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BUSINESS
MATHEMATICS
Quarter 3- Module 1:
Fractions, Decimals, Percent
Ratio and Proportion
Buying and Selling

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reviewed by educators from public and private schools, colleges, and
universities. We encourage teachers and other education stake
holders to email their feedback, comments, and recommendations to
the Department of Education at action @deped.gov.ph

We value your feedback and recommendations.

Department of Education ● Republic of the Philippines

 TABLE OF CONTENTS
What This Module is About …………………………………..…………………............i
What I Need to Know ………………………………………..……………............ii
General Instruction ……………………………………………...………………ii
Icons of this Module ……………………………………………………....……..iii
What I Know …………………………………………………………......iv
Lesson 1:
Conversion of Fraction to Decimal, Percent and Vice Versa
What’s In ………………………………….………………………….1
What’s New …………………………………….………………………..1
What is It ……………………………………….…………………….2
What’s More ………………………………………….…………………..4
What I have Learned …………………………………………….…………….5
What I can do ……………………………………………………………...6
Additional Activity ………………………………………………………….……..7
Lesson 2:
Ratio and Proportion
What’s In ………………………………….………………………….8
What’s New …………………………………….………………………..8
What is It ……………………………………….…………………….9
What’s More ………………………………………….………………….14
What I have Learned …………………………………………….……………15
What I can do ……………………………………………………………..16
Additional Activity ………………………………………………………….……16
Lesson 3:
Buying and Selling
What’s In ………………………………………………………………17
What’s New ……………………………………………………………….17
What is It ………………………………………………………………18
What’s More ……………………………………………………………….22
What I have Learned ……………………………………………………………22
What I can do ……………………………………………………………….23
Additional Activity ………………………………………………………………23
Assessment…………………………………………………………………………...24
 What I Need to Know

After reading this module, you are expected to:

1. express Fractions into decimal and percent and vice versa;
2. solve problems involving fractions, decimals, and percent;
3. identify the different kinds of proportions and write examples of real-life
situations;
4. solve Problems involving direct, inverse, and partitive proportion;
5. differentiate Mark-on, Mark down and Mark-up obtain Mark-on, Mark-down,
and Mark-up given price of a product;
6. differentiate mark-up from margins;
7. describe how gross margins is used in sales; and
8. compute single trade discounts and discount series.

General Instruction:

1. Read every detail in this module with comprehension.

2. Answer the activities diligently and intelligently.
3. Be mindful of the deadlines set. Submit activities and exercises on time.
4. Be responsible of this module, do not crumple or write anything.
5. Be honest at all times in answering the activities and assessments in this
module.

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 What I Know

Choose the best answer from the options provided in each number.
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1. What is 35 in percent?

a) 22.14% b) 22.86% c) 23.28% d) 23.50%

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2. What is 50 express in decimal?

a) 0.38 b) 0.48 c) 0.58 d) 0.28

3. Express 3.75 into Fraction.
3 1 3 1
a) 3 4 b) 3 4 c) 4 4 d) 4 4

4. 105% can be expressed in fraction as.

5 1 1 1
a) 2 100 b) 1 25 c) 1 20 d) 5 100

5. What is 3.75 into percent?

a) 0.375% b) 375% c) 0.0375% d) 3750%
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6. Convert 12 2 % into decimal.

a) 0.125 b) 12.5 c) 1.25 d) 0.0125

7. A poll taken in a certain subdivision on the operation of the Bataan Nuclear
Power Plant showed 235 citizens voting “No” and 47 citizens voting “Yes”.
What is the ratio of the No votes against the Yes votes?
a) 5:1 b) 2:5 c) 1:6 d) 5:3
8. In a certain City, 2,000 families owned cars, 3,000 families owned jeepneys,
and 500 do not own any automobile. What is the ratio among them?
a) 5:1:6 b) 2:5:1 c) 1:6:2 d) 4:6:1
9. Linda uses 2 eggs for every 3 cups of flour in her cupcakes. If she uses a
dozen eggs, how many cups of flour will she need?
a) 16 b) 26 c) 18 d) 40
10. A recipe has 10 cups of flour for every 4 cups of sugar. If you want to make a
recipe using 8 cups of flour, how much sugar does one use?
a) 1.5 cups b) 1.3 cups c) 3.2 cups d) 4.2 cups
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11. A syrup is made by dissolving 2 cups of sugar in 3 cups of boiling water. How
many cups of sugar should be used for 2 cups of boiling water?
a) 6 cups b) 4.3 cups c) 5.2 cups d) 6.5 cups

