UC3-Performing estimation and basic calculation

COMPETENCY-BASED LEARNING MATERIAL

Sector: AGRICULTURE AND FISHERIES

Qualification:

AGRICULTURAL CROPS PRODUCTION – NC III

Unit of Competency:

PERFORM ESTIMATION AND BASIC CALCULATION

Module Title:

PERFORMING ESTIMATION AND BASIC CALCULATION

MARCOS AGRO-INDUSTRIAL SCHOOL
2907 Brgy. Lydia, Marcos, Ilocos Norte

MAIS- PERFORM Date Developed: Document No. CC-ACP3-03
TESDA QA ESTIMATION AND July 18, 2020
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BASIC Developed by:
CALCULATION Instructional
Joffrey E. Gacula Materials Review

Associate Professor IV Committee

Revision # 00

HOW TO USE THIS
COMPETENCY-BASED LEARNING MATERIAL (CBLM)

Welcome to the competency-based learning material for the module:
Performing Estimation and Basic Calculation. This module contains training
materials and activities for you to accomplish.

This unit of competency “Perform Estimation and Basic Calculation”, is one
of common competencies which contains the knowledge, skills and attitudes required
for Agricultural Crops Production - National Certificate Level III (NC III).

You are required to go through a series of learning activities in order to
complete each learning outcomes of the module. In each learning outcome, there are
reference materials or instructional sheets for further reading to help you better
understand the required activities. Follow the activities at your own pace and answer
the self-check at the end of each learning outcome. If you have questions, please feel
free to ask for the assistance of your trainer/facilitator.
RECOGNITION OF PRIOR LEARNING (RPL)

You may have some or most of the knowledge and skills included in this
learner’s guide because you have:

❖Been working in the same industry for some time.
❖Already completed training in this area.
If you can demonstrate to your trainer that you are competent in a particular
skill, you don’t have to do the same training again.
If you feel that you have some skills, talk to your trainer about having them
formally recognized. If you have a qualification or certificate of competence from
previous trainings, show them to your trainer. If the skills you acquired are still
current and relevant to the unit of competency, they may become part of the evidence
you can present for RPL. If you are not sure about the currency of your skills, discuss
this with your trainer.

A Trainee Record Book (TRB) is given to you to record important dates, jobs
undertaken and other workplace events that will assist you in providing further
details to your trainer/assessor. A Record of Achievement/Progress Chart is also
provided to your trainer to complete/accomplish once you have completed the
module. This will show your own progress.

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Developed by: Instructional
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Associate Professor IV
Revision # 00

DIRECTION FOR USE OF THE CBLM

This module was prepared to help you achieve the required competency:
Perform Estimation and Basic Calculation. This will be the source of information
for you to acquire the knowledge and skills in this particular module with minimum
supervision or help from your trainer. With the aid of this material, you will acquire
the competency independently and at your own pace.

Talk to your trainer and agree on how you will both organize the training of
this unit. Read through the module carefully. It is divided into sections which covers
all the skills and knowledge you need to successfully complete in this module.

Work through all the information and complete the activities in each section.
Do what is asked in the INSTRUCTIONAL SHEET (TASK SHEET, OPERATION SHEET,
JOB SHEET) and complete the SELF-CHECK. Suggested references are included to
supplement the materials provided in this module.

Most probably, your trainer will also be your supervisor or manager. He is
there to support you and show you the correct way to do things. Ask for help.

Your trainer will tell you about the important things you need to consider
when you are completing activities and it is important that you listen and take notes.

You will be given plenty of opportunities to ask questions and practice on the
job. Make sure you practice your new skills during regular work shifts. This way, you
will improve both your speed and memory and also your confidence.

Talk to more experienced workmates and ask for their guidance.

Use the self-check questions at the end of each section to test your own
progress.

When you are ready, ask your trainer to watch you perform the activities
outlined in the module.

As you work through the activities, ask for written feedback on your progress.
Your trainer gives feedback/pre-assessment reports for this reason. When you have
successfully completed each element or learning outcome, ask your trainer to mark
on the reports that you are ready for assessment.

When you have completed this module (several modules) and feel confident
that you have had sufficient practice, your trainer will arrange an appointment to
qualified trainer to assess/evaluate you. The result of your assessment/evaluation
will be recorded in your ACHIEVEMENT AND PROGRESS REPORTS.

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Revision # 00

AGRICULTURAL CROPS PRODUCTION – NC III
COMPETENCY-BASED LEARNING MATERIAL

LIST OF COMPETENCIES

(COMMON COMPETENCIES)

No. Unit of Competency Module Title Code

1. Apply safety Applying safety AGR321201
measures in farm measures in farm
operations
operations

2. Use farm tools and Using farm tools AGR321202
equipment and equipment

3. Perform Performing AGR321203
estimation and estimation and
calculations calculations

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QUALIFICATION : AGRICULTURAL CROPS PRODCUTION - NC III
UNIT OF COMPETENCY : PERFORM ESTIMATION AND BASIC
CALCULATION

UNIT CODE : AGR321203
MODULE TITLE : PERFORMING ESTIMATION AND BASIC
CALCULATION

INTRODUCTION : This module covers the knowledge, skills and attitude required to
perform basic workplace

calculations relating to feeds, fertilizer and related
quantities.

NOMINAL DURATION : 6 HOURS

LEARNING OUTCOMES :

At the end of this module, you will be able to:

1. Perform estimation
2. Perform basic workplace calculation

ASSESSMENT CRITERIA:

1. Job requirements are identified from written or oral communications 2.
Quantities of materials and resources required to complete a work task are
estimated
3. The time needed to complete a work activity is estimated
4. Accurate estimate for work completion is made
5. Estimate of materials and resources are reported to appropriate person
6. Calculations to be made are identified according to job requirements 7.
Correct method of calculation identified
8. System and units of measurement to be followed are ascertained 9.
Calculation needed to complete work tasks are performed using the four basic
processes of addition, division, multiplication and subtraction
10. Calculate whole fraction, percentage and mixed when are used to complete the

instructions
11. Number computed is self-checked and completed for alignment PRE-

REQUISITE : BASIC AND COMMON COMPETENCIES (NC – II)

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DEFINITION OF TERMS

Calculation the act of finding or figuring out the answer to a problem. Digit the
symbol used to write the numbers (i.e. 1, 2, 3, . . . ,0) Estimation finding
something close to the exact answer; approximation.
Fraction is a part of a whole expressed as the quotient of the numerator divided by

the denominator, a/b where b ≠ 0.

Measurement comparison between and unknown quantity, capacity or
dimension of a unit of measure

Multiple the product of multiplying a number and the set of counting numbers

Non-terminating is a decimal that has an infinite number of digits in its
decimal representation.

Non-terminating is a nonterminating decimal that has a block of digits which
repeating decimal repeat indefinitely.

Numeral letters or symbols representing a number (i.e 1, 5, V, X, 0). Order the
position of a numeral.

