Page 1
IMPORTANT POINTS
1. Fundamental Operations : In mathematics, the operations : addition (+),
subtraction (-), multiplication (x) and division (÷) are called the four fundamental
operations.
2. Addition and Subtraction :
? Addition of Like Terms :
? When all the terms are positive, add their coefficients.
? When all the terms are negative, add their coefficients without
considering their negative signs and then prefix the minus sign to the
sum.
? Addition of Unlike Terms : As discussed above, the sum of two or more
like terms is a single like term ; but the two unlike terms cannot be added
together to get a single term.
? Subtraction of Like Terms : The same rules, as those for subtraction of
integers, are applied for the subraction of like terms. The result of
subtraction of two like terms is also a like term.
Add the positive terms together and negative terms separately together. Then, find the
result of two terms obtained.
EXERCISE 19(A)
Question 1.
Fill in the blanks :
(i) 5 + 4 = ………… and 5x + 4x = ………….
(ii) 12 + 18 = ………… and 12x
2
y + 18x
2
y = ………….
(iii) 7 + 16 = ………….. and 7a + 16b = …………
(iv) 1 + 3 = ………… and x
2
y + 3xy
2
= ………..
(v) 7 – 4 = …………… and 7ab – 4ab = …………..
(vi) 12 – 5 = ………… and 12x – 5y = ……………
(vii) 35 – 16 = ………….. and 35ab – 16ba = ………….
(viii) 28 – 13 = …………. and 28ax
2
– 13a
2
x = ………….
Solution:
(i) 5 + 4 = 9 and 5x + 4x = 9x
(ii) 12 + 18 = 30 and 12x
2
y + 18x
2
y = 30x
2
y
(iii) 7 + 16 = 23 and 7a + 16 b = 7a + 16b
(iv) 1 + 3 = 4 and x
2
y + 3xy
2
= x
2
y + 3xy
2
(v) 7 – 4 = 3 and 7ab – 4ab = 3ab
(vi) 12 – 5 = 7 and 12x – 5y = 12x – 5y
(vii) 35 – 16 = 19 and 35ab – 16ba = 19ab
(viii) 28 – 13 = 15 and 28ax
2
– 13a
2
x = 28ax
2
– 13a
2
x
Question 2.
Fill in the blanks :
Page 2
IMPORTANT POINTS
1. Fundamental Operations : In mathematics, the operations : addition (+),
subtraction (-), multiplication (x) and division (÷) are called the four fundamental
operations.
2. Addition and Subtraction :
? Addition of Like Terms :
? When all the terms are positive, add their coefficients.
? When all the terms are negative, add their coefficients without
considering their negative signs and then prefix the minus sign to the
sum.
? Addition of Unlike Terms : As discussed above, the sum of two or more
like terms is a single like term ; but the two unlike terms cannot be added
together to get a single term.
? Subtraction of Like Terms : The same rules, as those for subtraction of
integers, are applied for the subraction of like terms. The result of
subtraction of two like terms is also a like term.
Add the positive terms together and negative terms separately together. Then, find the
result of two terms obtained.
EXERCISE 19(A)
Question 1.
Fill in the blanks :
(i) 5 + 4 = ………… and 5x + 4x = ………….
(ii) 12 + 18 = ………… and 12x
2
y + 18x
2
y = ………….
(iii) 7 + 16 = ………….. and 7a + 16b = …………
(iv) 1 + 3 = ………… and x
2
y + 3xy
2
= ………..
(v) 7 – 4 = …………… and 7ab – 4ab = …………..
(vi) 12 – 5 = ………… and 12x – 5y = ……………
(vii) 35 – 16 = ………….. and 35ab – 16ba = ………….
(viii) 28 – 13 = …………. and 28ax
2
– 13a
2
x = ………….
Solution:
(i) 5 + 4 = 9 and 5x + 4x = 9x
(ii) 12 + 18 = 30 and 12x
2
y + 18x
2
y = 30x
2
y
(iii) 7 + 16 = 23 and 7a + 16 b = 7a + 16b
(iv) 1 + 3 = 4 and x
2
y + 3xy
2
= x
2
y + 3xy
2
(v) 7 – 4 = 3 and 7ab – 4ab = 3ab
(vi) 12 – 5 = 7 and 12x – 5y = 12x – 5y
(vii) 35 – 16 = 19 and 35ab – 16ba = 19ab
(viii) 28 – 13 = 15 and 28ax
2
– 13a
2
x = 28ax
2
– 13a
2
x
Question 2.
Fill in the blanks :
(i) The sum of – 2 and – 5 = …………. and the sum of – 2x and – 5x = …………….
