Performing basic shop computation

DLM 03 Developing print-based Learner’s Guide including all related documents
Notes Format of Learner’s Guide

Course: Machining NC II
Unit of competency: Perform Basic Shop Computation
Perform Basic Shop Computation
Module: At the end of the session, learners should be able to:
Learning outcomes:

Duration: 1. Interpret working drawings and instructions
2. Determine formulas/rules to be use in calculations
3. Perform basic calculations
20 Hours

Situating Learning: You are a machinist in a prominent Machine shop. The manager gives you
the drawing of a machine part from Nestle Philippines Inc. that cost
500,000.00 Php. He told you that you must finish fabricating the product in 5
days. He added that he will give you a bonus if you will come up with a good
product using minimal materials. In order to maximize your materials and to
have a good product, you should perform basic computations before
working.

Before proceeding to the machining process, you must:
1. Interpret working drawing
2. Solve for the missing dimensions and plan so that you can maximize
the use of the material
3. You should compute for the speed and feed rate of your machine in
order for you to have good surface finish and to prevent breakage of
tools.

As evidence of your work process, you should write your computations, and
sketch how you utilize the raw materials on an A4 size paper. You should
show that you are able to maximize the tools & material.

Assessment Criteria: Assessment requires evidence that the candidate performed calculations:
1.1 using four fundamental operations
1.2 involving fractions and mixed numbers
1.3 involving fractions and decimals
1.4 involving percentages
1.5 involving ratio and proportion
1.6 on algebraic expressions
1.7 of simple formulae

Pedagogical Training in Instructional Design & Delivery for TVET Page 1
© 2010, Institute of Technical Education, Singapore

DLM 03 Developing print-based Learner’s Guide including all related documents
Notes Format of Learner’s Guide

Learning chunk Performance Criteria Learning Activities Learning documents
(Brief description of (Documents
strategies, sequence of
lesson, evaluation) referenced by each
learning activity)

1. Perform Basic Shop Explain the overview 1.1 List the outline of the Answer Work Sheet
Basic Shop 1.1.1: The whole task
Computation of the whole task Computation

1.2 Plan the steps
to perform basic
shop computation

2. Perform basic Add, Subtract, multiply 2.1 List the actual use of
calculations and divide whole four fundamental
 Perform numbers. operation on whole
Four numbers
fundamental
operations 2.2 Perform the four Read Information
fundamental Sheet 2.2.1: Four
3. Perform basic operations on whole fundamental operation
calculations numbers (Add, on whole numbers
 Perform subtract, multiply and
Four divide)
fundamental
operations 2.3 On your group, Answer Work sheet
master the four 2.3.1: Number
fundamental problems
operations on whole
numbers (Add, Answer Work sheet
subtract, multiply and 2.4.1: Worded
divide) problems

2.4 Individual Drill and
Practice
(Short Quiz)

Add, Subtract, multiply 3.1 List the importance of

and divide fractions fraction inside the

machine shop

3.2 Perform the four Read Information
fundamental Sheet 3.2.1: Four
operations on fundamental operation
Fractions (Add, on fraction
subtract, multiply and
divide)

3.3 On your group, Answer Work sheet
master the four 3.3.1: Number
fundamental problems
operations on
fractions (Add,
subtract, multiply and
divide)

Pedagogical Training in Instructional Design & Delivery for TVET Page 2
© 2010, Institute of Technical Education, Singapore

DLM 03 Developing print-based Learner’s Guide including all related documents
Notes Format of Learner’s Guide

Learning chunk Performance Criteria Learning Activities Learning documents
(Brief description of (Documents
strategies, sequence of
lesson, evaluation) referenced by each
learning activity)

3.4 Individual Drill and Answer Work sheet
Practice 3.4.1: Worded
(Short Quiz) problems

4. Perform basic Add, Subtract, multiply 4.1 Identify the
calculations and divide Decimals importance of
decimals inside the
 Perform machine shop
Four
fundamental Perform 4.2 Perform the four Read Information
operations Four fundamental fundamental Sheet 4.2.1: Four
operations on whole operations on fundamental operation
numbers, fractions decimals (Add, on decimals
and decimals subtract, multiply and
divide)

4.3 On your group, Answer Work sheet
master the four 4.3.1: Number
fundamental problems
operations on
decimals (Add, Answer
subtract, multiply and Work sheet 4.4.1:
divide) Worded problems
Work sheet 4.4.2:
4.4 Individual Drill and Mixed exercise
Practice
(Long Quiz)

5. Perform basic Convert fractions to 5.1 Recall prior
calculations decimals and vice knowledge.
versa
 Perform basic
conversion 5.2 Explore the topic, Read Information
involving convert fraction to Sheet 5.2.1:
fraction, decimal and vice Conversion of
decimal, versa fractions to decimals
percentage and
ratio and 5.3 Individual Drill and Answer Work sheet
proportion Practice (Short quiz) 5.3.1: Number
problems
5.4 On your group,
master the Answer Work sheet
conversion of fraction 5.4.1: Word problems
to decimal and vice
versa

Pedagogical Training in Instructional Design & Delivery for TVET Page 3
© 2010, Institute of Technical Education, Singapore

DLM 03 Developing print-based Learner’s Guide including all related documents
Notes Format of Learner’s Guide

Learning chunk Performance Criteria Learning Activities Learning documents
(Brief description of (Documents
strategies, sequence of
lesson, evaluation) referenced by each
learning activity)

6. Perform basic Solve for values using 6.1 On your group, Read Information
calculations the principles of ratio discuss about the Sheet 6.1.1: Ratio
and proportion. difference and the and Proportion
 Perform basic connection between
conversion fraction, ratio and Answer Work sheet
involving proportion. 6.2.1: Number
fraction, . problems
decimal,
percentage and 6.2 Individual Drill and Answer Work sheet
ratio and Practice (Short quiz) 6.3.1: Word problems
proportion
6.3 On your group,
master the principle
of ratio and
proportion

7. Perform basic Convert decimal to 7.1 List the importance of
calculations percentage and vice percentage
versa
 Perform basic 7.2 On a pair, explore Read Information
conversion and Solve problems how to convert Sheet 7.2.1:
calculation involving percentage decimal to Converting decimal to
involving percentage and vice percentage
decimal, versa
percentage Answer Work sheet
7.3 Individual drill and 7.3.1: Number
practice (Short quiz) problems

7.4 On your group, study Read Information
percentage on Sheet 7.4.1:
worded problems. Percentage problems

7.5 On your group, Answer Work sheet
master the 7.5.1: Percentage
conversion involving problems
fraction, decimal,
percentage, ratio and
proportion

8. Determine Manipulate and use 8.1 Recall prior
formulas/rules to be basic shop formulas knowledge
used in calculations
8.2 List the formulas and
solve for values that Read Information
is required in order to Sheet 8.2.1: Basic
perform machine shop formulas and
operation equations