Place Value the value of a numeral by virtue of its position or place among other
numerals

Percent part of a hundred.

Proportion a statement that two ratios are equal.

Ratio comparison of two numbers or quantities as quotient. Reciprocal is
the inverse of the number.

System of a collection of units of measurement and rules relating them to
Measurements each other.

Terminating is a decimal that has a finite number of figures.
decimal

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LEARNING OUTCOME #1: PERFORM ESTIMATION

CONTENTS: 1. Basic Estimation Skills and Techniques

ASSESSMENT CRITERIA:

1. Job requirements are identified from written or oral communications 2.
Quantities of materials and resources required to complete a work task are
estimated
3. The time needed to complete a work activity is estimated
4. Accurate estimate for work completion is made
5. Estimate of materials and resources are reported to appropriate person

RESOURCES:

Pen/pencil Flashcards
Bond Paper Reference Materials
Instructional Sheets Laptop with Internet Access ➢Information
Sheets
➢Task Sheets
➢Assignment Sheets
➢Performance Criteria Checklists

ASSESSMENT METHOD:

Written examination
Practical Demonstration

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Associate Professor IV Committee

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LEARNING EXPERIENCES

LEARNING OUTCOME #1: PERFORM ESTIMATION

LEARNING ACTIVITIES SPECIAL INSTRUCTION
Compare to Answer Key 3.1-1.
1. Read Information Sheet 3.1-1 on
the meaning and Trainer/trainee evaluates
methods/techniques in basic performance using Performance
estimation. Criteria Checklist 3.1-1 and
makes recommendation.
2. Answer Self-Check 3.1-1.

3. Perform Task Sheet 3.1-1 on basic
estimation skill.

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Associate Professor IV

INFORMATION SHEET 3.1-1
BASIC ESTIMATION SKILLS AND TECHNIQUES

Learning Objectives:

After reading this Information Sheet, the trainee must be able to:
1. learn basic estimation skills; and
2. perform estimation skills in solving related problems.

INTRODUCTION

As you walk around and live your life, you are confronted
daily with big numbers. The alarming number of 9.61
million N-CoVid19 cases in the world; the increasing
population of the country which is 1.09 million; the

approved 2020 national budget of PhP4.1 trillion; a gold
player who wants to win a 400 000-dollar prize; the 2 GB
data usage of internet activities, etc., etc.!

Each time you come up with a figure of, say, more than one thousand, relate this
number to an imagine counting process (visual estimate).

WHAT IS ESTIMATION?

Let us assume that it takes a second to count one
number,
regardless of what the order of magnitude might be, and
that one has to count without any interruption, day and
night, until one reaches the final figure. So, if you come
up with a large number, you need to estimate how long
the counting procedure would last.

For example, you need to count 1million peso coins.
You
start right now and it takes 1 million seconds. How much time
will this take you? A day? Two days? A week?

To write estimate, we use the squiggly equal sign (≈). Estimation can help you
in various circumstances both in math and in real life.

Estimation can save you money. Always do a quick estimation of how much
you should pay. For example:

You want to buy five pencils that cost P9.75 each.
Is it right to have P50 in the pocket to buy the items?

“Five at P9.75 each is about 5 times 10, or about P50”.
So, P50 seems enough!

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Estimation can save you time when calculation does not have to be exact.
plant should be 50cm apart. How
many plants do you need?
Let us say:

“495 is almost 500, and 500 divided
by 50 is 10, so 10 plants is enough
for the row.

You want to plant a row of eggplants.
The row is 495cm long and each

Estimation can save you from making mistakes with your calculator. For
instance, you are calculating 105 times 26, and the calculator displays:

390 Is that right?

“105 times 26 is a bit more than 100 times 20, which is 2,000.”
Maybe, something went wrong . . . you fail to press the zero (0)

that only 15 x 26 were inputted, and without estimating you
could have made really a big mistake! Therefore, do not just rely

on calculators or computers. Use your estimation skill to double
check figures.

Lastly, estimation helps you focus on what is really going on.

Estimating makes us fun because it keeps the mind active but it takes skill to
get it.

Estimation is not always doing calculations. You can also quantify things
based on what you see. Take a look at
the box below, how many objects are
there?

You need not to give the exact answer,
just one that is close to it.

Try to make a guess, how many?

Visual Estimation is finding a value
that is close enough to the right answer.

• You are not trying to get the exact right answer (=)
• What you want is something that is good enough (≈)

To estimate means to find something close to the correct answer, usually with
some thought or calculation involved. In other words, you are approximating.

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GENERAL RULE OF ESTIMATING

When it comes to estimating in math, there is a general rule for you to follow.
This general rule tells you to look at the digit to the right of the digit you want to
estimate, and if it is less than 5 then you round down, and if it is greater than or
equal to 5, you round up.

So, for example, if you wanted to round to the nearest whole number here, you
would look at the digit right after the decimal since that is the digit to the right of the
digit you want to round.

Let's start rounding: 5.3
becomes 5;
3.7 becomes 4; 10.9 becomes 11. What
about
6.5?

When you round down, you
round
down to your nearest number. When it
came
to rounding 5.3, I rounded it down to 5
because that was the closest one. I can draw
it on the number line like this, and I can
plainly see that 5 is the closest whole number
to 5.3.

So, rounding down doesn't mean going down one whole number, it just means

going to the closest whole number which, when it comes to rounding down, means
you keep the same whole number that you see.

Rounding up means you go up to the next number. Like when I rounded 10.9
to 11. 11 is the closest whole number to 10.9. And, you can see it easily if you draw it
out on a number line.

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ESTIMATING TO DIFFERENT PLACES
You can estimate to whatever place you want. Let's say you wanted to estimate

to the nearest tens place. This means instead of estimating to the nearest whole
number, you estimate to the digit that is in the tens place or the second one to the
left of the decimal. To estimate this digit, you would look at the digit in the ones
place because that is the digit to the right of the digit you want to estimate.

Estimating these numbers to the tens place, the same general rule applies.
Therefore, 456 becomes 460; 234 becomes 230; 789 becomes 790; 154 becomes 150;
845 becomes 850, and 565 becomes 570. What about if we wanted to estimate to the
hundreds place? Which digit would we look at?