(ii) The sum of 8 and – 3 = ………….. and the sum of 8ab and – 3ab = ………….
(iii) The sum of – 15 and – 4 = …………….. and the sum of – 15x and -4y =
………………
(iv) 15 + 8 + 3 = ……….. and 15x + 8y + 3x = …………….
(v) 12 – 9 + 15 = …………… and 12ab – 9ab + 15ba = ……………..
(vi) 25 – 7 – 9 = and 25xy – 7xy – 9yx = ……………
(vii) – 4 – 6 – 5 = …………. and – 4ax – 6ax – 5ay = …………….
Solution:
(i) The sum of – 2 and – 5 = – 7 and the sum of – 2x and – 5x = -7x
(ii) The sum of 8 and -3 = 5 and the sum of 8ab and – 3ab = 5ab
(iii) The sum of – 15 and – 4 = – 19 and the sum of – 15x and – 4y = – 15x – 4y
(iv) 15 + 8 + 3 = 26 and 15x + 8y + 3x = 18x + 8y
(v) 12 – 9 + 15 = 18 and 12ab – 9ab + 15ba = 18ab
(vi) 25 – 7 – 9 = 9 and 25xy – 7xy – 9yx = 9xy
(vii) – 4 – 6 – 5 = – 15 and – 4ax – 6ax – 5ay = – 10ax – 5ay
Question 3.
Add:
(i) 8xy and 3xy
(ii) 2xyz, xyz and 6xyz
(iii) 2a, 3a and 4b
(iv) 3x and 2y
(v) 5m, 3n and 4p
(vi) 6a, 3a and 9ab
(vii) 3p, 4q and 9q
(viii) 5ab, 4ba and 6b
(ix) 50pq, 30pq and 10pr
(x) – 2y, – y and – 3y
(xi) – 3b and – b
(xii) 5b, – 4b and – 10b
(xiii) – 2c, – c and – 5c
Solution:
(i) 8xy + 3xy = 11xy
(ii) 2xyz + xyz + 6xyz = (2 + 1 + 6) xyz = 9xyz
Page 3
IMPORTANT POINTS
1. Fundamental Operations : In mathematics, the operations : addition (+),
subtraction (-), multiplication (x) and division (÷) are called the four fundamental
operations.
2. Addition and Subtraction :
? Addition of Like Terms :
? When all the terms are positive, add their coefficients.
? When all the terms are negative, add their coefficients without
considering their negative signs and then prefix the minus sign to the
sum.
? Addition of Unlike Terms : As discussed above, the sum of two or more
like terms is a single like term ; but the two unlike terms cannot be added
together to get a single term.
? Subtraction of Like Terms : The same rules, as those for subtraction of
integers, are applied for the subraction of like terms. The result of
subtraction of two like terms is also a like term.
Add the positive terms together and negative terms separately together. Then, find the
result of two terms obtained.
EXERCISE 19(A)
Question 1.
Fill in the blanks :
(i) 5 + 4 = ………… and 5x + 4x = ………….
(ii) 12 + 18 = ………… and 12x
2
y + 18x
2
y = ………….
(iii) 7 + 16 = ………….. and 7a + 16b = …………
(iv) 1 + 3 = ………… and x
2
y + 3xy
2
= ………..
(v) 7 – 4 = …………… and 7ab – 4ab = …………..
(vi) 12 – 5 = ………… and 12x – 5y = ……………
(vii) 35 – 16 = ………….. and 35ab – 16ba = ………….
(viii) 28 – 13 = …………. and 28ax
2
– 13a
2
x = ………….
Solution:
(i) 5 + 4 = 9 and 5x + 4x = 9x
(ii) 12 + 18 = 30 and 12x
2
y + 18x
2
y = 30x
2
y
(iii) 7 + 16 = 23 and 7a + 16 b = 7a + 16b
(iv) 1 + 3 = 4 and x
2
y + 3xy
2
= x
2
y + 3xy
2
(v) 7 – 4 = 3 and 7ab – 4ab = 3ab
(vi) 12 – 5 = 7 and 12x – 5y = 12x – 5y
(vii) 35 – 16 = 19 and 35ab – 16ba = 19ab
(viii) 28 – 13 = 15 and 28ax
2
– 13a
2
x = 28ax
2
– 13a
2
x
Question 2.
Fill in the blanks :
(i) The sum of – 2 and – 5 = …………. and the sum of – 2x and – 5x = …………….
(ii) The sum of 8 and – 3 = ………….. and the sum of 8ab and – 3ab = ………….
(iii) The sum of – 15 and – 4 = …………….. and the sum of – 15x and -4y =
………………
(iv) 15 + 8 + 3 = ……….. and 15x + 8y + 3x = …………….
