BUSINESS MATHEMATICS
QUARTER 1 - MODULE 3
Learning Outcome(s): At the end of the lesson, the learner is able to;
1. Divide fraction by another fraction, divide whole numbers by fraction, divide mixed numbers by mixed number; and
2. Apply knowledge of division of fraction to business problems.
3. Express fraction to decimal, convert fraction to percent, change decimal to fraction, express decimal to percent, convert
percent to decimal, change percent to fraction; and
Changing Fraction to Decimal and Percent and Vice Versa
Changing Fraction to Decimal and Percent and Vice Versa
To facilitate computation in business, we usually convert fraction to decimal, fraction to percent, decimal to fraction, or percent to fraction. For
example, if the net profit of a partnership is ₱ 40 000.00 and you, as a partner, share 25% in said profit, it would be easier to change the 25% to fraction
1 1 1 25
because 25% is and of ₱ 40 000.00 is ₱ 10 000.00. It is easier to divide the ₱ 40 000.00 by 4 (multiply it by ) than multiply it by 25% or
4 4 4 100
or 0.25.
Converting Fraction to Decimal
We said that the line separating the numerator and the denominator of a fraction indicates division. The denominator is the divisor and the
3
numerator is the dividend. To reduce fractions into decimal, we simply perform division. If we want to change into decimal, we divide 3 by 4:
4
3
.75 Therefore, = 0.75
4
4 ) 3.00
- 28
20
- 20
0
Other Examples:
5
0.625 1. = 8 ¿ 5.000 = 0.625
8
-4 8
20
- 16
40
-40
0
.8
4
1. = 5 ) 4.0 = 0.8
5
-4.0
0
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. =1÷ 2=0.5=50 %
2
5
2. =5÷ 12=0.41666=41.67 %
12
8
3. =8 ÷ 11=0.72727=72.73 %
11
Converting Decimal to Fraction
We previously defined decimals as parts of units divided into any power of 10. We said that 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 in multiples of 10
(10, 100, 1000, etc.) and reduce the said fraction to lowest terms. For example:
75
1. 0.75 = 0.75 has two decimal places. Our denominator has to have two zeros; hence, 100. We divide 75 by 25
100
75÷ 25 3
= = (HCF or highest common factor) and we get 3 and we divide 100 by 25 and get 4; the final answer is
100÷ 25 4
3
.
4
375 375
2. 0.375 = 375 has 3 decimal places. Our denominator should have 3 zeros; hence, 1 000. Reducing to lowest
1000 1000
terms,
375÷ 125 3 3
= = we divide 375 by 125 (HCF) to arrive 3; we divide 1000 by 125 to arrive 8; hence, our answer is .
1000÷ 125 8 8
286
3. .0286 = 0.0286 has 4 decimal places. Our denominator should have 4 zeros; hence 10000. The only common
10000
286÷ 2 143
= = denominator or the only number that can exactly divide 286 and 10 000 is 2. If we divide by 2, we
10000÷ 2 5000
143
reduce our fraction to .
5000
143
In cases like (3) above, we cannot reduce any further because there is no other umber that can divide both the numerator and the denominator
5000
exactly. Converting decimal to fraction is usually done to those that we can convert to smaller fraction.
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. 0.75 = 75% 3. 1.25 = 125% 5. 33.38 = 3 338%
2. 0. 0065 = .65% 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 sign (%). This is
exactly the opposite of what we did when we converted decimal to percent.
Examples:
1. 45% = .45 3. 3% = 0.03 5. 23.56% = .2356
2. 100% = 1 4. 250% = 2.5 6. 150.5% = 1.505
Converting Percent to Fraction
To convert percent to fraction, we first change the percent to decimal, then change the decimal to fraction and reduce to lowest terms.
Examples:
14 7 125 5 1
1. 14% = 0.14 == 3. 125% = 1.25 = = =1 5. 0.375% = 0.00375 =
100 50 100 4 4
375 75 3
= =
100 000 20 000 800
5 1 50 1
2. .5% = 0.005 = = 4. 50% = 0.50 = =
1000 200 100 2
As seen in examples (a), (c), and (d), if we are to convert percent involving whole numbers (no decimal parts), we can omit the part changing the same
to decimal; we can immediately change the percent sign (%) to /100 and change to lowest terms.
Thus:
14 7 125 5 1 50 1
1. 14% = = 2. 125% = = =1 3. 50% = =
100 50 100 4 4 100 2
.
BUSINESS MATHEMATICS
QUARTER 1 - MODULE 3
Name:_____________________________________Grade Level & Strand:_________
Teacher’s Name:_____________________________________________________
Evaluation
A. Change the following fractions to decimal.
5 4 25 27 2091
1. = 2. = 3. = 4. = 5.
8 5 100 1000 10
=
B. Change the following decimals to fraction, renaming in simplest form.
1. 0.16 = 2. 0.27 = 3. 0.175=
C. Change the following fractions to percent.
100 20 6
1. = 2. = 3. =
180 50 25
D. Change the following percent to fraction.
1. 28% = 2. 1%= 3. 0.05%=
E. Change the following decimals to percent.
1. 0.75= 2. 0.16 = 3. 0.25= 5. 0.38=
F. Change the following percent to decimal.
1. 75%= 2. 30%= 3. 15%=