For more fun games, visit: https://www.mathsisfun.com/numbers/estimation.html

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SELF-CHECK 3.1-1

I. ORAL TEST
DIRECTION: Perform what is required in every item. Give your
exact estimate.

1. Round-off the number to the nearest:

a) 12 345 tens
b) 31 173 thousand
c) 78.051 tenths
d) 8956. 12575 unit/ones

thousandths
ten thousand
ten thousandths

2. 1+ 2+ 3 + 4 = ____________

3. 4 + 24 + 72 = ____________

4. P1 + P2.25 + P0.50 + P5.75 + P20.50 = _____________

5. No of blue box.

6. Supply the missing data:

Quantity Description Unit Cost Total Cost
P40
5 kls 14-14-14 Fertilizer P325

3 btl Pesticide (100 mL)

10 m Nylon string P15
4 pks
2 pcs Ampalaya Seeds P75

Deeper P28

TOTAL AMOUNT

7. If the small box has an area of 1 sq. unit, what is the area of
the big box?

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ANSWER KEY 3.1-1

I. ORAL TEST

a. a) 12 350
b) 30 000
c) 78.1
d) 8956
8956.126
10000
8956.1258

2. 10
3. 100
4. P30.00
5. 20
6. P200

P975
P150
P300
P58
7. 24 sq. units

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Title: TASK SHEET 3.1-1

GUESSTIMATION (Basic Estimation)

Performance Given the necessary materials, you will be able to practice
Objective: estimation by guessing the answer to every problem within 5
seconds.
Supplies and Flashcards (Problem Set)
Materials
Tools and N/A
Equipment
1. Inform your trainer when ready for the task.
Procedure 2. When ready, trainer flashes one card in five (5) seconds

Assessment/ for you to answer also within five (5) seconds.
Evaluation 3. Your guess is accepted when estimate is the exact
Method answer. 4. You need to get 8 out of 10 to be competent.
Performance Test

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Performance Criteria Checklist 3.1-1

Performance Standard Yes No N/A

Correct estimate
1.
2.
3.
4.
5.
6.
7.
8.
9.

10.

Note: You must be able to get 80% from the total items to be COMPETENT.

Remarks/Recommendations:
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________

_________________________________
Trainer

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LEARNING OUTCOME #2: PERFORM BASIC WORKPLACE CALCULATION

CONTENTS: 1. Fundamental Operations
a. Whole Numbers and Decimals
b. Fractions

2. Percentage
3. Ratio and Proportion

4. Measurements
5. Perimeter and Area
6. Volume of Solids and Liquids

ASSESSMENT CRITERIA:

1. Calculations to be made are identified according to job requirements
2. Correct method of calculation identified
3. System and units of measurement to be followed are ascertained 4.
Calculation needed to complete work tasks are performed using the four basic
processes of addition, division, multiplication and subtraction 5. Calculate
whole fraction, percentage and mixed when are used to complete the
instructions
6. Number computed is self-checked and completed for alignment

RESOURCES:

Pen/pencil Conversion Table
Bond Paper Sample Problems/Worksheets Calculator Reference
Materials

Instructional Sheets
➢Information Sheets
➢Task Sheets
➢Assignment Sheets
➢Performance Criteria Checklists

ASSESSMENT METHOD:

Written examination
Practical Demonstration

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LEARNING EXPERIENCES

LEARNING OUTCOME #2: PERFORM BASIC WORKPLACE CALCULATION

LEARNING ACTIVITIES SPECIAL INSTRUCTION

1. Read Information Sheet 3.2-1a on the Compare to Answer Key 3.2-
addition of whole numbers and 1a. Compare to Answer Key
decimals. 3.2-1b.

2. Answer Self-Check 3.2-1a. Compare to Answer Key 3.2-
3. Read Information Sheet 3.2-1b on 1c. Compare to Answer Key
the subtraction of whole numbers and 3.2-1d.
decimals.
Compare to Answer Key
4. Answer Self-Check 3.2-1b. 3.2-2. Compare to Answer
5. Read Information Sheet 3.2-1c on Key 3.2-3. Compare to

the multiplication of whole
numbers and decimals.
6. Answer Self-Check 3.2-1c.
7. Read Information Sheet 3.2-1d on the
division of whole numbers and
decimals.
8. Answer Self-Check 3.2-1d.
9. Read Information Sheet 3.2-2 on
the fundamental operations involving
fractions.
10.Answer Self-Check 3.2-2.
11.Read Information Sheet 3.2-3
on percentage.
12.Answer Self-Check 3.2-3.
13.Read Information Sheet 3.2-4 on
ratio and proportion.
14.Answer Self-Check 3.2-4.
15.Read Information Sheet 3.2-5
on measurement.
16.Answer Self-Check 3.2-5.
17.Read Information Sheet 3.2-6
on perimeter and area.

Answer Key 3.2-4. Compare

to Answer Key 3.2-5.

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18.Answer Self-Check 3.2-6. Compare to Answer Key 3.2-6.
19.Perform Task Sheet 3.2-6 on Trainer evaluates output and
makes recommendation.
finding perimeter and area.
20.Read Information Sheet 3.2-7 on Compare to Answer Key 3.2-7.

volume of solids and liquids.
21.Answer Self-Check 3.2-7.

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INFORMATION SHEET 3.2-1a
ADDITION OF WHOLE NUMBERS AND DECIMALS

Learning Objectives:
After reading this Information Sheet, the trainee must be able to: 1. perform
calculations involving addition of whole numbers and decimals; and 2. apply
the operation in solving related problems in everyday life.

INTRODUCTION
The study of mathematics is an integral part of education that helps people

respond wisely and effectively to the demands of a changing world. Students who
study “mathematics” learn about numbers, the operations that can be performed
with these numbers and the rules or properties that “regulate” these numbers and
operations.

Addition, subtraction, multiplication, and division are the four fundamental
operations used in mathematics. Even in this age of digital technologies, the basic
skills in operating numbers are still needed.

FUNDAMENTAL OPERATION: ADDITION

The set of whole numbers consists of the set of counting numbers or natural
numbers i.e 1, 2, 3, . . . including zero (0). Many of our daily mathematical activities
involve whole numbers. When someone asks you of your age, you usually round off
your answer to a whole number. When buying items in a grocery store that is priced
at P9.95, you just pay for P10, no more change. It is a whole number. Can you think
of other examples?

Addition is the process of combining together similar numbers or quantities. It
is the sum or total of two or more numbers called addends. The answer or result of
addition is called sum or total.

In adding whole numbers, arrange the digits with the same place-value or
order in columns. Add the digits column by column from right to left. For decimal
numbers, the same rule applies but be sure that the decimal points are also
arranged in vertical line. Numbers may also be added horizontally but it is easier to
add when arranged vertically. Look at the examples below:

1. 23 2. 34 + 16 = 50 3. 1,234 4. 54.12 45 527 1.06 68 69 0.783 1,830
55.963

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Accuracy in adding numbers without the aid of adding machines or
calculators needs much concentration and skill. But no amount of concentration
can guarantee the accuracy of results, so certain techniques may be used to
eliminate errors.

Addition by Grouping

When there is a long series of addends, the possibility of errors can be reduced
by grouping the numbers into sub-groups. Then total each sub-group and for the
final answer, add the sub-total of each group.

For example, you will add the following numbers:

1. 132 2. 2,455
346 1,978
591 969 5,062 9,495
780 393
604 8,107
725 2,109 964 9,464
977 4,262
861 7,510
413 2,251 638 12,410
5,329 31,369

Addition by 10’s

In adding whole numbers, group and add numbers whose sum is 10.