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12. A school buys a gallon of juice for 50 kids. How many gallons do they need
for 75 kids?
a) 1 ½ gallons b) 2.3 gallons c) 4.3 gallons d) 3.5 gallons
13. An Acer laptop costs ₱22,700.00. The selling price is ₱33,650.00. What is
the rate of markup based on cost?
a) 47.78% b) 47.87% c) 48.24% d) 48.54%
14. What is the markdown rate if the cellphone is sold to ₱8,560.00 from
₱12,950.00 original price?
a) 51% b) 53% c) 55% d) 57%
15. The cost of a pair of shoes is ₱850.00; it is sold at 25% markup based on
cost. What is its gross margin?
a) ₱212.50 b) ₱1,062.50 c) ₱312.60 d) ₱1,052.12

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 Lesson FRACTIONS, DECIMALS,
AND PERCENTS
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What’s In

Fraction is part of a whole. It has 2 main parts, numerator and denominator. It

is separated by a vinculum which means division. Numerator tells how many parts
are taken from the whole, while the denominator tells the number of parts a whole is
divided into. When the numerator is lesser than the denominator, the fraction is
called proper fraction. If the numerator is greater than or equal to the denominator it
is called improper fraction. Improper fraction can be transformed into a mixed
number. You just have to divide the numerator by its denominator; the remainder will
be placed over the divisor or the denominator. Fractions can be converted into
decimals, and percent or the other way. These three are often used in our daily life
activities. Fraction is used in measuring mixtures. Decimals can be associated with
money. Percent is oftentimes used in business transactions.

What’s New

Activity1. Matching Fractions, Decimals and Percentages

Match the numbers below by drawing a line that will connect to its equivalent value.

0.8
0.6 2/5

12.5% 1/100

80% 1/400

0.0025 10%

1% 75/100

0.40 3/5

0.75 0.1
1/8

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 What is It

Converting Fraction to Decimal

You already learned that vinculum or the bar that separates the numerator
and the denominator indicates division. Therefore, in changing fraction to decimal we
simply divide the numerator by the denominator. Where, the denominator is the
divisor and the numerator is the dividend.

Example: (1)
7
Convert 9 into decimal. We divide 7 ÷ 9:
7
7 ÷ 9 = 0.7777 Therefore, = 0.7777
9

(2) (3)
2 2
= 2 ÷ 7 = 0. 2857 2) 5 = 2 ÷ 5 = 0. 4
7

Converting Fraction to Percent

To convert fractions to percent, we change the fraction into decimal (by
performing division) and move the decimal point two places to the right; then affix the
percent symbol (%).
Examples:
1
= 1 ÷ 8 = 0.125 = 𝟏𝟐. 𝟓%
8
7
= 7 ÷ 12 = 0.5833 = 𝟓𝟖. 𝟑𝟑% (𝑟𝑜𝑢𝑛𝑑 𝑜𝑓𝑓 )
12
3
= 3 ÷ 16 = 0.18.75 = 𝟏𝟖. 𝟕𝟓%
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Converting Decimal to Fraction

Decimals as parts of units divided into any power of 10. If a unit is divided into
10 parts, we have tenths; into 100 parts, we have hundredths; and so on. Therefore,
to change decimal to fraction, we convert a decimal to a fraction with a denominator

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in multiples of 10 (10, 100, 1000, etc.) and reduce the said fraction to lowest terms.

Example:
25 0.25 has two decimal places. Our denominator has to
1. 0.25 = 100
25 ÷ 25 have two zeros; hence, 100. We divide 25 by 25 (GCF or
100 ÷25 Greatest Common Factor) and we get 1 and we divide
𝟏 1
=𝟒 100 by 25 and get 4; hence the answer is 4

275 0.275 has 3 decimal places. Our denominator should have

2. 0.275 = 275
1 000
275 ÷ 25
3 zeros; hence, 1,000. Reducing 1 000 to the lowest term,
1 000 ÷25 we divide 275 by 25 (GCF) to arrive at 11; we divide 1,000
𝟏𝟏 11
= 𝟒𝟎 by 25 to arrive at 40; hence, our answer is 40
374 0.0374 has 4 decimal places. Our denominator should
3. 0.0374 = 10 000
374 ÷ 2 have 4 zeros; hence, 10 000. The only common
10 000 ÷2 denominator or the only number that can exactly divide
187
= 374 and 10 000 is 2. If we divide by 2, we reduce our
5 000 187
fractions to 5 000 .
Converting Decimal to Percent
To convert decimal to percent, we move the decimal point two places to the
right and affix the percent sign (%).