Pedagogical Training in Instructional Design & Delivery for TVET Page 4
© 2010, Institute of Technical Education, Singapore

DLM 03 Developing print-based Learner’s Guide including all related documents
Notes Format of Learner’s Guide

Learning chunk Performance Criteria Learning Activities Learning documents
(Brief description of (Documents
strategies, sequence of
lesson, evaluation) referenced by each
learning activity)
8.3 On your group,
master solving for the Answer Work sheet
required values. 8.3.1: Word problem

8.4 Individual drill and Answer Work sheet
practice. (Short quiz) 8.4.1: Word problems

9. Interpret working Solve for information 9.1 List information about Answer Work sheet
drawings and needed to produce the the given drawing 9.1.1: Identifying
instructions given product drawing elements
9.2 Check your work with
your partner

9.3 Check your work with
the trainer

9.4 Individual drill and Answer Work sheet
practice (short quiz) 9.4.1: Solving for
missing values

10. Perform Basic Perform basic shop 10.1 Recall the whole
task
Shop Computation computation

10.2 Compute for a basic Fill up the Job sheet
shop problem 10.2.1, 10.2.2 &
10.2.3: Basic shop
Assessment criteria problems. Have it
will be given by the signed by your trainer.
trainer.

10.3 Reflect if you are
able to perform the
whole task

Pedagogical Training in Instructional Design & Delivery for TVET Page 5
© 2010, Institute of Technical Education, Singapore

Information Sheet 2.2.1 : Four fundamental operation on whole numbers

Learning outcomes:
2 Perform four fundamental operations on whole numbers
Learning Activity:
2.2 Add, subtract, multiply and divide whole numbers

Let us face facts. We can quickly replace written operations with a calculator, but what
if you’re in a machine shop and you don't have a calculator? Therefore, you should master how

to perform four fundamental operations manually. That deserves to be called educational.

Four Fundamental Operations

These are the arithmetic skills introduced and practiced in elementary school. Basically,
the fundamental operations are addition, subtraction, multiplication, and division. However,
there are only two operations: namely addition and multiplication. Subtraction is just referred to
as the inverse of addition and division, the inverse of multiplication. Before proceeding to the
operation, we have to recall the following important terminologies.

Addition: Addends – the numbers that are added together
45 Sum – the result of addition

+ 27
72

Subtraction: Minuend – the number from which another is to be subtracted
98 Subtrahend – the number that is to be subtracted from another
39 Difference – the result of subtraction
59

Multiplication: Factors – the numbers that are to be multiplied
19 x 64 = 1216 Product – the result of multiplication

Division:
608

4256 7 = 608 this can also be written as 4256 / 7 = 608 or 7 4256

608 Quotient – the result of division
7 4256 Dividend – the number that is to be divided
Divisor – the number by which the dividend is divided

Note: Memorize and understand the following terms above because you will
encounter these terminologies on the next pages of this module.

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 2.2.1 : Four fundamental operation on whole numbers

Addition

When we combine two sets of objects and then determine the number of objects in the
bigger set.

Example: 4,674 + 422 + 5,533 + 40

Procedure: 4, 6 7 4
422
Step 1: Write the numbers under one another, taking care to align the same units;
that is, align the ones, the tens, the hundreds, the thousands etc.; and 5, 5 3 3
draw a line below the numbers. See Fig. 2.1 40

Fig. 2.1

Step 2: Starting with the ones on the right, add each column. When the sum of a column is 9 or
less, write that sum under the line. But when that sum is more than 9, write the ones of
that sum and "carry" the tens digit onto the next column.

Study this Example:

11
4 thousands + 6 hundreds + 7 tens + 4 ones

4 hundreds + 2 tens + 2 ones
5 thousands + 5 hundreds + 3 tens + 3 ones

4 tens + 0 ones
10 thousands + 6 hundreds + 6 tens + 9 ones

On adding the ones column, we get 9. But on adding the tens column, we get 16.
Now, 16 tens = 10 tens + 6 tens

Write 6, and carry 10 tens onto the hundreds column -- because 10 tens are equal to
1 hundred. Therefore when we add the hundreds, we have

1 + 6 + 4 + 5 = 16 hundreds.
But…

16 hundreds = 10 hundreds + 6 hundreds.

Write 6, and carry 10 hundreds onto the thousands column -- because 10 hundreds
are equal to 1 thousands.

When we add the thousands, then, we get

1 + 4 + 5 = 10.
The sum of those numbers is 10,669.

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 2.2.1 : Four fundamental operation on whole numbers

Subtraction 9 + 5 = 14
Smaller + Difference= Larger
The inverse of addition, it is the problem of finding 14 − 9 = 5
the difference between two numbers. It is the problem of Larger – Smaller = Difference
finding what number we have to add to 9 to get 14. See Fig.
2.2 Fig. 2.2

From the figure, we can also say that the difference
of two numbers is the distance between them. How far is it
from 9 to 14? A distance of 5.

Procedure:

There are two methods of written subtraction. One is the familiar subtraction with
regrouping ("borrowing"). The other is the less familiar but simpler, subtraction by
compensating. For this module we will only discuss subtraction by compensating.

Step 1: Write the smaller number under the larger, taking care to align the 5, 3 1 2
same units and put a line under. 2, 5 7 9

Step 2: Starting with the ones on the right, subtract each digit on the bottom from the
corresponding digit on top. If a bottom digit is smaller, there is no problem of
subtracting, but, if a bottom digit is greater, consider the top digit increased by 10. To
compensate, add 1 to the next bottom digit.

Study this Example:

5,312

− 2,579

2,733
"9 from 12 is 3."
(add 10 to 2 to make it 12, then add 1 to the next bottom digit which is 7 making it 8)
"8 from 11 is 3."
(add 10 to 1 to make it 11, then add 1 to the next bottom digit which is 5 making it 6)
"6 from 13 is 7."
(add 10 to 3 to make it 13, then add 1 to the next bottom digit which is 2 making it 3)
"3 from 5 is 2."

The Difference of those numbers is 2,733.

Since subtracting is finding what number to add to the smaller number, you can always check
your answer by adding.

2,733 + 2,579 = 5,312

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 2.2.1 : Four fundamental operation on whole numbers

Multiplication

This operation is often viewed as a repeated addition. Thus, 3 x 5 is a shorter way of
saying 5 + 5 + 5 whose pictorial representation is:

3 sets of 5

Procedure: 6 2 8 – Multiplicand
X 7 – Multiplier
Step 1: Write the factors vertically. Make sure that the ones digit of
the multiplier is aligned with the ones digit of the multiplicand
then put a line under.

Step 2: Multiply each digit of the multiplicand. Write the ones digit of each product below the
line. If there is a tens digit, carry it -- add it -- to the next product.