Examples: 10 10
1. 2. 10
7 . 26 10

3

2 35 10 10
6 70

1 13 10

9 97 29 325

Checking Addition using Reverse Addition

The best way to check addition process is by reverse addition that is, by
adding a column in the opposite direction. The answers must agree. Let’s try adding
the numbers below and check the addition using reverse addition.

Example: Reverse 43,061
34,298 Addition 34,298
209 209 8,452 8,452
102 102
43,061

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Checking Addition using Casting-Out 9’s
Casting-out 9s is probably the easiest and fastest way of checking addition. Simply
add the digits in every number then cast-out if digit sum is 9. Digit sum of un-casted
9’s in the addends must agree with the digit sum of un-casted 9’s in the answer. Let’s
try adding the numbers below and check the addition using casting-out 9’s.

Example: Casting 34,298 out 9’s 34,298 - 8
209 209 - 2 8,452 8,452 -
10 1 102 102 - 3 43,061
43,061

4+1=5
2+3=5

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SELF-CHECK 3.2-1a

I. ORAL DRILL:
1. 8 + 6 + 2 + 3 + 7 = ______ 3. 11 + 12 + 8 + 9 + 6 = _______ 2. 9 + 7
+ 1 + 3 + 2 = ______ 4. 23 + 18 + 7 + 12 = ______ 3. 2 + 5 + 9 + 3 + 4
= ______

II. Find the sum of each of the following numbers and check answers using
any technique.

1. 503 + 20,393 + 2,049 + 76 + 3 = __________

2. 0.097 + 2.321 + 39.485 + 24.021 = __________

3. 30,090 4. 45,390.2 5. 27,000.86

2,091 24.98 9,752.
416,824 9,812.347 0.1694
3,009 26.989 197.59
3,000,029 729.91 12.63

8, 458
67,102
554

III. APPLICATION EXERCISES: Solve the following problems correctly.

1. Shown below is the record of sales of organic eggs produced in the MAIS
Organic Farm for the month of June. How many eggs were sold for the
month and how much is the total sales?

Date No. of Eggs Amount of Sales

June 5 120 P720.00

12 160 960.00

19 98 588.00

26 142 852.00

TOTAL

2. Mr. Gacula spent one week preparing the land for transplanting rice
seedlings. He started clearing the area for 4 hours on Monday;
continued working at the irrigation canal for 4.25 hours the following
day; a whole work-day for plowing the land on Wednesday; another
6.75 hours spent for harrowing on Thursday; and half-day distribution
of rice seedling on Friday ready for transplanting the following day.
How many hours did he prepare the land for transplanting?

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ANSWER KEY 3.2-1a

I. ORAL DRILL

1. 26 3. 46
2. 22 4. 60
3. 23

II. COMPUTATION SKILLS
1. 23,024 4. 55,984.426
2. 65.924 5. 36,963.2494

3. 3,528,157

III. PRACTICAL EXERCISES No. of Eggs Amount of Sales
1. P720.00

Date 960.00
588.00
June 5 120 852.00
P3,120.00
12 160

19 98

26 142

TOTAL 520

2. Monday 4 Hours
Tuesday 4.25

Wednesday 8
Thursday 6.75

Friday 4
Total 27 Hours

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INFORMATION SHEET 3.2-1b
SUBTRACTION OF WHOLE NUMBERS AND
DECIMALS Learning Objectives:

After reading this Information Sheet, the trainee must be able to: 1. perform
calculations involving subtraction of whole numbers and decimals; and
2. apply the operation in solving related problems in everyday life.

INTRODUCTION
Farmers usually gamble themselves in agricultural production because of the

unpredictable weather conditions due to climate change. They expect to have a good
harvest during the main crop season but because of natural calamities like typhoons,
floods and hurricane that struck the country have resulted to a loss of investment.
Business phenomenon does not only account addition in the form of profits, but also
subtraction in the form of costs of losses.

FUNDAMENTAL OPERATION: SUBTRACTION
Subtraction is thought to be the inverse of addition. It is the process of taking

away an amount or a number or a quantity from another similar amount, number or
quantity. It is the process of finding the difference between two numbers. We take
away from a larger number or quantity called minuend, and the smaller amount or
quantity is called subtrahend. The result of the process of subtraction is called
difference or remainder.

Like in addition, subtraction may be operated horizontally or vertically but the
latter is more preferred. The digits are arranged in columns then subtract from right
to left.

There are two ways of checking the accuracy of the result:

1. reverse addition (adding the difference to the subtrahend to obtain the
minuend.

2. subtracting the difference from the minuend to obtain the subtrahend.

Study the examples below.
Example 1: Subtract 11,100 from 31,173 then check.

Solution: 31,173 minuend
- 11,100 subtrahend
20,073 difference or remainder

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Check: a. 20,073 b. 31,173
+ 11,100 - 11,100
31,173 20,073

Example 2: Find the difference of 8.2571 and 3.1649.

Solution: 8.2571
- 3.1649
5.0922

Check: a. 5.0922 b. 8.2571
+ 3.1649 - 5.0922
MAIS- 8.2571 3.1649
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SELF-CHECK 3.2-1b

I. Find the difference of each of the following and check:
1. 89,753 2. 230.005 3. P100.75 - 46,168 - 39.421 - 59.50

4. Subtract 293,368 from 561,120
5. From P0.925 subtract P0.3148

II. Complete the table by finding the net sales and totals.
(Net Sales = Gross Sales – Returns)

No. Gross Sales Returns Net Sales
1 620 138
2 2,378 529
3 987 416
4 8,367
5 17,298 281
6 7,901 2,561
7 6,290 5,347
8 9,102 562
1,025
Totals

III. Practical Exercise
Solve the following problems:

1. Mang Pedro withdrew eight thousand pesos from the cooperative bank to buy
sacks of complete fertilizer that cost five thousand three hundred twenty-
five pesos for his agricultural crops. How much will be left with him for the
daily subsistence?

2. Yannah’s father is interested in buying a new farm equipment. A “reaper”
priced at P1,350,580 and a tractor that costs P550,825. How much more
does the harvester cost?

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ANSWER KEY 3.2-1b

I. FIND THE DIFFERENCE

1. 43,589
2. 190.584
3. P41.25
4. 267,752
5. 0.6102

II. COMPLETE THE TABLE Returns Net Sales
No. Gross Sales P138 P482
529 1,849
1 P620 416 57
8,367 8,931
2 2,378 2,810 5,091
2,561 3,729
3 987 5,347 3,759
562 463
4 17,298
P20,730 P24,361
5 7,901

6 6,290

7 9,102

8 1,025

Totals P45,091

III. PRACTICAL EXERCISES

1. P2,675.00
2. P799,755.00

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INFORMATION SHEET 3.2-1c
MULTIPLICATION OF WHOLE NUMBERS AND

DECIMALS Learning Objectives:

After reading this Information Sheet, the trainee must be able to: 1. perform
calculations involving multiplication of whole numbers and decimals; and
2. apply the operation in solving related problems in everyday life.