Examples:
1). 0.95 = 95% 3) 2.35 = 235% 5) 33.38 = 3338%
2). 0.0025 = .25% 4) 2 = 200% 6) 0.015 = 1.5%

Converting Percent to Decimal

To convert percent to decimal, we move the decimal point two places to the
left (as in dividing by 100) and we drop the percent (%). This is exactly the opposite
of what we did when we converted decimal to percent.
Examples:
65% = .65 3) 8% = 0.08 5) 33.46% = .3346
500% = 5 4) 656% = 6.56 6) 973.8% = 9.738

Converting Percent to Fraction

To convert percent to fraction, we first change percent to decimal, then
change the decimal to fraction and reduce to the lowest terms.

Examples:
24 6 875 35 7
1) 24% = 0.24 = = 25 5) 0.875%= 0.00875= = =
100 100,000 4,000 800
6 3
2) .6% = 0.006 = 1000 = 500

275 75 3
3) 275%= 2.75 = =2 =2
100 100 4

70 7
4) 70% = 0.70 = = 10
100

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 What’s More

Activity 1 Self- Assessment

Study the figures in column A and match its equivalent value in column B. Write
only the letter of the correct answer after each figure.

A B

1 13
1.)2 A. 2000

2.) 0.375 B. 0.0185

3.) 0.015 C. 0.0875

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4.) 6 4 % D. 50%

E. 150%
5.) 0.20
F. 7/8
6.) .08%
G. 3/8
7) 0.0065
27
8) 0.875 H. 400

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9) 8 % I. 1/ 1250
4
1
37 J.
10.) 2000 5

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K. 200

Activity2. Your Turn

1. Thirty- five out of sixty students preferred to eat their lunch at school rather
than going home during lunch break. Express the numbers in decimal.
2. A lessor is asking for 2/5 of the value of the condominium unit Stephanie
would be renting. How can this be written in percent form?

3. Tricia has travelled 0.75 km of the distance from her home to school. How
much has she travelled in fraction?
4. Only 0.60 of the students went to school during the first day of class. Express

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 in percent form.

5. Tristan got 7/8 of the questions correct in an employment examination for a

store manager. What is the decimal form of this fraction?

What I have Learned

Fractions can be converted to decimal by simply dividing numerator by its

denominator. Decimal can be transformed into fraction by putting denominators that
are multiple of 10,100,1000 and more. Always express the answer to the lowest
term. In converting decimal to percent, it can be done by moving two places to the
right and attach the percent symbol. Reversely, if percent will be changed to decimal,
move two places to the left and remove the percent symbol. Moreover, percent can
be changed to fraction by converting first to decimal and repeat the process on how
decimal is converted to fraction.

Reflective Question:
How can conversion of fraction, decimal, percent be used in business? Answer in
your own words based on what you have learned in this lesson.

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 What I Can Do

Activity 3 My Budget Plan

Interview someone from your household who manages the monthly budgeting plan.
Do what are asked below and write your output in your activity notebook.

1. Show the monthly budget in your household.

2. Enumerate the expenses incurred on a monthly basis with the corresponding
amount.
3. Beside the amount, express the numbers into decimal, percentage, and in
fraction.
4. Show your monthly household budget expenses by drawing a pie chart
indicating the portion of each expense.
5. Mention the biggest and the smallest portion of your household expenses.

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 Additional Activities

Complete the sentence below.

After doing the activities:
1. I noticed __________________________________________________

__________________________________________________________

__________________________________________________________
2. One question I have is _________________________________________

__________________________________________________________

__________________________________________________________
3. I’m not sure ________________________________________________

__________________________________________________________

__________________________________________________________
4. I realized ___________________________________________________

___________________________________________________________
___________________________________________________________