10_addition of Dissimilar Fractions

M A T H E M A T I C S

5

Modified In-School Off-School Approach Modules (MISOSA)

Distance Education for Elementary Schools

SELF-INSTRUCTIONAL MATERIALS

ADDITION OF DISSIMILAR FRACTIONS

Department of Education

BUREAU OF ELEMENTARY EDUCATION 2nd Floor Bonifacio Building DepEd Complex, Meralco Avenue Pasig City

Revised 2010 by the Learning Resource Management and Development System (LRMDS),

DepEd - Division of Negros Occidental under the Strengthening the Implementation of Basic Education

in Selected Provinces in the Visayas (STRIVE).

This edition has been revised with permission for online distribution through the Learning Resource Management Development System (LRMDS) Portal (http://lrmds.deped.gov.ph/) under Project STRIVE for BESRA, a project supported by AusAID.

Section 9 of Presidential Decree No. 49 provides: “No copyright shall subsist in any work of the Government of the Republic of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit.” This material was originally produced by the Bureau of Elementary Education of the Department of Education, Republic of the Philippines.

1

ADDITION OF DISSIMILAR FRACTIONS

Objective: Add dissimilar fractions

Find the least common denominator (LCD) of the following sets of fractions.

1) 5

1,

3

1

2) 8

5,

7

1

3) 9

4,

12

6 4)

8

1,

4

2,

3

1

5) 10

3,

8

1,

5

2 6)

2

1,

4

3,

7

4

Sarah bought 2

1 kilogram of lanzones and

4

1 kilogram of grapes for her

grandmother. How many kilograms of fruits did she buy in all?

What shall we do to solve the problem? We shall add.

What are we going to add? 2

1 and

4

1

What kind of fractions are 2

1 and

4

1? They are dissimilar fractions.

Do you know how to add dissimilar fractions? Look closely as we solve the problem.

Review

Study and Learn

2

Through illustration: + + + =

The sum is 4

3. Therefore, Sarah bought

4

3 kilogram of fruits in all.

By computation: Find the least common denominator (LCD).

2

1 =

4

4

1 =

4

Find fractions equal to the given fractions.

2

1 x

2

2 =

4

2

4

1 =

4

1

Change to similar fractions

2

1

4

1

4

2

4

1

Add the numerators and use the same denominators.

4

2

4

1

4

3

STEP 1

STEP 2

3

Add the numerators and use the common

denominator. Reduce to lowest term if possible.

2

1

4

2

+ 4

1 +

4

1

4

3

Likewise, the answer is 4

3.

Let’s have another example.

45

=9

3

45

15=

5

5x

9

3

45

15

45=

5

3+ +

45

27=

9

9x

5

3

45

27

15

11=

45

33

The sum is 15

11.

A. Solve and copy the correct answer on your paper.

1) )12

11,

12

10,

12

8(=

4

1+

3

2

2) )20

51,

20

11,

20

31(=

4

1+

2

1+

5

2

3) )12

12,

12

22,

12

32(=

2

1+

6

5+

4

3

STEP 3

Try These

4

4) )3

21,

6

21,

3

11(=

6

1+

3

2+

10

5

5) )24

11,

24

61,

24

51(=

8

3+

3

2+

6

1

In adding dissimilar fractions, follow these steps:

Find the LCD of the given fractions.

Change the fractions into similar fractions.

Add.

Always express the answer in lowest terms.

Find the sum and express it in its lowest terms.

1) =3

2+

11

3 2) =

5

3+

4

1

3) =4

3+

8

1+

5

3 4) =

4

3+

3

1+

9

4

5) =6

3+

3

1+

5

2

Check your answer with the answer key. If you get…

4-5 Excellent! You may now proceed to the next lesson.

3 You need to review the processes you missed.

0-2 You need to repeat the whole process. Ask your teacher or elder to help you.

Wrap Up

On Your Own

5

Key to Correction ADDITION OF DISSIMILAR FRACTIONS REVIEW 1) 15 2) 56 3) 36 4) 24 5) 40 6) 28 TRY THESE

1) 12

11

2) 20

31

3) 2

12

4) 3

11

5) 24

51

ON YOUR OWN

1) 33

31

2) 20

17

3) 40

191

4) 36

191

5) 30

71