INTRODUCTION
The increasing costs of commodities greatly affect our lives especially those

who do not have a lucrative source of income. The effect of this pandemic due to N-
CoViD19 has brought all prices doubly-up so customers buy goods in bulk or in
large quantities because it is cheaper than buying one article at a time. Finding the
cost would require repeated addition of the unit price – multiplication.

FUNDAMENTAL OPERATION: MULTIPLICATION

Multiplication is the fastest way of adding equal numbers. It is the process of
adding or taking a number or quantity several times. It is the short cut of addition.
The number taken several times is called multiplicand and the number of times it is
taken or considered is called multiplier. The result of multiplication is called product.
The numbers being multiplied to form a product are called factors of the product.

Consider the examples below:

Example 1: 15 + 15 + 15 is “3 times 15”, which is equal to 45 and may be written as

3 x 16 = 45 or 16 -
multiplicand
x 3 - multiplier
48 - product

Example 2: 12 times 135 135 - multiplicand
x 12 - multiplier

factors

270 - partial product (2 x 135)
135 - partial product (1 x 135) 1620 - product

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Example 3: 0.251 x 43.56

43.56 - multiplicand (2 decimal places)
x 0.271 - multiplier (3 decimal places)

4356 - partial product (1 x 4356)
30492 - partial product (7 x 4356)
8712 - partial product (2 x 4356)

11.80476 - product (point-off 5 decimal places from the right)

In the examples above, each digit of the multiplicand is multiplied by each
digit of the multiplier. In examples 2 and 3, partial products are obtained. Simply
add all these to get the product. If the factors are decimals as shown in example 3,

count the number of decimal places in the multiplicand and multiplier and point off
as many decimal places in the product.

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SELF-CHECK 3.2-1c

I. PRACTICAL EXERCISES
Direction: Solve the following problems:

1. Find the total number of eggs in three baskets, if each basket contains
five dozen.

2. If a hectare of land can use 5.5 sacks of fertilizer to grow his crops, how
many sacks are needed for 2.5 hectares?

3. The table below shows the daily wage rate and the number of days
worked for ten farmworkers in the operation of the MAIS Organic Farms
for the month of June. Find the total amount earned (wage) by each
worker and their total earnings.

Farmworker Daily Rate Days Wage
Worked

Al P350.00 19.5

Ben 400.00 20

Carl 300.00 15.5

Den 400.00 20.5

Edd 350.00 24

Fred 450.00 19.5

Greg 375.00 24

Hanz 400.00 21

Ian 425.00 15.5

Jeff 500.00 24

TOTAL

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ANSWER KEY 3.2-1c

I. PRACTICAL EXERCISES

1. 180 eggs
2. 13.75 sacks

3. Wage
Farmworker Daily Rate Days
Worked P6,825.00
8,000.00
Al P350.00 19.5 4,650.00
8,200.00
Ben 400.00 20 8,400.00
8,775.00
Carl 300.00 15.5 9,000.00
8,400.00
Den 400.00 20.5 6,587.50

Edd 350.00 24 12,000.00
P80,837.50
Fred 450.00 19.5

Greg 375.00 24

Hanz 400.00 21

Ian 425.00 15.5

Jeff 500.00 24

TOTAL

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INFORMATION SHEET 3.2-1d
DIVISION OF WHOLE NUMBERS AND

DECIMALS Learning Objectives:

After reading this Information Sheet, the trainee must be able to: 1. perform
calculations involving division of whole numbers and decimals; and 2. apply
the operation in solving related problems in everyday life.

INTRODUCTION
“A success of one is a success of all”. This is a famous adage of a democratic

society where people work for the betterment of an organization. A good leader shares
responsibility to every member of the team in achieving a common goal. In other
words, there is division of labor. Everyone exercises his/her own talents and skills-
potentials toward the attainment of organizational objectives. The distribution of
responsibility to every member of the team requires the skill in division.

FUNDAMENTAL OPERATION: DIVISION

Division is the process of determining the number of times a number or
quantity is contained in another similar number or quantity. It can be thought of as
repeated subtraction. It is the inverse of multiplication. The number that contains
another number (number to be divided) is the dividend and the number contained in
it (number that divides) is the divisor. The number of times a divisor is contained in
the dividend is called the quotient. Division is usually exact, but if it is not, the
quotient has a left-over called remainder.

There are several cases to be considered in dividing whole numbers and
decimals. Study the examples below on how division of whole numbers and decimals
are done.

CASE I: Dividing a whole number by a whole number.

Example: Divide 144 by 6

Solution 1: Check:
4 - quotient 36 - divisor

36 │144 - dividend x 36 - quotient divisor 144 144 - dividend 0

Solution 2: 144 – 36 = 108; 108 -36 = 72; 72 – 36 = 36; 36 – 36 = 0

1234

It took 4 steps of subtracting 36 from 144 to reach zero, so 144 ÷ 36 = 4.

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CASE II: Dividing a decimal by a whole number

Example: 4.2012 ÷ 16

Solution: Check:

16│4.201 x 16 0.262 0.262 – (3 decimal places)

3 2 1572 96 4192
100 262 41 + 9

32 4.201
9 point-off 3 decimal places

from the right

RULE: To divide a whole number or a decimal number by a whole number, perform the
following steps:

1. Consider a partial dividend which contains the divisor.
2. Determine the number of times the divisor is contained in the partial dividend. 3.
Write the answer in the appropriate space.
4. Subtract the number of times the divisor is contained in the partial dividend

from the partial dividend.
5. Form another partial dividend with the remainder (if any) by bringing down the next

digit of the dividend.

6. Repeat the process until the quotient is obtained.

CASE III: Dividing a whole number by a decimal number
Example: 8250 ÷ 0.25

Solution: 33000 Check: 75 x 0.25 (2 decimal places)
0.25│825000 33000 75 165000

00 point-off 2 decimal 00 places from the right 75 66000
00 00 8250.00
00

00
0

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CASE IV: Dividing a decimal number by a decimal number

Example: 0.1496 ÷ 2.9

Solution: Check: 0.051 0.051
^ ^ 1 45 459 46 102 2.9│.1496 29│1.496 x 29

29 1479
17 + 17

1.496

RULE: To divide whole numbers or decimal numbers by a decimal number:

1. Make the decimal divisor a whole number by moving the decimal point to the
right.
2. Move the decimal point of the dividends as many places as was done in the
divisor or annex as many zeros if the dividend is a whole number.