Study these Examples:

15

6 2 8 = 6 hundreds + 2 tens + 8 ones

X 7= 7 ones

4 3 9 6 - Product 5 6 ones

1 4 tens

4 2 hundreds
4 3 9 6 – Product

"7 times 8 is 56." Write 6, carry 5.
"7 times 2 is 14, plus 5 is 19." Write 9, carry 1.
"7 times 6 is 42, plus 1 is 43." Write 43.

When the multiplier has more than one digit

628 Partial Products
x257
4 3 9 6 - ones
3 1 4 0 - tens
1 2 5 6 - hundreds
1 6 1 3 9 6 – Final Product

Multiply the multiplicand by each digit of the multiplier. Place the ones digit of each
partial product in the same column as the multiplying digit. Then add the partial
products to get the final product.

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 2.2.1 : Four fundamental operation on whole numbers

Division

Consider as the inverse operation of multiplication. It involves finding the missing factor.
Thus, 15 ÷ 3 = ? Could mean the number multiplied by 3 that gives 15 that is, 3 x ? = 15. This
would yield 3 x 5 = 15

In division we are to name the number of times one number, called the divisor, is
contained in another number, called the dividend. Thus, 15 ÷ 3 = 5 answer the question how
many 3s are there in 15?

Procedure:
There are two methods of written division. One is the familiar long method. The other is

the less familiar but simpler, short method. For this module, we will discuss short method.

Step 1: Write the given numbers on the division box. ? Quotient
In performing written division, you should pay Divisor Dividend
attention to the location of your given numbers. 7 2 5 2

252 ÷ 7 = ? : Dividend ÷ Divisor = Quotient

Step 2: From the left of the dividend (252), take as many digits as necessary 36
to form a partial dividend that will contain the divisor (7) at least once 7 25 42
but less than ten times.

For this example the partial dividend is (25).

Divide that partial dividend by the divisor, and obtain the first digit of the quotient (3).

Write it over the last digit (5) of the partial dividend – and write the remainder (4) beside

the next digit of the dividend. This will give you the next partial dividend (42).

Divide 42 by the divisor (7) you will get (6).

Place (6) beside the first quotient (3) to get the final quotient of 36.

Study these Examples:

Example 1: This problem shows that over every digit in the dividend, we must write a

digit in the quotient:

?

2, 160, 243 ÷ 4 = ? 4 2160243

5 4 0 0 6 0 R3
4 21 16 00 02 24 03

Example 2: This problem shows how to divide with a divisor having more digits:

?

3, 164 ÷ 25 = ? 25 3 1 6 4

Code No. 1 2 6 R4 Date: Developed Date: Revised Page #
MEE722204 25 3 1 66 164 April 28, 2010 3

Perform Basic Shop Computations

Information Sheet 2.2.1 : Four fundamental operation on whole numbers

Precedence of Operation

The operations discussed earlier are binary operations, that is they have to be
performed with two numbers. In performing a series of operation, some rules or order of
precedence have to be observed. Remember that the four fundamental operations are to be
performed in this specific order and not just at what they appear from left to right.

Example: NOT 9 + 4 ÷ 2 = 11
9+4÷2=6 EQUAL 4 divided by 2 equals 2,

(9) plus (4) equals (12), plus 9 equals 11
divided by (2) equals (6)

Rule of Precedence of Operation: (MDAS)
Multiplication or Division first and then Addition or Subtraction

There are instances when it is convenient to perform a series of operations enclosed
with grouping symbols. The grouping symbols commonly used are parenthesis ( ), brace { }
and bracket [ ]. When there are several operations enclosed with grouping symbols, the
innermost operations are to be performed first.

Example: [ { (2 x 5) x 6} ÷ 3] – 4 = ?
[ {10 x 6} ÷ 3] – 4 = ?
[60 ÷ 3] – 4 = ?
20 – 4 = 16

To evaluate the expression [ { (2 x 5) x 6} ÷ 3] – 4 = ?
You will start with the innermost which is 2 x 5, hence, we have
[ {10 x 6} ÷ 3] – 4 = ?

The next operation to be performed will be 10 x 6, then we have
[60 ÷ 3] – 4 = ?
20 – 4 = 16

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Worksheet 2.3.1 : Number Problems

Learning outcomes:
2 Perform four fundamental operations
Learning Activity:
2.3 Add, subtract, multiply and divide whole numbers

General Instruction: Solve for the following. Use scratch paper for your solution and
write your final answer on the box after each equal sign. Erasures
means wrong. You have 45 minutes to answer this worksheet.

Test I – Addition of whole numbers (1 point each)
1. 2,348 + 9,325 + 850 + 27 + 63 =

2. 10,585 + 246 + 21,100 + 6,541 =

3. 126,234 + 342 + 761 + 12,345 =

4. 35 + 386 + 16 + 294 + 213 + 8 =

Test II – Subtraction of whole numbers (1 point each)

1. 36,476 – 24,587 = 3. 12,968 – 3,020 =

2. 125,456 – 11,679 = 4. 45,321 – 23,678 =

Test III – Multiplication of whole numbers (1 point each)

1. 3,960 x 243 = 3. 21,325 x 278 =

2. 43 x 2,136 = 4. 453 x 33,687 =

Test IV – Division of whole numbers (1 point each)

1. 1770 / 59 = 3. 19240 / 296 =

2. 2314 / 26 = 4. 29,430 / 654 =

Test V – Four fundamental operations on whole numbers (2 points each)

1. 21 + 49 – 6 x 8 / 2 = 3. (45 / 3) x 3 + 319 – 78 =
2. 32 x 29 / 4 + 900 – 987 = 4. 322 + 78 x 17 – 296 =

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Worksheet 2.3.1 : Number Problems

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Worksheet 2.4.1 : Worded Problems

Learning outcomes:
2 Perform four fundamental operations
Learning Activity:
2.4 Solve worded problems

General Instruction: Solve for the following worded problem. Use the space provided after
the problem for your solution and box your final answer. Erasures
means wrong. You have 15 minutes to answer this worksheet.
(5 points each)

1. A rectangular swimming pool has a length of 20 meters and a width of 10 meters. Your
boss gave you 100 meters long of fencing material. He instructed you to build a fence
that surrounds the swimming pool; he added that the pool should be at the center of the
fence. What is the distance between the fence and the side of the pool?

2. You are instructed to create plate that has a length of 4 inches, width of 2 inches and a
height of 1 inch. If you are given 3 pieces of raw material that has the following
dimensions: L = 11 inches, W = 7 inches and H = 1 inch. What is the maximum number
of plate that can be produced?

3. You are given 20 pieces of 6,000 millimeters long angular bar. Your supervisor
instructed you to cut those angular bars into smaller pieces that has a length of 355
millimeters. What is the maximum number of angle bars that you can produce?

