BUSINESS MATHEMATICS

QUARTER 1
FUNDAMENTAL OPERATIONS ON FRACTIONS, DECIMALS, AND PERCENTAGE

COURSE DESCRIPTION:
This course will provide an understanding of the basic concepts of mathematics as applied in business. It includes a review of the fundamental mathematics
operations using decimals, fractions, percent, ratio and proportion; mathematics concepts and skills in buying and selling, computing gross and net earnings, overtime and
business data presentation, analysis and interpretation. The use of computer and software applications for computation and data presentation is encouraged.
LEARNING OUTCOME(s): At the end of the lesson, the learner is able to;
1. demonstrate an understanding of fractions;
2. recall types of fractions as they have learned;
3. add and subtract similar fraction, dissimilar fraction and mixed fraction.

FRACTIONS
Fractions are expressed in mathematics as a number value that defines a part of a whole or group of objects. Fraction is a component or sector of
a given quantity taken from the whole, which might be a number, a specified value, or an item.
A fraction represents a part of the whole or group of objects. In a fraction, numerator (top number) and denominator (bottom number) are
separated by a horizontal bar known as the fractional bar. The denominator represents the number of equal parts the whole is divided into or total number
of objects in a group. The numerator represents the number of parts of the whole or the number of objects from the group is taken.
1
Let us better understand fractions with the help of an example. A chocolate bar is divided into four equal parts. Each part of the whole bar represents ,
4
1
which depicts 1 out of 4 equal parts. The fraction is read as ‘1 by 4’ or one-fourth.
4
Types of Fractions
Proper Fractions - These are fractions that express amounts which are less than a unit. As such, the numerator is always less than the
denominator.
1 1 3 2 5 11
Ex.
4 2 4 3 8 12
Improper Fractions - These are fractions that express amount which are equal to or greater than a unit. Hence, the numerator is either equal to or
greater than the denominator.
3 6 7 11 18
Ex.
3 5 4 6 11
These fractions can be reduced to whole numbers or to mixed fractions.
Mixed Fractions - it is a combination of a whole number and a proper fraction. These are also called mixed numbers.
1 3
Ex. 1 (read as “one and one-third”) 5 (read as “five and three-fourth”)
3 4
3 1
2 (read as “two and three-fifth”) 8 (read as “eight and one-fourth”)
5 4
Similar Fractions – These are fractions with the same denominators.
10 1 9 3 8 1 7 5 13 11
Ex. , , , , , , , ,
11 11 11 11 11 6 6 6 6 6
Dissimilar Fractions – These are fractions with different denominators.
1 1 2 5 11 3 6 7 11 18
Ex. , , , , , , , ,
4 2 3 8 12 3 5 4 6 11
Equivalent Fractions - Fractions that represent the same value after being simplified are called equivalent fractions. To get equivalent fractions we
can multiply or divide both the numerator and the denominator of the given fraction by the same number.
1 5 6 10 8 2 4 6 8 10
Ex. , , , , , , , ,
2 10 12 20 16 3 6 9 12 15
Operations on Fractions
Addition of Fractions
Adding Similar Fractions - The rules for adding and subtracting fractions with the same denominator are really simple and straightforward.
Here are the steps in adding fractions with the same denominator:
Step 1: Add the numerators of the given fractions.
Step 2: Keep the denominator the same.
Step 3: Simplify.
a b a+b
+ = … where c ≠ 0.
c c c
1 2 1+2 3 1 3 1+ 3 4 1
Ex. 1. + = = 2. + = = =¿
4 4 4 4 8 8 8 8 2
Adding Dissimilar Fractions - Addition and subtraction of fractions with unlike denominators can be a little bit tricky since the denominators are not
the same. So, we need to first convert the unlike fractions into like fractions.
We can make the denominators the same by finding the Least Common Multiple (LCM) of the two denominators. Once we calculate the
LCM, we multiply both the numerator and the denominator with an appropriate number so that we get the LCM value in the denominator.
3 3
Ex. +
5 2
Step 1: Find the LCM (Least Common Multiple) of the two denominators.
The LCM of 5 and 2 is 10.
Step 2: Convert both the fractions into like fractions by making the denominators same.
3× 2 6
=
5× 2 10
3× 5 15
=
2× 5 10
Step 3: Add the numerators. The denominator stays the same.
6 15 21
+ =
10 10 10
Step 4: Convert the resultant fraction to its simplest form if the GCF if the numerator and denominator is not 1.
 21
The fraction
is already in its simplest form.
10
3 3 21
Thus, + =
5 2 10
Subtraction of Fractions
Subtracting Similar Fractions
Here are the steps to subtract fractions with the same denominator:
Step 1: Subtract the numerators of the given fractions.
Step 2: Keep the denominator the same.
Step 3: Simplify.
a b a−b
− = … where c ≠ 0
c c c
4 1 4−1 3 1
Ex. 1. − = = = .
6 6 6 6 2
Subtracting Dissimilar Fractions
Let’s learn how to subtract fractions when denominators are not the same. To subtract unlike fractions, we use the LCM method.
5 2
Ex. −
6 9
Step 1: Find the LCM of the two denominators.
LCM of 6 and
Step 2: Convert both the fractions into like fractions by making the denominators same.
5 ×3 15
=
6 ×3 18