3. Follow the rule for dividing numbers by whole numbers.

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SELF-CHECK 3.2-1d

I. FIND THE QUOTIENT AND CHECK
1. 6804 ÷ 14 4. 4161 ÷ 0.015
2. 51038 divided by 107 5. 1.38│90542
3. 0.34│19.8662

II. PRACTICAL EXERCISES
Direction: Solve the following problems.

1. Complete the table below. (Divide the total cost by the quantity)

Quantity Items Unit Cost Total Cost

2 pks Ampalaya seeds, 20g P234.50

2 pcs Hand trowel 375.00
3 dozen Pencil 324.00
3 dozen Ballpen 990.00
Insecticides, 50ml 1,500.00
4 btls Nylon string 1,050.00
2 rolls Potatoes 157.50
3.5 kls

2. Mr. Gacula paid six thousand eight hundred fifty pesos for the hired
tractor to plow a hectare of land for planting. What is the rate per
square meter?

3. The people of Sitio Filipinas organized a drive to raise money to build a
reading center. Each contribution to the fund was called “hollow block
for the center”. A donation of P15 was asked for each “hollow block”.
The drive yielded P76,500. How many contributions were received?

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ANSWER KEY 3.2-1d

I. FIND THE QUOTIENT AND CHECK

1. 486

2. 476 r. 106
3. 58.43
4. 277400
5. 65610 r. 20

II. PRACTICAL EXERCISES

1. Items Unit Cost Total Cost
Quantity P117.25 P234.50
187.50 375.00
2 pks Ampalaya seeds, 20g 9.00 324.00

2 pcs Hand trowel

3 dozen Pencil

3 dozen Ballpen 27.50 990.00
4 btls Insecticides, 50ml 375.00 1,500.00
2 rolls Nylon string 525.00 1,050.00
3.5 kls Potatoes
45.00 157.50

2. P0.685/sq.m 1hectare = 10,000 sq.m

3. 5,100 hollow blocks(contributions)

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INFORMATION SHEET 3.2-2
FUNDAMENTAL OPERATIONS INVOLVING

FRACTIONS Learning Objectives:

After reading this Information Sheet, the trainee must be able
to: 1. define fraction operationally;
2. distinguish the types of fraction;
3. convert fractions to other forms;
4. perform calculations involving fractions; and
5. apply the operation in solving related problems in everyday life.

INTRODUCTION

Everybody wants to have a happy and satisfied life. Simple and healthy living
is enough that all basic necessities in life are complete: food, clothing, shelter,
sanitation, education, and healthcare are provided. Despite the meager income and
resources of the family, wise planning and budgeting is essential to ensure that a
part
of the whole income is allotted to every consumption including savings for security
reasons. This good practice of management employs the concept of fraction in order
to plan wisely our daily budget for family expenditures.

The number tree shows that fraction is rational number that can be expressed
as the ratio of two integers, a/b where b is not equal (≠) to zero, may be written in
many forms. It may be as fraction (3/2), a mixed number (1½), a decimal (1.5) or a
percent (150%). A rational number, since it is a ratio, may be thought as division
problem a ÷ b where, a is the dividend or numerator and b is the divisor or
denominator.

CONCEPT OF FRACTION
A fraction is a part of a whole. It is an ordered pair of whole numbers

expressed as numerator and denominator separated by fraction line or fraction bar,
a/b, where b ≠ 0. The denominator indicates into how many equal parts is the whole
divided while the numerator tells how many are “considered”.

Figure 1, is a picture of a pie divided into four equal parts.
One part of it is equal to one-fourth or ¼, so that 4-one fourths
makes one whole.

So, 1/4 is a fraction where, 1 - numerator Figure1. Pie
4 - denominator
fraction line/bar

When the numerator is lower than its denominator, the fraction is called
proper fraction. But if the numerator is higher than the denominator, it is called
improper fraction. However, if it is a combination of a whole number and proper
fraction then it is called mixed numbers.

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RENAMING FRACTIONS

Fractions different in form which name the same rational number are called
equivalent fractions. Two fractions a/b and c/d are equal if a * d = b * c.

Let us consider a=1, b=2, c=3, d=6 so that a/b = 1/2 and c/d =
3/6. So, if a * d = b * c then 1 x 6 = 2 x 3 therefore 6 = 6. This
means that the two fractions 1/2 and 3/6 are equivalent fractions.

Renaming fraction means changing the fractions to its equivalent (a) lowest
terms, (b) lower terms, (c) higher terms, (d) mixed number or improper fraction, and
(e) decimals.

A. Any fraction can be reduced to its lowest terms by:
1. Successive Division
2. Greatest Common Factor (GCF)

Example: Express 24/56 in lowest term.

1. Successive Division
24 ÷ 4 = 6 ÷ 2 = 3
56 ÷ 4 14 ÷ 2 7

2. Greatest Common Factor (GCF)

Factors of 24 (F24) = 2,3,4,8,12,24
Factors of 56 (F56) = 2,7,8,14,56 therefore, the GCF is 8.

24 ÷ 8 = 3
56 ÷ 8 7

B. A fraction can also be raised to a higher term by multiplying both numerator
and denominator by the same number.

Example 1: Raise 2/3 to the twelfths

Solution: 2 x 4 = 8
3 x 4 12

Example 2: Raise 4/7 to the twenty-first

Solution: 4 x 3 = 12
7 x 3 21

C. Mixed numbers are converted to improper fractions by multiplying the whole
number by the denominator plus the numerator of the improper fraction. For
the denominator of the improper fraction, copy the same denominator.

Example: Change 2 5/6 to an improper fraction

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Solution: Multiply 2 by 6 and add 5

666 5 = 2 x 6 + 5 = 17
2

D. An improper fraction is converted to a mixed number by dividing its numerator
by its denominator.

Example: Change 8/5 to a mixed number

Solution: Divide 8 by 3 hence, 8/5 = 1 3/5.

1
5│8

5
3

E. When renaming fractions to decimals:

1. For a fraction whose denominator is a factor of a power of 10

Example: 2 = 2 x 2 = 4 = 0.4
5 5 x 2 10

2. For a fraction whose denominator is a multiple of a power of 10.

Example: 6 ÷ 3 = 2 = 0.2
30 ÷ 3 10

3. When the fraction is not basic and its denominator cannot be easily
changed to a power of 10, the indicate division must be performed to get
the decimal representation.

0.875 – terminating decimal
Case I. Example: 7/8 Solution: 8│7.000

64

60
56

40
40
0

0.666 2/3 or 0.666…

Case II. Example: 2/3 Solution: 3│2.000
68
20 18 Nonterminating decimal

20 18 2

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ADDITION AND SUBTRACTION OF FRACTIONS

Just like in the addition of whole numbers and decimals, only similar or like
fractions like 1/12, 3/12 and 5/12 may be added directly. Unlike or dissimilar
fractions like ½ , ¼, and ⅛ may, however, be converted/renamed to similar
fractions.

Example 1: 1/2 + 3/2 + 5/2 = ______

Solution: 1 + 3 + 5 = 1+3+5 = 9 or 3
12 12 12 12 12 4

Example 2: Find the sum of ½, ¼ , and ⅛.