4. Circle A and C has the same diameter which is twice as the diameter of circle B.
If the radius of circle B is 35 millimeters, what is the distance between the center of
circle A and C?

AB C

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 8

Information Sheet 3.2.1 : Four fundamental operation on fractions

Learning outcomes:
3 Perform four fundamental operations on fractions
Learning Activity:
3.2 Add, subtract, multiply and divide fractions

Whole numbers are used in telling how much and how many are in a collection of
things. Counting, recording, grouping objects are done easily with these numbers. But, As
civilization became more complex, the need to break a unit or a whole and to record finer
subdivisions of a measuring instrument brought about the need for Rational numbers or what
we called as Fractions.

Parts of fractions

1 Numerator – The number of equal parts being considered
6 Denominator – The total number of equal parts

Types of fractions

Proper fractions – the numerator is smaller than the denominator
Examples: 1 , 2 , 3
457

Improper fractions – the numerator is greater than or equal to its denominator
Examples: 2 , 5 , 8
235

Mixed number – a combination of a whole number and a proper fraction

Examples: 1, 5, 8

235

Similar fractions – fractions that has the same denominator
Examples: 2 and 1 , 3 and 4
4 45 5

Dissimilar fractions – fractions that has different denominator
Examples: 7 and 2 , 5 and 1
9 3 3 12

Note: Memorize and understand the following terms above because you will
encounter these terminologies on the next pages of this module.

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 3.2.1 : Four fundamental operation on fractions
Before going to the fundamental operations, it is required to master the following conversions:
Changing improper fraction to mixed number

Example: 11 11 ÷ 3 = 3 remainder 2
3

Changing mixed number to improper fraction

Example: 3 x 3 + 2 = 11
33

Changing dissimilar fraction to similar fractions

1 and 2 are dissimilar fractions, here are the steps to change it to similar fractions:
24

Step 1: Find the Least common denominator (LCD). The LCD is the number which can be
divided by the denominators. In the given above the LCD is 4, because 4 can be
divided by the denominators 2 and 4

Step 2: Divide the LCD by the denominator then multiply by the numerator then take the LCD
as the denominator.

Example: 1 4÷2=2x1= 2 2 4÷4=1x2= 2
24 44

2 and 2 are now similar fractions
44

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 3.2.1 : Four fundamental operation on fractions

Changing fractions to Lowest Term

To reduce fraction to lowest terms, find the largest number that will divide evenly into both the
numerator and denominator.

Example: Reduce 4 to lowest term
16

The largest number that will divide evenly both the numerator (4) and denominator (16) is 4.
4 ÷ 4= 1
16 ÷ 4 = 4

Thus, the lowest term of 4 is 1
16 4

Note: Master those conversion above because you will use it in performing the
four fundamental operations on fractions.

Addition of Fraction

In adding fraction, there are 3 basic steps
Step 1: Make sure the bottom numbers (denominators) are the same. In short you can only

add similar fractions.

Step 2: Add the top numbers (the numerators). Put the answer over the same denominator.

Step 3: Simplify the fraction (if needed).

Example: 1 1 2 1 2+ 1 3 1
3 6 6 2
66 6

Change the Add the numerator and Express your
fractions to copy the common answer to
similar fractions denominator lowest term

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 3.2.1 : Four fundamental operation on fractions

Subtraction of Fraction

In subtracting fraction, there are 3 basic steps
Step 1: Make sure the bottom numbers (denominators) are the same. In short you can only

subtract similar fractions.

Step 2: Subtract the top numbers (the numerators). Put the answer over the same
denominator.

Step 3: Simplify the fraction (if needed).

Example: 1 1 3 1 3-1 2 1
2 6 6 2
66 6

Change the Subtract the numerator Express your
fractions to and copy the common answer to
similar fractions denominator lowest term

Multiplication of Fractions

In multiplying fraction, there are 3 basic steps
Step 1. Multiply the top numbers (the numerators).

Step 2. Multiply the bottom numbers (the denominators).

Step 3. Simplify the fraction (if needed).

Example: 1 4 1x4 = 4 1
2 6 2 x 6 = 12 3

Multiply the Multiply the Express your
numerator to the denominator to answer to
numerator denominator lowest term

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 3.2.1 : Four fundamental operation on fractions

Division of Fractions

In dividing fraction, there are 3 basic steps
Step 1: Turn the second fraction (the one you want to divide by) upside-down (this is now a

reciprocal).

Step 2: Multiply the first fraction by that reciprocal

Step 3: Simplify the fraction (if needed).

Example: 1 4 4 1x6 = 6 3
2 6 6 2x4 = 8 4

Turn the second Proceed to the Express your
fraction to get process of answer to
the reciprocal multiplication lowest term

Four fundamental operations on mixed numbers

In adding, subtracting, multiplying and dividing mixed numbers, there are 3 basic steps
Step 1. Covert mixed number into improper fraction

Step 2. Perform the indicated operation
Step 3: Convert the answer to mixed number and simplify the fraction (if needed).

Example: 2 ½ x 2 ½

55 5 x 5 = 25 61
22 2x2 = 4 4

Convert mixed Perform the Express your
number to indicated answer to mixed
improper fraction operation number

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Worksheet 3.3.1 : Number Problems

Learning outcomes:
3 Perform four fundamental operations
Learning Activity:
3.3 Add, subtract, multiply and divide fractions

General Instruction: Solve for the following. Use scratch paper for your solution and
write your final answer on the box after each equal sign. your answer
must be in simplified form. Erasures means wrong. You have 25
minutes to answer this worksheet.

Test I – Addition of fractions (1 point each)

1. 1/6 + 2/6 + 3/6 = 4. 2/128 + 1/64 =
2. 1/16 + 5/16 = 5. 7/64 + 7/128 =
3. 1/2 + 1/4 + 2/8 = 6. 3 ¼ + 1 ½ =

Test II – Subtraction of fractions (1 point each) 4. 3 ¼ – 1 ½ =
1. 3/12 – 1/12 = 5. 3/16 – 1/64 =
2. 1/2 – 1/8 = 6. 4/5 – 1/2 =
3. 4 ¾ - 3 ¼ =

Test III – Multiplication of fractions (1 point each)

1. 1/4 x 1/4 = 4. 2 ¾ x 2 ¼ =
2. 1/2 x 2/4 = 5. 15/16 x 12/24 =
3. 1/16 x 1/8 = 6. 5/16 x 2/128 =

Test IV – Division of whole numbers (1 point each)

1. 4 ¼ ÷ 2 ½ = 4. 12/32 ÷ 8/12 =
2. 5/16 ÷ 3/6 = 5. 1/16 ÷ 1/128 =
3. 3 ¼ ÷ 3/4 = 6. 1/32 ÷ 3/256 =

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Worksheet 3.3.1 : Number Problems

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Worksheet 3.4.1 : Worded Problems
Learning outcomes:
3 Perform four fundamental operations
Learning Activity:
3.4 Solve worded problems
General Instruction: Solve for the following worded problem. Use the space provided after

the problem for your solution and box your final answer. Erasures
means wrong. You have 15 minutes to answer this worksheet.
(5 points each)
1. You are given a diameter 1 ½ pipe that has a length of 45 inches. If you cut a length of
25 ¾ inches, what is the remaining length of the pipe? Your answer is in inches.

