4" " 8 16 7 1 7 "1" " 16 16 + 48 17" " 17"3" 20" 12"8" 1’-8” 16 STEP 2 STEP 3

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 20 Handout 14 Name

Skill Check 1: Working with Fractions

Using the drawing below, add the given dimensions together, and fill in the blank box with the appropriate overall length dimension.

1 5/8” 2 3/8” 5 1/2” 1 3/16” 1 3/4”

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 21 Overhead 15

Answer Key: Skill Check 1

Using the drawing below, add the given dimensions together, and fill in the blank box with the appropriate overall length dimension.

12 7/16”

1 5/8” 2 3/8” 5 1/2” 1 3/16” 1 3/4”

1 5/8 = 1 10/16 Step One: Convert all fractions to lowest common denominator 2 3/8 = 2 6/16 5 1/2 = 5 8/16 1 3/16 = 1 3/16 1 3/4 = 1 12/16 = 10 39/16 Step Two: add whole numbers and fractions = 12 7/16 Step Three: reduce

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 22 Handout 16 Working with Tolerances

Tolerances in Drawings

 Tolerances tell us how accurate a part or measurement needs to be made.

 There are two types of tolerances – symmetrical and asymmetrical tolerances.

 A symmetrical tolerance has a target and a +/- tolerance [example – a dimension on a hole might be .250 +/- .005 (target of one quarter inch plus or minus five thousandths). This means that the hole has to measure between .245 and . 255. inch.]

 Sometimes there is a minimum dimension so that we can’t use a symmetrical tolerance. This might occur, for example, when a bolthole is dimensioned near an obstruction of some sort. The consequences of placing the bolthole too close to the obstruction may result in the bolt head not allowing the bolt to fit into the hole. This is called an asymmetrical tolerance. [Example -- .250 +.010/-.000. This means that the target is still a quarter inch. The hole can be ten thousandths larger than that, but not any smaller.]

Examples of Symmetrical and Asymmetrical Tolerances:

Symmetrical Tolerances

 .375 +/- .004 means that the part has to measure between .371 and .379.

 .750 +/- .003 means that the part has to measure between .747 and .753.

 1.500 +/- .002 means that the part has to measure between 1.498 and 1.502

Asymmetrical Tolerances

 .375 +.005/-.002 means that the part has to measure between .373 and .380.

 .750 +.008/-.003 means that the part has to measure between .747 and .758.

 1.500 +.005/-.002 means that the part have to measure between 1.498 and 1.505.

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 23 Handout 17 Practice with Tolerances

For the tolerances below, fill in the minimum and maximum sizes for the targets and tolerances in the tables.

No. Target Dimension Tolerance Minimum Size Maximum Size 1 0.250 +/- .008 2 1.375 +/- .006 3 3.25 +/- .004 4 4.5 +/- .002 5 8.21 +/- .003 6 5.256 +/- .006 7 3.24 +/- .012 8 6.75 +/- .013 9 3.5 +/- .003 10 4.387 +/- .006

No. Target Dimension Tolerance Minimum Size Maximum Size 1 0.250 + .006/-.003 2 1.375 + .008/-.004 3 3.25 + .012/-.006 4 4.5 + .003/-.006 5 8.21 + .012/-.006 6 5.256 + .002/-.008 7 3.24 + .011/-.000 8 6.75 + .006/-.003 9 3.5 + .004/-.002 10 4.387 + .004/-.002

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 24 Overhead 18 Answer Key: Practice with Tolerances

For the tolerances below, fill in the minimum and maximum sizes for the targets and tolerances in the tables.

No. Target Dimension Tolerance Minimum Size Maximum Size 1 0.250 +/- .008 0.242 0.258 2 1.375 +/- .006 1.369 1.381 3 3.25 +/- .004 3.246 3.254 4 4.5 +/- .002 4.498 4.502 5 8.21 +/- .003 8.207 8.213 6 5.256 +/- .006 5.250 5.262 7 3.24 +/- .012 3.228 3.252 8 6.75 +/- .013 6.737 6.763 9 3.5 +/- .003 3.497 3.503 10 4.387 +/- .006 4.381 4.393

No. Target Dimension Tolerance Minimum Size Maximum Size 1 0.250 + .006/-.003 0.247 0.256 2 1.375 + .008/-.004 1.371 1.353 3 3.25 + .012/-.006 3.244 3.262 4 4.5 + .003/-.006 4.494 4.503 5 8.21 + .012/-.006 8.204 8.222 6 5.256 + .002/-.008 5.248 5.258 7 3.24 + .011/-.000 3.240 3.251 8 6.75 + .006/-.003 6.747 6.756 9 3.5 + .004/-.002 3.498 3.504 10 4.387 + .004/-.002 4.385 4.391

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 25 Handout 19 Application: Working With Tolerances

As mentioned before, a drawing for a given part will typically show the minimum number of dimensions required to build the part and it will often be necessary to determine additional dimensions from the drawing for reference. When working with tolerances, this process of determining other dimensions can get a little tricky. Consider the drawing below. To calculate the blank dimension, first look at the other provided dimensions and determine the two most extreme cases (i.e. what configuration of the surrounding dimensions will cause the desired dimension to be at its maximum, and what configuration will cause a minimum).