2× 2 4
=
9 ×2 18
Step 3: Subtract the numerators. The denominator stays the same.
15 4 11
− =
18 18 18
Step 4: Convert the resultant fraction to its simplest form if the GCF of the numerator and denominator is not 1.
15 4 11
Thus, − =
18 18 18
Addition of Mixed Fractions
1 3 1 1
A mixed fraction is a whole number and a fraction. 1 , 2 , 15 , and 10 are mixed fractions. To add mixed fractions, we have two methods:
2 4 6 8
First Method:
To add mixed numbers, add the whole numbers then add the fractional parts:

1. 2
1
2
+5
1
3
= (2 + 5) +
( 12 + 38 ) = 7+
( 4 +88 ) = 7+
7
8
= 7
7
8
Second Method: Another method of adding mixed numbers is to change the mixed numbers into improper fractions and then add:
1 3
1. 2 +5
2 8
5 43
= +
2 8
20+43
=
8
63
=
8
7
=7
8
1 5 2
2. 3 +6 +1
4 8 5
13 53 7
= + +
4 8 5
130+265+56
=
40
451
=
40
11
= 11
40
Compare the results we obtained above with the results we got using the first method. They have the same answers.

Subtraction of Mixed Fractions

8
2
3
1
3
2 1
– 3 =( 8−3 )+ −
3 3 [ ] We subtract the whole number numbers 8 – 3 = 5

1 1 2 1 1 1
=5+ = 5 Next, we subtract − = . Our answer, therefore, is 5 .
3 3 3 3 3 3
2. If the mixed fractions have fractional parts which are not similar, then we change the fractional parts into similar fractions and then proceed as in
above.
2 8 2
12 =12 We deduct 8 from 12 to get 4. We change and to similar fractions. The LCD for 3and 4 is 12 so
3 12 3
1 3 2 8 1 3
8 =8 12 ÷ 3 = 4; 4 x 2 = 8; therefore, = . Again, 12 ÷ 4 = 3; 3 x 1 = 3; therefore, = . So, we deduct
4 12 3 12 4 12
3 8 5 5
from to get ; hence, the answer is 4 .
12 12 12 12
5
12
3. If the fraction in the subtrahend is greater than the fraction in the minuend, convert one unit of the minuend into an improper fraction with the
correct denominator and add this unit to the existing fraction in the minuend. Then, the whole number in the minuend is reduced by one. After that, we can
proceed with the subtraction.
1 1 9 8
23 = 23 = 22 From 23, we borrow one unit expressed as a fraction with the denominator of 8, that is, , which
8 8 8 8
we
3 6 6 1 9 3
-15 = 15 = 15 add to to arrive at . Next, we convert into a fraction with 8 as denominator. 8 ÷ 4 = 2; 2 x
4 8 8 8 8 4
3 = 6.
3 6 6 9 3
becomes . Now, we deduct 15 from 22 to get 7, and from to get . Our
4 8 8 8 8
answer, therefore, is
3 3
7 7 .
8 8

BUSINESS MATHEMATICS
QUARTER 1 - MODULE 1

NAME: __________________________Grade Level & Strand:________ Teacher’s Name_____________________

________1. A whole class is always bigger than its parts.

________2. A fraction of something is always equal to a fraction of another something.

8
________3. is greater than 1.
8
16 20
________4. is equal to .
4 5
2 4
________5. is equal to .
3 8

B. Identify the following as a proper fraction ( PF ), an improper fraction ( IF ), or a mixed Fraction ( MF ).

3 5 7 23
____1. 4 ____4. ____7. ____10.
3 12 8 12
12 8 16 13
____2. ____5. ____8. ____11.
5 7 18 15
1 9 21 21
____3. 6 ____6. ____9. ____12.
3 9 21 22

C. Find the sum and difference.

6 2 9 1 2 3 1 5
1. - = 3. 7 +3 -5 = 5. 10 + 12 + 21 =
1 10 10 4 3 8 6 13
 3 5 1 1 11 8 7
2. 1 +8 = 4. 26 - 17 = 6. 7 +3 + 18 =
4 6 8 12 2 5 6

II.
FRACTION COOKIE JAR SORTING

This equivalent fractions sorting activity, is a great individual, small group and a whole-class activity to consolidate students’ understanding of equivalent fractions.

Directions: Draw the six cookie jars on the space provided below and label it with the corresponding fractions given, then draw the cookies into the correct cookie jars,
according to its equivalent.

Given:
1 1 1 1 1 1
Cookie Jars: , , , , ,
2 3 4 5 6 8

10 50 3 10 2 5 25 4 4 3 3 10 10 5 2 5 20 2 3 5 2
Cookies: , , , , , , , , , , , , , , , , , , , ,
20 100 6 30 6 20 100 16 20 15 18 60 80 40 4 30 100 10 9 15 8