2. You are given 20 pieces of 20 ½ feet long angular bar. Your supervisor instructed you to
cut those angular bars into smaller pieces that has a length of 2 ¼ feet. What is the
maximum number of angle bars that you can produce?

3. If a gear has a hole of 1 ½ inches and the shafting has a diameter of 15/16 inches, what
is the wall thickness of the bushing?

4. Circle A and C has the same diameter which is twice as the diameter of circle B.
If the radius of circle B is 3 2/16 inches, what is the distance between the center of circle
A and C?

AB C

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 8

Information Sheet 3.2.1 : Four fundamental operation on fractions
Learning outcomes:
3 Perform four fundamental operations on Decimals
Learning Activity:
3.2 Add, subtract, multiply and divide Decimals

Decimals

Decimals are related to fractions. If fractions show the parts or portions of a whole,
decimals also indicate a certain part of a whole. Decimals are useful in making some
computations simpler and easier. There are some concepts which are better understood by
using decimals. When discussing finances, decimal is the most practical way of expressing
parts of a peso. Decimal has its own uses and like fractions it is very much a part of everyday
living.

Addition of Decimal

When decimals are added the numbers are arranged so that the decimal points are in
the same column. The numbers are then added in the same manner that whole numbers are
added.

Study this Examples:

1. 4.26 + 35.87 + 16.524 + 418.4

4.26
35.87
16.524
418.4
475.054

2. 1425.62 + 74.9 + 238.66 + 195

1425.62
74.9

238.66
195
1934.18

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 3.2.1 : Four fundamental operation on fractions

Subtraction of Decimal

When decimals are subtracted the numbers are arranged so that the decimal points are
in the same column. The numbers are then subtracted in the same manner that whole
numbers are subtracted.

Study this Examples: zeroes are
added to 82.57
1. 14.75 – 8.9

14.75
8.9
5.85

2. 82.57 – 39.82 64

82.5700
39.82 64
42.7436

Multiplication of Decimal

Decimals are multiplied the way that whole numbers are multiplied. To determine the
decimal point of a product, the number of digits to the right of the decimal point in the
multiplicand and multiplier are counted and this is the number of digits, counted from the right
of the product, where the decimal point is to be placed.

Example: 24.6 x 3.5

24.6 Two numbers after
x 3.5 the decimal point

1230 Two decimal places
738
8 6.1 0

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 3.2.1 : Four fundamental operation on fractions

There are two digits after the decimal point in the multiplicand and one digit after the
decimal point in the multiplier. Therefore three digits are counted from the right of the product
and this is where the decimal point is placed.

Example: 3.68 x 4.5 → 3.68
x 4 .5

1840
1472

1 6.5 6 0

There are cases where zeroes have to be added because there are not enough digits in
the product for the position of the decimal point.

Study these examples:

1. 1.029 x 0.08 → 1.029
x 0.08

0.08232

2. 2.35 x .0062 → 2.35

x 0.0062

470
1410

0.014570

Division of Decimal

In dividing decimals, the same process as in division of whole numbers is followed, only
the position of the decimal point in the quotient has to be considered.

A. Dividing decimal by a whole number: 28.56 ÷ 8 =

3.57
8 28.56

24
45
40
56
56
0

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 3.2.1 : Four fundamental operation on fractions

The dividend is divided by the divisor the way whole numbers are divided.

0.8

Example: 4 ÷ 5 5 4.0

-4 0

0

The decimal point is placed in the quotient.

Zero is added after the decimal point to be able to divide four by five.

B. Dividing decimal by another decimal number.
Example 1: 73.728 ÷ 2.4

30 . 7 2
2.4 73.7 . 2 8

72
17

0
17 2
16 8

48
48

0

The divisor is multiplied by 10 to make it a whole number.
The dividend is also multiplied b 10.
The decimal point in the quotient is placed right above the decimal point in the dividend.
The division is the same as the division of whole number.

Example 2: 615.45 ÷ 8.25

74.6
8.25 615.45.0

5775
379 5
330 0

49 5 0
49 5 0

0

Since there are two decimal places in the divisor, it is multiplied by 100 to make it a
whole number.

The dividend is multiplied also by 100.

The decimal point in the quotient is placed above the decimal point in he dividend.

Follow the process of division.

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Worksheet 4.3.1 : Number Problems

Learning outcomes:
4 Perform four fundamental operations
Learning Activity:
4.3 Add, subtract, multiply and divide decimals

General Instruction: Solve for the following. Use scratch paper for your solution and
write your final answer on the box after each equal sign. your answer
must be in two decimal places. Erasures means wrong. You have 25
minutes to answer this worksheet.

Test I – Addition of Decimals (1 point each)

1. 2.04 + .538 + 42.6 + 11.72 = 4. 215.72 + 973.4 =
2. 38.6 + 72.9 + 8.74 + 9.84 = 5. 148.5 + 2.479 + 2 =
3. 148.5 + 2.479 + 513.62 = 6. 6.84 + 16.16 + 9.87=

Test II – Subtraction of Decimals (1 point each)

1. 37.04 – 19.25 = 4. 415.6 - 297.324 =
2. 248.631 – 139.95= 5. 187.7 – 98.9 7=
3. 563.91 – 378.636= 6. 329.16 – 178.9 =

Test III – Multiplication of Decimals (1 point each)

1. 47.2 x 5.8 x 0.007 = 4. 3.6 x 2.7 =
2. 0.6 x 4.91 x 120.3 = 5. 42.5 x 5.4 =
3. 1.4 x 3.06 x 2.9 = 6. 48.6 x 2.72 =

Test IV – Division of whole numbers (1 point each)

1. 24 ÷ 1.2 = 4. 507.06 ÷ 0.9 =
2. 17.86 ÷ 3.8 = 5. 108.29 ÷ 17 =
3. 21.638 ÷ 0.62 = 6. 235.072 ÷ 17 =

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Worksheet 4.3.1 : Number Problems

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Worksheet 4.4.1 : Worded Problems
Learning outcomes:
4 Perform four fundamental operations
Learning Activity:
4.4.1 Solve worded problems
General Instruction: Solve for the following worded problem. Use the space provided after

the problem for your solution and box your final answer. Your answer
must be in two decimal places. Erasures means wrong. You have 15
minutes to answer this worksheet. (5 points each)
1. If the actual inside diameter of a “one-inch pipe” is 1.04 inches and the actual outside
diameter is 1.315 inches. What is the wall thickness of the pipe?

