SIM for Mathematics; Addition and Subtraction of Rational Numbers

Addition &
Subtraction
of Rational Numbers
(Fractions)a Strategic Intervention Material
by: JAY AHR EBUEN SISON
Bancal Integrated School
Division of Zambales
Region III

How to use this material?
ANSWER
CARD
ENRICHMENT CARD
ASSESSMENT CARDS
ACTIVITY #4
Addition/Subtraction of
Dissimilar Fraction ACTIVITY #3
Least Common Multiple ACTIVITY #2
Addition/Subtraction of
Similar Fraction
ACTIVITY #1
SIMILAR or DISSIMILAR
OVERVIEW
GUIDE CARD
Hey guys, Let’s start with this
one.

GUIDE CARD
LEARNING COMPETENCY
Least Mastered Skill
Addition and subtraction of similar and dissimilar fractions
Sub-Tasks:
1. Define and identify similar fractions and dissimilar fractions
2. Perform addition and subtraction of similar fraction
3. Determine Least Common Denominator (LCD) between Dissimilar
Fractions
4. Evaluate rational expressions involving addition and subtraction
3/4 + 1/3 = 1 1/12 how we do we compute it
mathematically?
Let’s take a look at this…
+ = = =

ACTIVITY #1
Similar or Dissimilar ?
Similar fractions are fractions that have same or common denominator. They
are often called like fractions. If they are NOT same or common, then they are
dissimilar fractions.
Let’s try to identify the following pairs of fractions as similar or dissimilar.
Write
S if they are similar fractions or D if they are dissimilar fractions in the space
provided
for each number.
___ 1.
2
5
and
4
5
___ 2.
5
6
and 2
1
3
___ 3.
19
12
and 3
1
12
___ 4.
18
36
and
12
24
___ 5. 3
5
6
and
11
6
These seem so easy,
right?

ACTIVITY #2
Addition and Subtraction of Similar
Fractions
In addition or subtraction of similar fractions, we only add or subtract their
numerator and rewrite the same or common denominator.
Example #1: find the sum of
2
5
+
4
5
2
5
+
4
5
=
4 + 2
5
=
6
5
= 1
1
5
Example #2: Find the difference of 3
5
6
-
13
6
3
5
6
-
13
6
=
23
6
−
13
6
=
23 −13
6
=
8
6
=
4
3
= 1
1
3
Answers should always express in simplified form.

ACTIVITY #2
Addition and Subtraction of Similar
Fractions
Now, let’s try to perform the indicated operation of the following similar
fractions.
1.
3
10
+
5
10
2.
7
6
+
4
6
3. 1
1
8
-
3
8
4.
17
12
-
7
12
5.
5
20
+
7
20
-
6
20
Let’s do this…

ACTIVITY #3
Least Common Multiple (LCM)
Least common multiple is the smallest multiple that is exactly divisible by
every member of a set of numbers. This is use to make dissimilar fractions be
similar by changing them into equivalent fractions having LCM as their common
denominator.
Example: Find the least common multiple of 12 and 18.
by listing:
multiples of 12: 12 , 24 , 36 , 48 , 60 , 72 , 84 , 96
multiples of 18: 18 , 36 , 54 , 72 , 90 , 108 , 126
since we have two common multiples on the list, 36 & 72,
and the least common multiple between them is 36
by factoring:
factors of 12: 2 × 2 × 3 least common multiple can get
factors of 18: 2 × × 3 × 3 by listing down all common &
LCM: 2 × 2 × 3 × 3 = 36 uncommon factors and multiply
them.

ACTIVITY #3
Least Common Multiple (LCM)
Let’s try to fine the least common multiple of these given set of numbers.
1. 4 and 6
2. 6 and 18
3. 12 and 16
4. 24 and 18
5. 4 , 6 and 9
You can find the LCM
through listing
multiples or by
factoring. You can
use any of the said
methods

ACTIVITY #4
Addition and Subtraction of Dissimilar
Fractions
Find the sum of
5
12
+
7
18
. Dissimilar fractions, right? The LCM of the
denominators of each fractions is also known as the Least Common Denominator
(LCD).
Let’s make these dissimilar fractions into similar fractions. Identify first the
LCM.
Using factoring: factors of 12: 2 × 2 × 3
factors of 18: 2 × × 3 × 3
LCM: 2 × 2 × 3 × 3 = 36
then change the given fractions to their equivalents fraction using LCM as
their least common denominator (LCD).
5
12
=
36
15
36
7
18
=
36
14
36
Now that we have similar fractions, we can proceed to the operation
To find the numerator of the equivalent
fractions, divide the LCD by the given
denominator and multiply the result to the
given numerator.

Assessment Card
Addition and Subtraction of Dissimilar
Fractions
Determine the least common multiple of each denominators, and perform the
indicated operations.
1.
3
4
+
1
6
2.
8
21
+
5
14
3.
8
3
- 1
1
4
4. 2
5
16
- 1
3
5
5.
2
3
+
7
4
- 1
1
5
You can find the LCM
through listing
multiples or by
factoring. You can
use any of the said
methods

Enrichment Card
Work Problem
It takes 3 hours for Tim to mow the lawn. Linda can mow the same lawn in 5
hours. How long will it take John and Linda, work together, to mow the lawn?
together, to mow the lawn?
Note: If A can do a piece of work in n time, then A’s rate of work =
1
𝒏
Tim’s rate of work (
1
𝟑
) + Linda’s rate of work (
1
𝟓
) = (
1
𝒙
)
x = time spend of both working together
1
𝒙
=
1
𝟑
+
1
𝟓
=
1 5 +1 (3)
𝟏𝟓
=
5+3
𝟏𝟓
=
8
𝟏𝟓
x =
15
8
= 1.825 hours
1
𝒙
=
8
𝟏𝟓
multiply both side by 15x therefore, it takes 1 hours 52
minutes
and 30 seconds for John & Linda
15 = 8x divide both side by 8 working together to mow the lawn.
rate of work when
they
both working
together

Reference Card
Mathematics 7 Learner’s Module, pp.48 – 51
CPM Educational Program 2011
http://pdfs.cpm.org/skillBuilders/MC/MC_Addition_Subtraction_of_Fraction
btraction_of_Fractions.pdf
Spectrum Math Grade 7, pp. 27 - 48

Answer Card
Activity #1 Assessment
1. S 1.
4
𝟓
2. D 2.
17
𝟐𝟏
3. S 3. 1
5
𝟏𝟐
4. D 4.
1
𝟐
5. S 5. 1
13
𝟔𝟎
Activity #2
1.
4
𝟓
2. 1
5
𝟔
3.
3
𝟒
4.
5
𝟔
5.
3
𝟏𝟎
Activity #3
1. 12
2. 18
3. 48
4. 72
5. 36

SIM for Mathematics; Addition and Subtraction of Rational Numbers

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