Step One: calculate the minimum and maximum space lost to other holes:

Step Two: Subtract from the maximum or minimum overall part length:

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 26 Overhead 20 Application Answer Key: Working With Tolerances

As mentioned before, a drawing for a given part will typically show the minimum number of dimensions required to build the part and it will often be necessary to determine additional dimensions from the drawing for reference. When working with tolerances, this process of determining other dimensions can get a little tricky. Consider the drawing below. To calculate the blank dimension, first look at the other provided dimensions and determine the two most extreme cases (i.e. what configuration of the surrounding dimensions will cause the desired dimension to be at its maximum, and what configuration will cause a minimum).

Step One: Calculate the minimum or maximum space lost to other holes.

1 15 1 1" 16 " 0" 16 " 1" 16 " 1 15 1 2" 16 " 1" 16 " 2" 16 " 1 15 Minimum hole 1 Maximum 2" 16 " 1" 16 " encroachment. 2" 16 " hole 1 15 1 encroachment. 2" 16 " 1" 16 " 2" 16 " + + 60 12 3 4 1 3" 16 " 6" 16 " 6 4 " 7" 16 " 7 4 "

Step Two: Subtract from maximum or minimum overall part length.

8 1/16 – 6 3/4: 7 15/16 – 7 1/4:

1 17 1 15 8" 16 " 7" 16 " 8" 16 " 7" 16 " 3 12 1 4 6" 4 " 6" 16 " 7" 4 " 7" 16 " - - 5 11 116 " 0 16 "

MAX 1 5/16” MIN 11/16”

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 27 Handout 21 Name Skill Check 2: Working with Tolerances

Using the drawing provided below, calculate the maximum and minimum cases of the dimension marked with a blank box. Place your answer in the space provided beneath the drawing.

1  3/8” 2  1/8” 1  1/2” 2  1/4” 1  3/4”

MAX MIN

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 28 Overhead 22 Name Answer Key: Working with Tolerances

Using the drawing provided below, calculate the maximum and minimum cases of the dimension marked with a blank box. Place your answer in the space provided beneath the drawing.

7  11/16”

1  1/8” 2  1/16” 1  1/16” 2  3/16” 1  1/4”

Calculate maximum possible value Calculate minimum possible value (working left to right) (working left to right) 1 1/8 = 9/8 = 18/16 7/8 = 14/16 2 1/16 = 33/16 1 15/16 = 31/16 1 1/16 = 17/16 15/16 2 3/16 = 35/16 1 13/16 = 29/16 + 1 1/4-=5/4 = 20/16 + 3/4 = 12/16 123/16 = 7 11/16 101/16 = 6 5/16

MAX. 7 9/16” MIN. 6 5/16”

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 29 Handout 23 The Metric System The Metric System  The metric system is used by some companies in the US and by most of the other countries in the world. The basic measure in the metric system is the meter, which is where the name of the system came from.

 The metric system is based on the number 10. It uses the following prefixes: kilo = 1,000 hecto = 100 deca = 10 deci = 1/10 centi = 1/100 milli = 1/1000

 The distance measures used most commonly are the kilometer, meter, centimeter and millimeter.

Converting from the Metric System  The most common metric conversions are the following. It is good to memorize these: 1 kilometer = 0.62 miles 1 meter = 3.28 feet 1 inch = 2.54 centimeters 1 inch = 25.4 millimeters 1 liter = 0.9 quart 1 kilogram = 2.2 pounds

 Think of the conversions above as equations. The only rule to follow, when making a conversion is that whatever you do to the left side of the equation you have to do the same to the right side.

CONVERSION EXAMPLES

Assume we wanted to know how many miles were in 15 kilometers.  Looking at the kilometer to mile conversion (1 kilometer = 0.62 miles), multiply both sides of the equation to get an equivalent for 15 kilometers: 15 * 1 kilometer = 15 * 0.62 miles --> 15 kilometers = 9.3 miles

Assume we wanted to convert 25 miles to kilometers.  First, divide both sides by 0.62 to get a ‘1’ on the miles side: 1/0.62 kilometers = 1 mile

 Next, multiply both sides of the equation by 25 to get an equivalent for 25 miles: 25*1/0.62 kilometers = 25 miles --> 40.3 kilometers = 25 miles

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 30 Handout 24 Practice with the Metric System Prefixes 1. 1 kilometer = ______meters.