2. Find the diameter at A of the tapered shank if the difference between the small diameter
and the diameter at A is 0.392 inch.

3. Find the missing measurement of the hexagon.

4. Fourteen holes, equally spaced, are to be drilled as shown in the figure below. Find the
center to center distance of adjacent holes.

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 8

Worksheet 4.4.2 : Mixed Exercise

Learning outcomes:
4 Perform four fundamental operations
Learning Activity:
4.4.2 Performing four fundamental operations on whole number, fraction and decimal

General Instruction: Solve for the following. Use scratch paper for your solution and
write your final answer on the box after each equal sign. your answer
must be in simplified form (Lowest term for fractions and two decimal
places for decimals. Erasures means wrong. You have 25 minutes to
answer this worksheet.

1. (12 ÷ 4) + (6 x 2) + (10 – 5) – 12 =
2. 50 x 2.5 + 40 ÷ 8 – 80 ÷ 4.2 =

3. 556.8 ÷ 0.87 + 0.9 x 0.012 =
4. 60 ÷ 12 + 4.5 x 8 – 6.025 =
5. 125.5 x 2.05 – 5.2 x 15.75 =
6. 56.6 x 4.82 – 9.12 x 7.53 =
7. 0.47 + 8.45 + 213 + 1.2 =

8. 46.4 ÷ 0.18 + 2 x 76.05 =

9. 8,325 + 123 + 985.25 =

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

11. 0.524 x 0.07 + 3,214 =

12. 5/8 ÷ 1/4 + 1/2 x 3/8 =

13. 5.52 ÷ 8 + 3.4 x 2.5 =

14. 2/3 ÷ 8/9 + 1 1/3 =

15. 6/5 ÷ 3 =

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Information Sheet 5.2.1 : Conversion of fractions to decimals
Learning outcomes:
5 Convert fractions to decimals and vice versa
Learning Activity:
5.2 Converting fractions to decimals and vice versa

Changing Fractions to Decimals

A fraction is changed to a decimal by changing it to an equivalent fraction with a denominator
of 10 or any power of 10.

Example A: 4 2 Example C:
5 2 Example D:
4
5

Example B:

A fraction may also be changed to a decimal by dividing the numerator by the denominator.

Example A: Example B:

Example C:

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 5.2.1 : Conversion of fractions to decimals

Changing Decimals to Fractions

A decimal is changed to a fraction by using 10 or any power of 10 (based on the
number of decimal places) as a denominator of the number, and if possible reduce it to its
lowest term.

Example A: 0.3 = Example C: 0.25 = or

Example B: 0.4 = or Example D: 0.328 = or

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Worksheet 5.3.1 : Number Problems

Learning outcomes:
5 Convert fractions to decimals and vice versa
Learning Activity:
5.3 Converting fractions to decimals and vice versa

General Instruction: Convert the following. Use scratch paper for your solution and
write your final answer on the box after each equal sign. Your answer
must be in simplified form (lowest term for fraction and two decimal
places for decimals). Erasures means wrong. You have 20 minutes to
answer this worksheet.

Fraction to Decimal

1. = 4. =

2. = 5. =

3. = 6. =

Decimal to Fraction

1. 0..2 = Perform Basic Shop Computations Date: Developed Date: Revised Page #
2. 0.65 =
3. 0.125 = April 28, 2010 7
4. 0.8 =
5. 0.35 =
6. 0.725 =

Code No.
MEE722204

Worksheet 5.3.1 : Number Problems

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Worksheet 5.4.1 : Worded Problems
Learning outcomes:
5 Convert fractions to decimals and vice versa
Learning Activity:
5.4 Solve worded problems
General Instruction: Solve for the following worded problem. Use the space provided after

the problem for your solution and box your final answer. Your answer
must be in simplified form (lowest term if fraction and two decimal
places if decimal). You have 20 minutes to answer this worksheet.
(5 points each)
1. A round piece of work is 1 5/8 inches in diameter. How deep a cut should be taken to
bring the diameter down to 1.59 inches? (answer in fraction)

2. There are bolts inside a box. If a bolt weighs 7/8 pounds. How many such bolts are
there if the box weighs 250 pounds?

3. Supply the missing dimension if the over – all length is 1.625 inches.
(Answer in decimal)

4. How many 3/32 inch thick washers can be made from a piece of stock 25.5 inches
long? Put 0.0625 inch allowance for each cut.

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 8

Information Sheet 6.1.1: Ratio and Proportion

Learning outcomes:
6 Solve for values using the principles of ratio and proportion.
Learning Activity:
6.1 Solving values related to Ratio and Proportion

The concepts of ratio and proportion are closely related to the rational numbers.

Ratio

A ratio of one number to another “non zero” number is the quotient of the first number
divided by the second number. The ratio of a to b can be expressed as a/b or a ÷ b or a : b are
called the terms of ratio.

A ratio is used to compare quantities. This is an indicated quotient of two numbers. The
ratio of 5 to 6 may be written as 5 : 6 or 5/6. A ratio is just another way of thinking about
rational numbers

For example, the ratio between the number of computers and printers in an office is 12 : 6

The ratio of 12 : 6 is 12 to 6 or 12/6, the fraction 12/6 is equivalent to 2/1. Therefore, for every
2 computers in the office, there is 1 printer.

Study this Sample worded problem

Example 1: Jojo produces 400 pieces of workpiece in 35 hours while Chris produces 1500
pieces of the same workpiece in 129 hours. Which machine operator works faster?

Solution: To determine which operator is faster, we set up a ratio between the number of work
and the time. We get:

Jojo Chris

400 pieces 1500 pieces
35 hours 129 hours

= 400 ÷ 35 = 11.43 pieces per hour = 1500 ÷ 129 = 11.63 pieces per hour

Thus, Jojo works faster than Chris

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 6.1.1: Ratio and Proportion

Example 2: If an alloy is 2 parts copper, 3 parts lead and 4 parts tin, how many kilograms of
each are there in an alloy weighing 108 Kg?

Solution: Calculate the total number of parts. 2 + 3 + 4 = 9 parts
To determine how many Kg of element in a 108 kg alloy, we set up a ratio between
the Kilogram of alloy and the total number of parts. We get:

108 kilogram = 12 kilograms per part
9 parts

12 x 2 = 24 Kg. copper; 12 x 3 = 36 kg. lead; and 12 x 4 = 48 kg. tin

Proportion

A proportion is a statement of equality of two ratios. For instance, we have 8/12 = 4/6,
read “the ratio of 8 to 12 is equal to the ratio of 4 to 6”. In symbols, we could also write the
proceeding in the form 8 : 12 = 4 : 6 read “8 is to 12 as 4 is to 6”. The four numbers involved

are called the terms of the proportion.

