 Practice the questions given in the Worksheet on Addition of Unlike Terms and know various models of questions framed on the topic. Unlike Like Terms, we can’t add them together to obtain a single sum result. Explore all the problems on adding unlike fractions over here and know how to add unlike terms in an algebraic expression.

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Read Similar Articles: Worksheet on Subtraction of Unlike Terms

I. Find the sum of:
(i) 6x and 3y
(ii) 5b and 4b2
(iii) 7y2z and 2y2
(iv) 4xy, 2x and 5y
(v) 2p, 5p2 and 9p3
(vi) mn, np, and pm

Solution:

(i) Given 6x and 3y
The sum of 6x and 3y is 6x+3y.
(ii) Given 5b and 4b2
The sum of 5b and 4b2 is 5b+4b2
(iii) Given 7y2z and 2y2
The sum of 7y2z and 2y2 is 7y2z + 2y2
(iv) Given 4xy, 2x and 5y
The sum of 4xy, 2x and 5y is 4xy+2x+5y.
(v) Given  2p, 5p2 and 9p3
The sum of 2p, 5p2 and 9p3 is 2p + 5p2+9p3
(vi) Given mn, np, and pm
The sum of mn, np, and pm is mn+np+pm.

II. Simplify the following:
(i) -2x and 8y
(ii) 6c and -3b
(iii) -y2 and y
(iv) ab and -bc
(v) –XYZ and XY
(vi) a2b and –ab2

Solution:

(i) Given, -2x and 8y
=-2x+8y
Hence, the sum of unlike terms -2x and 8y is -2x+8y.
(ii) Given, 6c and -3b
=6c+(-3b)
=6c-3b
Hence, the sum of unlike terms 6c and -3b is 6c-3b.
(iii) Given, -y2 and y
= -y2 +y
Hence, the sum of unlike terms -y2 and y is -y2 +y.
(iv) Given, ab and -bc
=ab+(-bc)
=ab-bc
Hence, the sum of unlike terms ab and -bc is ab-bc.
(v) Given, –XYZ and XY
=-XYZ+XY
Hence, the sum of unlike terms –XYZ and XY is -XYZ+XY.
(vi) Given, a2b and –ab2
=a2b+(-ab2)
=a2b -ab2
Hence, the sum of unlike terms a2b -ab2.

(i) m, 5m and 4n
(ii) 3p, 5p and 6pq
(iii) 2b, 7c and 8c
(iv) 4mn, 3nm and 9n
(v) 20xy, 16yx and 18xz
(vi) 8a2b, 4ab and 6ba2

Solution:

(i) Given, m, 5m and 4n
=m+5m+4n
=6m+4n
Therefore, By adding m, 5m and 4n we get 6m+4n.
(ii) Given, 3p, 5p and 6pq
=3p+5p+6pq
=8p+6pq
Therefore, by adding 3p, 5p and 6pq is 8p+6pq.

(iii) Given, 2b, 7c and 8c
=2b+7c+8c
=2b+15c
Therefore, by adding 2b+7c+8c we get 2b+15c.
(iv) Given, 4mn, 3nm and 9n
=4mn+ 3nm+ 9n
=7mn+9n
Therefore, by adding 4mn+3nm+ 9n we get 7mn+9n.
(v) Given, 20xy, 16yx and 18xz
=20xy+ 16yx + 18xz
=36xy+18xz
Therefore, by adding 20xy, 16yx, and 18xz we get 36xy+18xz.
(vi) Given, 8a2b, 4ab and 6ba2
=8a2b+4ab+6ba2
=14a2b+4ab
Therefore, by adding 8a2b, 4ab and 6ba2 we get 14a2b+4ab.

Iv. Evaluate the following by arranging the unlike terms together:
(i) 8x – 2y – 4x
(ii) 15mn – 7mn + 4np
(iii) a – 8a + 4b + 7a
(iv) 14x + 2y – 4x – y
(v) 2xy + 4yx + 18
(vi) 7abc – 10ab + 12abc

Solution:

(i) Given, 8x – 2y – 4x
By arranging the unlike terms together,
=8x-4x-2y
=4x-2y
Hence, By evaluating 8x – 2y – 4x is 4x-2y.
(ii) Given, 15mn + 4np – 7mn
By arranging the unlike terms together,
=15mn-7mn+4np
=7mn+4np
Hence, By evaluating 15mn + 4np – 7mn is 15mn + 4np – 7mn.
(iii) Given, a – 8a + 4b + 7a
By arranging the unlike terms together,
=a – 8a + 7a + 4b
=8a-8a+4b
=4b
Hence, By evaluating a – 8a + 4b + 7a is 4b.
(iv) Given, 14x + 2y – 4x – y
By arranging the unlike terms together,
=14x-4x+2y-y
=10x+y
Hence, By evaluating 14x + 2y – 4x – y is 10x+y.
(v) Given,2xy + 4yx + 18-xy
By arranging the unlike terms together,
=2xy-xy+4yx+18
=xy+4yx+18
=5yx+18
Hence, By evaluating 2xy + 4yx + 18-xy is 5yx+18.
(vi)Given, 7abc – 10ab + 12abc
By arranging the unlike terms together,
=7abc+12abc-10ab
=19abc-10ab
Hence, By evaluating 7abc – 10ab + 12abc is 19abc-10ab.

V. Sameera bought m apples and n oranges from the fruit market. How many fruits did she buy altogether?

Solution:

Given,
Sameera bought apples=m
Sameera bought oranges=n
Total no. of fruits bought by Sameera=m+n.
Hence, Sameera bought m+n fruits from the market.

VI. Mahesh scored X marks in Maths and Y marks in science. How many marks did he score altogether in two subjects?

Solution:

Given,
Mahesh scored marks in Maths=X
Mahesh scored marks in Science=Y
Mahesh scored marks in both the subjects=X+Y.
Therefore, Mahesh scored X+Y marks in both subjects.

VII. Sarath walked X km on Friday and Y km on Saturday. How many km did he run on both days?

Solution:

Given,
No. of Km Sarath walked on Friday=X km
No. of  km Sarath walked on Saturday=Y km
No. of km Sarath walked on both the days=X+Y.