2. 1 liter = ______milliliters

3. 1 meter = ______centimeters

4. 1 centimeter = ______millimeters

5. 1 kilogram = ______grams

6. 25 kilometers = ______meters

7. 10 centimeters = ______meters

8. 10 liters = ______milliliters

9. 25 millimeters = ______centimeters

10. ½ kilogram = ______grams

Conversions

11. 10 kilometers = ______miles

12. 25 centimeters = ______inches

13. 10.5 meters = ______feet

14. 76.2 millimeters = ______inches

15. 1/2 centimeter = ______inches

16. 10 inches = ______centimeters

17. 1/8 inch = ______millimeters

18. 4 liters = ______quarts

19. 10 kilograms = ______pounds

20. If someone tells you they weigh 50 kilograms, how many pounds it that? ______

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 31 Overhead 25 Answer Key: Practice with the Metric System Prefixes 1. 1 kilometer = ____1000___ meters.

2. 1 liter = ____1000___ milliliters

3. 1 meter = ____100___ centimeters

4. 1 centimeter = ____10____ millimeters

5. 1 kilogram = ____1000___ grams

6. 25 kilometers = ___25,000___ meters

7. 10 centimeters = ____0.1___ meters

8. 10 liters = ___10,000___ milliliters

9. 25 millimeters = ___2.5____ centimeters

10. ½ kilogram = ____500___ grams

Conversions 11. 10 kilometers = ____6.2____ miles

12. 25 centimeters = ___9.84____ inches

13. 10.5 meters = ____34.44____ feet

14. 76.2 millimeters = ____3____ inches

15. 1/2 centimeter = _____0.197_____ inches

16. 10 inches = ____25.4______centimeters

17. 1/8 inch = ____3.175______millimeters

18. 4 liters = ___3.6____ quarts

19. 10 kilograms = ___22_____ pounds

20. If someone tells you they weigh 50 kilograms, how many pounds it that? ___110_____

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 32 Handout 26 Name Skill Check: Converting From English to Metric Units

Remembering that 1 inch = 2.54 centimeters and that there are 10 millimeters in a centimeter, convert the following measurements below from inches to millimeters. HINT: it is generally helpful to convert fractions to decimals before making conversions.

A: 13 3/4” = mm B: 14 3/8” = mm

C: 14 15/16” = mm D: 16 7/32” = mm

E: 16 9/16” = mm F: 17 1/32” = mm

G: 17 13/32” = mm H: 12/64” = mm

I: 29/64” = mm J: 1 5/64” = mm

K: 1 45/64” = mm L: 2 13/64” = mm

M: 2 38/64” = mm N: 3 21/64” = mm

O: 4 19/64” = mm

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 33 Overhead 27 Name Answer Key: Converting From English to Metric Units

Remembering that 1 inch = 2.54 centimeters and that there are 10 millimeters in a centimeter, convert the following measurements below from inches to millimeters.

A: 13 3/4” = 349.25 mm B: 14 3/8” = 365.125 mm

C: 14 15/16” = 379.4125 mm D: 16 7/32” = 411.956 mm

E: 16 9/16” = 420.6875 mm F: 17 1/32” = 432.594 mm

G: 17 13/32” = 442.1188 mm H: 3/16” = 4.7625 mm

I: 29/64” = 11.5094 mm J: 1 5/64” = 27.384 mm

K: 1 45/64” = 43.2594 mm L: 2 13/64” = 55.959 mm

M: 2 19/32” = 65.8812 mm N: 3 21/64” = 84.534 mm

O: 4 19/64” = 109.1406 mm

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 34 Handout 28a Final Skill Check

The drawing below is inconsistent. It has both Metric and English units. Some of the English units are fractions others are decimals. The drawing on the next page has blank dimensions. Fill in the dimensions with their appropriate values. Make all of the dimensions in English units with fractions.

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 35 Handout 28b Name Final Skill Check: Student Answer Sheet

Using the drawing on the previous page, convert as necessary and fill in the blank dimensions on the drawing below.

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 36 Overhead 29 Answer Key: Applied Mathematics Final Skill Check

Using the drawing on the previous page, convert as necessary and fill in the blank dimensions on the drawing below.

11" 4 1 22"

1 dia 24" 1" " 3 8 " 9 8 / 1 ± " 3 4 1 " 8 5 4 " 6 " 1 / " 1 1 2 0 + - 4 " 2 " " 6 1 8 / / 1 1 + - "

3 8 1 1 14" 2" 31" 3 4 14" " 1 2 " 1 8 2 " 3 4 2 1 " 7 8

ã Manufacturing Technology Advisory Group 2004 Applied Mathematics, p. 37