Two types of proportion

Direct Proportion – if one variable increases and the other also increases, one
variable is said to be directly proportional to the other

Generally, we have a : b = c : d. Here a, the first term and d, the fourth term, are called
extremes, while b, the second term and c, the third term, are called means.

a:b=c:d

means
extremes

A general rule governing direct proportion is as follows: ac

The product of the extremes is equal to the product of the means, that is if b = d therefore,
ad = bc.

Example: 1 : 2 = ___ : 6

Therefore:
1 x 6 = 6 = 2 x ___ = 6
1x6=6 = 2x 3 =6

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 6.1.1: Ratio and Proportion

Study this Sample worded problem

Example 1: If it takes 30 calamansi fruits to make 5 cups of calamansi juice, how many fruits
will it take to make 45 cups of juice?

Solution: Let x = the number of fruits needed

30 X
5 = 45

= (5) (x) = (45) (30) (5) (x) 1350 x = 270
= (5) (x) = 1350 = 5

5

Thus, you should have 270 calamansi to make 45 cups of juice

Example 2: Paulo can produce 200 metal plates in 2 days. How long will he be able to make
3600 metal plates?

Solution: Let x = the number of days

200 3,600
2=
x

= (200) (x) = (3,600) (2) (200) (x) = 7,200 x = 36
= (200) (x) = 7,200
200 200

Thus, Paulo will take 36 days to finish 3600 metal plates

Inverse Proportion – if one variable increases and the other decreases, one
variable is said to be inversely proportional to the other

A general rule governing inverse proportion is as follows:
The product of the first ratio is equal to the product of the second ratio.

ac
that is if b = d

therefore, ab = cd

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 6.1.1: Ratio and Proportion

Study this Sample worded problem

Example 1: If 15 men can finish a construction job in 28 days, how long can 21 men finish the
same job?

Solution: Let x = the number of days

= (15) : (28) = (21) : (x)

= (15) (28) = (21) (x) (420) = (21) (x) x = 20
21 21

Thus, 21 men can finish a construction job in 20 days

Example 2: The number of tiles needed to cover a particular area is inversely proportional to
the size of each tile. If 25 tiles are required to cover a certain space when each tile
has an area of 36 sq. cm, how many tiles with an area of 10 sq. cm are needed to
cover the same space?

Solution: Let x = the number of tiles needed

= (25) : (36) = (10) : (x)

= (25) (36) = (10) (x) (900) = (10) (x) x = 90
10 10

Thus, 90 pieces of 10 sq. cm tiles are required to cover the space.

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Worksheet 6.2.1 : Number Problems

Learning outcomes:
6 Solve for values using the principles of ratio and proportion.
Learning Activity:
6.2 Solving values related to Ratio and Proportion

General Instruction: Solve for the following. Use scratch paper for your solution and
write your final answer on the box after each equal sign. Erasures

means wrong. You have 30 minutes to answer this worksheet.

Activity 1: Ratio

Direction: Express the following quantities as ratios in the simplest form using the ratio
symbol. Number 1 is done as an example.

1. 9 meters of ribbons to 3 dresses = 9 : 3 3:1
2. 20 chairs to 4 tables =
3. 6 boys to 18 marbles =
4. 18 cm to 24 cm =
5. 10 hours to 18 hours =
6. 6 months to 1 year =
7. 24 days to 3 weeks =
8. 20 cents to 1 peso =
9. 6 hours to 1 day =
10. 30 minutes to 15 minutes =

Activity 2: Proportion

Direction: Identify which of the following equations are proportional. Put a check if the
equation is proportional and put an X if the statement is not proportional. Write your
answer on the box after the equation.

1. 2 : 5 = 15 : 60 6. 8 : 18 = 16 : 36
2. 1 : 3 = 12 : 8 7. 1.2 : 0.4 = 1.5 : 0.5
3. 8 : 5 = 16 : 10 8. 13 : 15 = 52 : 60
4. 2 : 1 = 8 : 5 9. 4 ½ : 7 1/3 = 54 : 88
5. 4 : 8 = 5 : 9 10. 8 : 3 = 8 4/9 : 3 1/6

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Worksheet 6.3.1 : Worded Problems
Learning outcomes:
6 Solve for values using the principles of ratio and proportion.
Learning Activity:
6.3 Solve worded problems
General Instruction: Solve for the following worded problem. Use the space provided after

the problem for your solution and box your final answer. Erasures
means wrong. You have 15 minutes to answer this worksheet.
(5 points each)
1. If a machine can produce 2,550 metal parts in 7 ½ hours, how many hours would it take
the machine to produce 4,080 metal parts?

2. A certain map is drawn to scale such that a line segment 3 cm long represents 25 km.
How many kilometers are represented by a segment 21 cm long?

3. A certain alloy contains 50 parts Carbon, 30 parts Aluminum, 8 parts Iron and 12 parts
gold. How many grams of each metal are contained in 2,400 grams of this alloy?

4. Spur Gear A has 72 teeth, while Spur gear B has 24 teeth. How many times did gear B
rotates if Gear A rotates 5 times?

AB

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 8

Information Sheet 7.2.1: Converting decimal to percentage

Learning outcomes:
7 Convert decimal to percentage
Learning Activity:
7.12 Converting decimal to percentage

Percentage

Means hundredths or parts of a hundred. It is another way
of expressing a part of a whole and it is indicated by the
symbol “%”.

A rectangle made up of 100 small squares can
represent a totality.

if the 46 squares are shaded, this is 46 out of 100
and can be expressed as 46%.

Changing Percents to Decimals

To change percent to decimal number, multiply the number by 0.01 and drop the percent sign.
Percent means hundredths. Therefore 32% means 32 x 0.01 = 0.32

Examples: 1. 7% is 7 x 0.01 = 0.07
2. 45% is 45 x 0.01 = 0.45
3. 63% is 63 x 0.01 = 0.63

The short way of changing percent to decimal number is by moving the decimal point two
places to the left and omitting the sign of percent.

Examples: 1. 25% = 2 5 % = 0.25
2. 6.8% = 0 6 8% = 0.068
3. 9% = 0 9% = 0.09

Changing Decimals to Percent

Changing a decimal number to percent, multiply the number by 100 and affix the percent sign.

Examples: 1. 0.2 x 100 = 20%
2. 0.14 x 100 = 14%
3. 2.3 x100 = 230%

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 7.2.1: Converting decimal to percentage

The short way of changing decimal number to percent is by moving the decimal point two
places to the right and affixing the percent sign to the new number.