Solution: Find for the least common multiple (LCM) of the denominators
Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16
Multiples of 4 = 4, 8, 12, 16
Multiples of 8 = 8, 16, 24

So, the LCM = 8 (least/lowest)

1=4
28

+1=2=4+2+1=7
4888

1=1
88

Example 3: 4/5 – 1/5

Solution: 4/5 – 1/5 = 4 – 1 = 3
55

Example 4: 3/4 – 1/2

Solution: 3/4 – 1/2 = 6 – 4 = 2 or 1
884

RULE:
When adding/subtracting fractions of the same denominator,

add the numerators and copy the common denominator.

When adding/subtracting unlike/dissimilar fractions, express
as similar fractions then proceed as in addition/subtraction of
like fractions.

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MULTIPLICATION OF FRACTIONS

Multiplication of fractions is much easier than the process of addition or
subtraction. Simply, multiply the numerators to get the resulting numerator. And
the denominators are also multiplied together to get the resulting denominator.
Consider these examples:

Example 1: 2/3 x 1/5 = 2 x 1 = 2
3 x 5 15

Example 2 : 1/2 x 3/4 x 2/3 = 1 x 2 x 3 = 6 or 1
2 x 4 x 3 24 4

Example 3 : a c = ac
b d bd

DIVISION OF FRACTIONS

In our previous discussion, division is the inverse process of multiplication.
So, in dividing a fraction by another fraction, invert the divisor and multiply.
Inverting the divisor means getting the reciprocal of the divisor. Look at the
examples below.

Example 1: 3/8 ÷ 2/5

Solution: 3 ÷ 2 = 3 x 5 = 15
8 5 8 2 16

Example 2: 5 ½ ÷ 2 ¾

Solution: 5 ½ ÷ 2 ¾ = 11 ÷ 11 = 11 x 4 = 44 or 2
2 4 2 11 22

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SELF-CHECK 3.2-2

I. Perform what is required in every item. Express answer in lowest
term.
1. 5/9 + 3/9 + 4/9 = ___________________
2. 8 ¼ + 4 ½ + 1⅜ = ____________________
3. 15/21 – 3/7 = _____________________
4. 15 ⅞ - 6⅜ = ______________________
5. 1 ¼ x 1 ½ x 1 ⅝ = __________________
6. 5/8 of 128 = ______________________
7. 25 divided by 1/5 = ________________
8. 11/15 ÷ 2/3 = ____________________

II. PRACTICAL EXERCISES
Solve the following problems. Express your answer in lowest term.
1. The farm that Mr. Mamuad owned is shaped irregularly. One side
measured 85 2/5 meters, the second side is 98 3/10 meters, the third
side is 121 1/4 meters and the remaining side measures 105 1/2
meters. How many meters of barbed wire would be enough to fence the

farm three times around?

2. Jansen has a sack of fertilizer weighing 60 kilograms. He has to use 1/3
kilogram of fertilizer for 5 fruit trees in his farm. How many trees will
be fertilized per sack?

3. A farmer has 12 hectares of land. He planted half of it with tomatoes, ¼
of it is garlic. What part of his land can be planted with other crops?
How many hectares can be planted with other crops?

4. Joe takes 1 ½ hours to clean a field while Pedro takes2 ¼ hours in the
same field. How much longer does it take Pedro to clean the field?

5. Mayla has 20 piglets and each piglet consumes ¼ kilo of feeds per day.
How many of kilos of feeds will the piglets consume in a day? In a
month?

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ANSWER KEY 3.2-2

I. 1. 12/9 or 1 1/3
2. 14 1/8
3. 2/7
4. 9 5/8
5. 3 3/64
6. 80
7. 125
8. 11/10 or 1 1/10

II. PRACTICAL EXERCISE

1. 1231 7/20

2. 15 trees

3. 1/6; 2 hectares

4. ¾ hour

5. 5 kilos/day; 150 kilos/month

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INFORMATION SHEET 3.2-3
PERCENTAGE

Learning Objectives:
After reading this Information Sheet, the trainee must be able
to: 1. define percent;
2. describe the relationship that exist among fraction, decimal and percent;
3. solve problems involving percent; and
4. apply the concept in everyday life situations.

INTRODUCTION
The concept of percentage is always applied in business and commerce.

Persons who buy and sell usually charge a certain percent of the goods bought or
sold. Profits are also expressed in terms of percent. Government employees pay for
their taxes at a certain percentage of the monthly income. Return of investment,
which is one of the indicators in the evaluation of a business is also measured in
term of percent. Therefore, it necessary for students to learn the concept of percent.

CONCEPT OF PERCENT
Per cent comes from the Latin word per centum meaning “part of a hundred”

or “by the hundred” or “for every hundred” in symbol “%”. Thus n% = n/100 = 0.01n
= n (1/100).

Percent, decimal and fraction are only different ways of naming the same
rational number. There exists a relationship among them. Let us consider the
following examples:

Example 1: 1% = 1/100 = 0.01
Example 2: 50% = 50/100 or 1/2 = 0.50
Example 3: 0.2% = 0.2/100 = 2/1000 or 1/500 = 0.002
Example 4: 1.25% = 1.25/100 = 125/10000 or 1/8 = 0.0125
Example 5: 1 = 1 x 100% = 100%
Example 6: 0.3 = 03 x 100% = 30%
Example 7: 2.15 = 2.15 x 100% = 215%
Example 8; 4/5 = 80/100 = 0.80 x 100% = 80%

Example 9: 3 ½ = 3.50 or 350%

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RULE:
To change percent to fraction or decimal, divide the
number of percent by 100 and omit the sign of percent.

To change whole numbers, decimal or fractions to
percent, multiply them by 100%.

PERCENTAGE PROBLEMS

In dealing with percent problems, there are three quantities involved. These
are the whole, the part, and the percent. The whole or standard basis of comparison
is called base, the percent of the number of hundredth is called rate, the fractional
part of the whole is called the percentage. Consider the examples below:

a. Finding the Percentage

Example 1: 15% of P100 = P15

Rate(R) Base(B) Percentage(P)

Solution:
Given: R = 15% = 0.15 Find: P
B = P100

Formula: Percentage = Base x Rate

P=BxR
P = P100 x 0.15 = P15

Example 2: What is 2/5 of 60?
Solution:

Given: R = 2/5 Find: P
B = 60

P=BxR
P = 2 x 60 = 120 = 24
55

b. Finding the Base

Example 3: P150 is 60% of what amount?
Solution:

Given: P = 150 Find: B
R = 60% = 0.60

Formula: B = P/R
B = 150/0.60 = P250

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Example 4: 25% of what number is 14?
Solution:

Given: P = 14 Find: B
R = 25% = 0.25

B = P/R
B = 14/0.25 = 56

c. Finding the Rate

Example 5: What percent of 70 is 35?
Solution:

Given: B = 70 Find: R
P = 35

Formula: R = P/B
R = 35/70 = ½ or 0.50 or 50%

Example 6: 15 is what part of 75?
Solution:

Given: B = 75 Find: R
P = 15

R = P/B
R = 15/75 = 2/3

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SELF-CHECK 3.2-3

I. Complete the table below:

Percent Fraction Decimal
45% 3/5 0.75

250% 0.12 ½
22 ½%

II. Find the unknown in each of the following:

1. What is 3/8 of 400?
2. P260 is 13% of what amount?
3. 1/5 of what amount is P60?
4. P101 is 3/5 of what amount?

III. PRACTICAL EXERCISES
Solve the following problems:

1. Jeff has completed 95% of the components that make up his project. If
the project has 35 components, how many more are left to be
completed?

