Addition or Combining Like Terms is a mathematical process for simplifying the expressions. Worksheet on Addition of Like Terms available here helps children to understand the concept of simplification of algebraic expressions. The Math Adding Like Terms Worksheets will guide students to carefully summarize and examine each term carefully.
Students can use these Addition of Like Terms Worksheets PDF as a practice to self-assess their preparation level and understanding of concepts. Download the easily accessible Adding Like Terms Worksheet and practice anywhere and anytime you want.
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Adding Like Terms Worksheet PDF
I. Fill in the blanks
(i) 4 + 2 = ____ and 4x + 2x = ____
(ii) 7 + 10 = ____ and 7a + 10a = ____
(iii) 5 + 6 = ____ and 5mn + 6mn = ____
(iv) 12 + 15 = ____ and 12abc + 15abc = ____
(v) 8 + 18 = ____ and 8a + 18b = ____
(vi) 3 + 8 = ____ and 3abmn + 8abmn =_______
Solution:
(i) 6,6x
(ii) 17, 17a
(iii) 11,11mn
(iv) 27,27abc
(v)26,8a+8b
(vi) 11, 11abmn
II. Evaluate
(i) 2x + 6x + 4x + 3x
(ii) a + b + c + a + b + c
(iii) 3xy + 4x2y + 3y + 7y
(iv) xy + yz + zx+ yz + zy + yx
(v) 4a3b + 6bc3 + 5c3b + c3b
(vi) abc + 12bac + 13cab + 4cba
(vii) x2+2xy+y2+3xy+3y2
(viii) ab+bc+Ca+3bc+2ca
Solution:
(i) Given 2x + 6x + 4x + 3x
=15x
Therefore, 2x + 6x + 4x + 3x=15x.
(ii) Given a + b + c + a + b + c
By adding a,b,c we get
=2a+2b+2c
Therefore, a + b + c + a + b + c=2a+2b+2c.
(iii) 3xy + 4x2y + 3y + 7y
By adding 3y and 7y we get
=3xy+4x2y+10y
Therefore,3xy + 4x2y + 3y + 7y=3xy+4x2y+10y.
(iv) Given xy + yz + zx+ yz + zy + yx
By adding xy and yz we get
=2xy + 3yz+zx
(v) Given 4a3b + 6bc3 + 5c3b + c3b
By adding 5c3b + c3b we get 6c3b
= 4a3b + 6bc3 + 6c3b
Therefore, 4a3b + 6bc3 + 5c3b + c3b we get 4a3b + 6bc3 + 6c3b.
(vi) Given x2+2xy+y2+3xy+3y2
By adding 2xy and 3xy,y2,3y2 we get 5xy,4y2.
x2+5xy+4y2
Therefore, By adding x2+2xy+y2+3xy+3y2 we get x2+5xy+4y2.
(viii) Given ab+bc+Ca+3bc+2ca
= ab+ 4bc + 3ca
Therefore, By adding ab+bc+Ca+3bc+2ca we get ab+4bc+3ca.
III. If P = x2 + 2xy + y2, Q = 3x2 – 4xy + 2y2 and R = 5x2 – xy – 6y2, find P + Q + R.
Solution:
Given,
P = x2 + 2xy + y2, Q = 3x2 – 4xy + 2y2 and R = 5x2 – xy – 6y2
P+Q+R= x2 + 2xy + y2 + 3x2 – 4xy + 2y2 + 5x2 – xy – 6y2
=9x2-3xy-3y2
IV. Add arranging the like terms:
(i) 7ab and 2ab
(ii) 4abc, abc and 3abc
(iii) 2a, 3a and 4b
(iv) 3a and 2b
(v) 2ab, 4ba and 6bc
(vi) 4x, 5x and 2xy
(vii) 3xy,6xy
(viii) ab,2ab, and 7ab
Solution:
(i) Given 7ab and 2ab
7ab+2ab=9ab
Hence, By adding 7ab and 2ab we get 9ab.
(ii) Given 4abc, abc and 3abc
4abc + abc + 3abc= 8abc.
(iii) Given 2a, 3a and 4b
2a+3a+4b=5a+4b
Hence, By adding 7ab and 2ab we get 5a+4b.
(iv) Given 3a and 2b
3a+2b
Hence, By adding 3a and 2b we get 3a+2b.
(v) Given 2ab, 4ba and 6bc
2ab+4ba+6bc=6ab+6bc
Hence, By adding 2ab,4ba and 6bc we get 6ab+6bc.
(vi)Given 4x, 5x and 2xy
=4x+5x+2xy
=9x+2xy
Hence, By adding 4x,5x and 2xy we get 9x+2xy.
(vii) Given 3xy,6xy
=3xy+6xy
=9xy
Hence, By adding 3xy,6xy we get 9xy.
(viii) Given ab,2ab, and 7ab
=ab+2ab+7ab
=3ab+7ab
=10ab
Hence, By adding ab,2ab, and 7ab we get 10ab.
V. Fill in the blanks:
(i) The sum of -4 and – 3 = ____ and the sum of -4x and – 3x = ____
(ii) The sum of 15 and – 5 = ____ and the sum of 15x and – 5x = ____
(iii) The sum of -5 and – 12 = ____ and the sum of -5abc and – 12abc = ____
(iv) The sum of 15 and 8 = ____ and the sum of 15xyz and 8xyz = ____
(v) 13 + 6 + 2 = ____ and13m + 6 + 2m = ____
(vi) 12 – 17 + 8 = ____ and12mn – 17mn + 8mn = ____
(vii) 16+4-2=______ and 16x+4x-2x=_______
Solution:
(i) -7,-7x
(ii) 10,10x
(iii) -17,-17abc
(iv) 23,23xyz
(v) 21,21m
(vi) 3, 3mn
(vii) 18, 18x