Examples: 1. 0.86 = 0 . 8 6 = 86%
2. 0.20 = 0 . 2 0 = 20%
3. 0.12 = 0 . 1 2 = 12%

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Worksheet 7.3.1 : Number Problems

Learning outcomes:
7 Convert decimals to percentage and vice versa
Learning Activity:
7.3 Converting decimals to percentage and vice versa

General Instruction: Convert the following. Use blank space of the paper for your solution
And write your final answer on the box after each equal sign. Erasures
means wrong. You have 15 minutes to answer this worksheet.

Decimal to Percentage

1. 0.26 =
2. 1.4 =
3. 0.75 =
4. 0.831 =
5. 2.92 =
6. 0.5 =
7. 0.64 =
8. 4.9 =
9. 0.013 =
10. 0.009 =

Percentage to Decimal 6. 1.9% =
7. 8% =
1. 0.1% = 8. 6.8% =
2. 0.7% = 9. 39% =
3. 24% = 10. 275% =
4. 4.5% =
5. 627%=

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Information Sheet 7.4.1: Percentage problems

Learning outcomes:
7 Solve problem involving percentage
Learning Activity:
7.4 Solving problem involving percentage

Three Types of Percentage Problems

There are three types of problems that can be solved involving percentage.

Percentage is the product of the rate multiplied by the base. In formula form,
this is p = r x b.

Example:

20% of 100 = 20
 
rate base percentage

Percentage: Finding a Certain Percent of a Number

The rate and the base are given, the percentage is unknown.

Example A:
What is 3% of 94?
Given: rate = 3%, base = 94
Formula: p = r x b
Solution: p = 3% x 94
= 0.03 x 94
p = 2.82

Example B:
Find 12% of 28?
Given: rate = 12%, base = 28
Formula: p = r x b
Solution: p = 12% x 28
= 0.12 x 28
p = 3.36

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 7.4.1: Percentage problems

Rate: Finding What Percent a Number is of Another Number

The percentage and the base are given, the rate is unknown.

Example A: Example B:

What percent of 80 is 50? What percent of 175 is 75?
Given: percentage = 50, base 80 Given: percentage = 75, base 175

Formula: P = r Formula: P = r
b b

Solution: r = 50 = % Solution: r = 75 = %
80 175

r = 0.625 = 62.5% r = 0.428 = 42.8%

Base: Finding a Number When the Percent is Given

The percentage and the rate are given, the base is unknown.

Example A: Example B:

8% of what number is 40? 30 is 12% of what number?
Given: rate = 8%, percentage = 40 Given: rate = 12%, percentage = 30

Formula: P = b Formula: P = b
r r

Solution: 40 = 8% of ___ Solution: 30 = 12% of ___
40 = 500 30 = 250
0.08 0.12

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 7.4.1: Percentage problems

Study these worded problems

Problem 1: Out of 56 boys, nine are wearing eyeglasses. What percent of the boys are
Wearing eyeglasses?

Given: 56 = Base
9 = Percent

What is asked: Rate

Solution: r = P = 9 = 0.1607 = 16.07 %
b 56

Problem 2: There are 345 fourth year students. The twenty percent are members of the glee
club. How many are the members of the glee club?

Given: 345 = Base
20% = Rate

What is asked: Percent

Solution: P = r x b = 345 x 0.2 = 69 members

Problem 3: Jocris saved 12% of her allowance for one week. If her savings is Php14.40, how
much is his weekly allowance?

Given: 12% = Rate
14.40 = Percent

What is asked: Base

Solution: b = P = 14.40 = 120 = Php120
r 0.12

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Worksheet 7.5.1 : Percentage Problems

Learning outcomes:
7 Solve problems involving percentage
Learning Activity:
7.5.1 Solving problems involving percentage

General Instruction: Convert the following. Use blank space of the paper for your solution
And write your final answer on the box after each equal sign. Erasures
means wrong. You have 30 minutes to answer this worksheet.

1. What percent of 84 is 12? =
2. What is 2 ½ % of 22 =
3. 28 is what percent of 42 =
4. 30 is what percent of 75 =
5. What is 9 ½ % of 44? =
6. 14% of what number is 42 =
7. What is 5.5% of 84 =
8. 96 is 32% of what number? =
9. 26% of what number is 78? =
10. What is 6 ¾ % of 95 =

Worded Problems
1. A motor receiving 8 h.p. delivers 6.8 h.p. of work. What percent of the input is the
output?

2. Out of total production of 2715 ball bearings manufactured during a day, 107 were
rejected by the inspectors as imperfect. What percent of the output is good?

3. A machine shop job required 42 hours on the lathe, 7 ½ hours on the milling machine,
and 11 ¼ hours on the planer. What percent of the total time should be charged to each
machine?

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204
April 28, 2010 7

Information Sheet 8.2.1 : Basic shop formulas and equations

Learning outcomes:
8 Manipulate and use basic shop formulas
Learning Activity:
8.2 Solving basic shop problems using the appropriate formula

On the previous lessons, you recall and even learn more about basic arithmetic
operations. On this part, we will talk about basic shop formulas that are used on the machine
shops. We will talk about Cutting speeds, machining time, drill sizes and some conversion of
measurements.

Cutting Speeds

The Cutting Speed is the rate at
which a tool passes over a piece of work.
For the Lathe, cutting speed may be
defined as the distance on the surface of
the work that passes the point of the tool
in one minute.

Most machining operations are conducted on machine tools having a rotating spindle.
Cutting speeds are usually given in feet or meters per minute and these speeds must be
converted to spindle speeds, in revolutions per minute, to operate the machine. Conversion is
accomplished by use of the following formulas:

Where:
N = spindle speed in Revolutions per Minute (RPM)
V = Cutting speed in feet per minute (fpm) for English units and millimeters per minute (m/min)
for metric units.

In turning:
D = diameter of the work piece

In milling, drilling, reaming and other operations that use a rotating tool:
D = Cutter diameter in inches for English units and in millimeters for Metric units

= 3.1416
1000 and 12 is constant

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3

Information Sheet 8.2.1 : Basic shop formulas and equations

Study this Example:
The Cutting speed for turning a 4 inch (101.6 mm) diameter bar has been found to be 575 fpm
(175.3 m/min). Using both the inch and metric formulas, calculate the Lathe spindle speed.

ENGLISH METRIC

Step 1: Write the formula to calculate
spindle speed

Step 2: Substitute the given values to the
formula and calculate for the final
answer.

Here is the table for estimated cutting speed for common kind of material:

Material to be drilled (HSS tool) Cutting speed

Aluminum 70-100

Brass 35-50

Bronze (phospor) 20-35

Cast iron (grey) 25-40

Copper 35-45

Steel (medium carbon/mild steel) 20-30

Steel (alloy, high tensile) 5-8

Thermosetting plastic 20-30

Code No. Perform Basic Shop Computations Date: Developed Date: Revised Page #
MEE722204 April 28, 2010 3