2. If 32 grams of pure sugar is mixed with 48 grams of pure starch, what
percent by mass of the resulting mixture is sugar?

3. Sixty-two and one-half percent of a number is 3 less than 75% of the
number. What is the number?

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ANSWER KEY 3.2-3

I. Complete the table below:

Percent Fraction Decimal
0.45
45% 9/20 0.75

75% 3/4

60% 3/5 0.60
12 ½ % 1/8 0.12 ½
25
250% 9/40 2.5
22 ½% 0.225

II. Find the unknown in each of the following:

1. 150
2. P2000
3. P300
4. P168 1/3 or P168.33

III. PRACTICAL EXERCISES

1. 1.75 or 1¾
2. 40%
3. 24

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INFORMATION SHEET 3.2-4
RATIO AND PROPORTION

Learning Objectives:
After reading this Information Sheet, the trainee must be able to:
1. differentiate ratio and proportion;
2. distinguish the parts;
3. solve problems involving ratio and proportion; and
4. apply the concept in everyday life situations.

INTRODUCTION

Real life applications of ratio and proportion are numerous! The concept
occurs in many places in mathematics. When preparing recipes in the kitchen,
painting a house, or even repairing gears in a large machine or in car transmission,
you use ratio and proportion. Say a recipe to make brownie requires 4 cups of flour
for 6 people. You may want to know how much flour to put for 24 people. So, when
we wat to express a relationship between two similar quantities, we use ratio.

BASIC PRINCIPLES OF RATIO

Ratio is the comparison of two numbers or quantities as a quotient. The two
numbers in a ratio are called its terms in the same way that the numerator and
denominator of a fraction are called terms of the fraction. Thus, a ratio may be
written in fraction form. Let say, “15 boys in a class of 25, 10 days in a month, and 4
out of 10” involve ratio. In the ratios,

15:25 (read as 15 is to 25)
10:30 (read as 10 is to 30)
4:10 (read as 4 is to 10);

15, 10, and 4 are the antecedents and 25, 30 and 10 are called the
consequents. Thus, we say that the ratio of the number a to a number b, where b is
not equal to zero is a/b or a:b.

Example 1: There are 20 males and 23 females enrolled in the ACP-NC3 class.
What is the ratio of the males to the females in the class? females
to males? males to the whole class? females to the whole class?

Solution: 20 males is to 23 females or 20:23
23 females is to 20 males or 23:20
20 males is to 43 or 20:40

23 females is to 43 or 23:40

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When the terms of the ratio are mixed numbers, they are simplified in the
same way as fractions are simplified.

Example 2: Simplify the ratio 2 ¼ to 3 ½.

Solution: 2 ¼ : 3 ½ = 9/4 ÷ 7/2
= 9/4 x 2/7
=9x2
4x7
= 18/28 = 9/14 or 9:14

Ratio is also express as rate. Rate is the comparison of two quantities which
have different units. It is written also as a fraction.

Example 3: It takes 40 minutes for a car to travel 30 kilometers. What is the
rate?

Solution:
30 km ÷ 40 minutes = 0.75 km/min

PROPORTIONS

When two ratios are equal, then there is a proportion. Thus, a proportion has
four terms.

means

Example 1: 1/2 = 3/6 or 1 : 2 = 3 : 6

extremes

Solution: 1 x 6 = 2 x 3
6=6

The first and last terms (1 and 6) are called extremes, while the second and
third terms (2 and 3) are called means of the proportion. The product of the extremes
and the product of the means are equal. This is the principle of proportion. So, with
use of this principle, we can also find any missing term of a proportion.

Example 2: 4 : 8 = x : 120
Solution: 4 = x

8 120

By cross multiplication, the two ratios are written as fractions. The top
part of one ratio is then multiplied with the bottom part of the other.

4x
8 120

8x = 480
x = 60

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SELF-CHECK 3.2-4

I. Simplify the following ratios:
1. 18 months to 2 years
2. 21 to 14
3. 1 ½ to 2 ¼

II. Find the missing terms of the following proportions:
1. x/10 = 12/20
2. 3/8 = 9/x

3. 1 ¼ = 4
x 2½

III. PRACTICAL EXERCISES
Solve the following problems:

1. Mj harvested 50 cavans of rice during the main crop season while his
cousin, Cj has 75 cavans. What is the ratio of Mj’s harvest to CJ?

2. Live chicken costs P133.00 a kilo. How much will a chicken weighing 2
1/3 kilos cost?

3. Determine the fertilizer ratio for a recommendation of 1.5lbs of nitrogen,
0.5lb of phosphate, and 0.5lb of potash. (Use the nutrient with the
lowest weight as divisor.)

4. In a bag of red and green sweets, the ratio of red sweets to green sweets
is 3:4. If the bag contains 120 green sweets, how many red sweets are
there?

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ANSWER KEY 3.2-4

I. Simplify the following ratios:
1. 3:4
2. 3:2
3. 2:3

II. Find the missing terms of the following proportions:
1. 6
2. 24
3. 25/32

III. PRACTICAL EXERCISES
1. 2:3
2. P310 1/3 or P310.33

3. 3:1:1

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INFORMATION SHEET 3.2-5
MEASUREMENTS

Learning Objectives:

After reading this Information Sheet, the trainee must be able
to: 1. define measurement operationally;
2. differentiate the systems of measurement;
3. identify the prefixes of measurement and give its meaning;
4. covert one unit of measure to another unit; and
5. solve problems involving measurements.

INTRODUCTION
Ancient people used units of measure that were based on parts of the human

body. These cannot be considered standard units because they vary from person to
person.

Today accurate measurements play an important role in different vocations
and professions. Carpenters measure the wood they use in building houses;
dressmakers measure the cloth they sew; mothers measure the amount of milk for
their children; scientists measure physical quantities involved in their experimental
works; and farmers measure the mixture of fertilizers for their plants as well as feed
ration for animal production.

MEASUREMENT

Measurement is the comparison between an unknown quantity, capacity or
dimension of a unit of measure. It consists of two parts: a number and the standard
being used (standard unit).

Example:

5 meters → 5 m

There are two systems of units commonly used that carry different
standardized units:

1. Metric System – developed in France and being used in daily life. It has the
advantage of having decimal basis thus, simplifying conversions and
calculations. This was officially named and known worldwide as the