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Properties of Addition of Fractions

The associative and commutative properties of natural numbers hold good in the case of fractions also.


I: Commutative Property of Addition of Fractions: 

While adding two fractions we may add them in either order. The sum of the fractions remains the same.

Add:

23 + 14

L.C.M. of 3, 4 is 12

23 + 14

= 812 + 312

= 1112

Add:

14 + 23

L.C.M. of 4, 3 is 12

14 + 23

= 312 + 812

= 1112

                       i.e., 23 + 14 = 14 + 23


II: Associative Property of Addition of Fractions:

While adding more than two fractions, we may add them in any order; the sum of the fractions remains the same.

Add:

[25 + 34] + 13    

L.C.M. of 5 and 4 is 20.

[25 + 34] + 13 = [820 + 1520] + 13

[25 + 34] + 13 = 2320 + 13

L.C.M. of 20 and 3 is 60.

= 6960 + 2060 = 8960 = 12960

Add:

25 + [34 + 13]

L.C.M. of 4 and 3 is 12.

= 25 + [912 + 412]

= 251312

L.C.M. of 5 and 12 is 60. 

= 24606560

8960 = 12960

              i.e., [25 + 34] + 1325 + [34 + 13]


III: Zero Property of Addition of Fractions:

If zero is added to any fraction we get back the same fraction.

Add:

12 + 0 = 12 + 02 = 1+02 = 12

Therefore, 12 + 0 = 0 + 12 = 12

Add:

56 + 0 = 56 + 06 = 5+06 = 56

Therefore, 56 + 0 = 0 + 56 = 56

Properties of Addition of Fractions


Questions and Answers on Properties of Addition of Fractions:

I. Fill in the Blanks:

(i) 35 + 14 = 14 + ______

(ii) 16 + ______ = 18 + ______

(iii) 715 + 35 + 29 = 29 + ______ + 35

(iv) 920 + 415 + ______ = 35 + 920 + 415


Answer:

I. (i) 35

(ii) 18; 16

(iii) 715

(iv) 35



II. Verify the following (show that left hand side = right hand side)

(i) 35 + 28 = 28 + 35

(ii) [16 + 23] + 14 = 16 + [23 + 14]



4th Grade Math Activities

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