(v) 12 – 9 + 15 = …………… and 12ab – 9ab + 15ba = ……………..
(vi) 25 – 7 – 9 = and 25xy – 7xy – 9yx = ……………
(vii) – 4 – 6 – 5 = …………. and – 4ax – 6ax – 5ay = …………….
Solution:
(i) The sum of – 2 and – 5 = – 7 and the sum of – 2x and – 5x = -7x
(ii) The sum of 8 and -3 = 5 and the sum of 8ab and – 3ab = 5ab
(iii) The sum of – 15 and – 4 = – 19 and the sum of – 15x and – 4y = – 15x – 4y
(iv) 15 + 8 + 3 = 26 and 15x + 8y + 3x = 18x + 8y
(v) 12 – 9 + 15 = 18 and 12ab – 9ab + 15ba = 18ab
(vi) 25 – 7 – 9 = 9 and 25xy – 7xy – 9yx = 9xy
(vii) – 4 – 6 – 5 = – 15 and – 4ax – 6ax – 5ay = – 10ax – 5ay
Question 3.
Add:
(i) 8xy and 3xy
(ii) 2xyz, xyz and 6xyz
(iii) 2a, 3a and 4b
(iv) 3x and 2y
(v) 5m, 3n and 4p
(vi) 6a, 3a and 9ab
(vii) 3p, 4q and 9q
(viii) 5ab, 4ba and 6b
(ix) 50pq, 30pq and 10pr
(x) – 2y, – y and – 3y
(xi) – 3b and – b
(xii) 5b, – 4b and – 10b
(xiii) – 2c, – c and – 5c
Solution:
(i) 8xy + 3xy = 11xy
(ii) 2xyz + xyz + 6xyz = (2 + 1 + 6) xyz = 9xyz
Question 4.
Evaluate :
Solution:
Page 4
IMPORTANT POINTS
1. Fundamental Operations : In mathematics, the operations : addition (+),
subtraction (-), multiplication (x) and division (÷) are called the four fundamental
operations.
2. Addition and Subtraction :
? Addition of Like Terms :
? When all the terms are positive, add their coefficients.
? When all the terms are negative, add their coefficients without
considering their negative signs and then prefix the minus sign to the
sum.
? Addition of Unlike Terms : As discussed above, the sum of two or more
like terms is a single like term ; but the two unlike terms cannot be added
together to get a single term.
? Subtraction of Like Terms : The same rules, as those for subtraction of
integers, are applied for the subraction of like terms. The result of
subtraction of two like terms is also a like term.
Add the positive terms together and negative terms separately together. Then, find the
result of two terms obtained.
EXERCISE 19(A)
Question 1.
Fill in the blanks :
(i) 5 + 4 = ………… and 5x + 4x = ………….
(ii) 12 + 18 = ………… and 12x
2
y + 18x
2
y = ………….
(iii) 7 + 16 = ………….. and 7a + 16b = …………
(iv) 1 + 3 = ………… and x
2
y + 3xy
2
= ………..
(v) 7 – 4 = …………… and 7ab – 4ab = …………..
(vi) 12 – 5 = ………… and 12x – 5y = ……………
(vii) 35 – 16 = ………….. and 35ab – 16ba = ………….
(viii) 28 – 13 = …………. and 28ax
2
– 13a
2
x = ………….
Solution:
(i) 5 + 4 = 9 and 5x + 4x = 9x
(ii) 12 + 18 = 30 and 12x
2
y + 18x
2
y = 30x
2
y
(iii) 7 + 16 = 23 and 7a + 16 b = 7a + 16b
(iv) 1 + 3 = 4 and x
2
y + 3xy
2
= x
2
y + 3xy
2
(v) 7 – 4 = 3 and 7ab – 4ab = 3ab
(vi) 12 – 5 = 7 and 12x – 5y = 12x – 5y
(vii) 35 – 16 = 19 and 35ab – 16ba = 19ab
(viii) 28 – 13 = 15 and 28ax
2
– 13a
2
x = 28ax
2
– 13a
2
x
Question 2.
Fill in the blanks :
(i) The sum of – 2 and – 5 = …………. and the sum of – 2x and – 5x = …………….
(ii) The sum of 8 and – 3 = ………….. and the sum of 8ab and – 3ab = ………….
(iii) The sum of – 15 and – 4 = …………….. and the sum of – 15x and -4y =
………………
(iv) 15 + 8 + 3 = ……….. and 15x + 8y + 3x = …………….
(v) 12 – 9 + 15 = …………… and 12ab – 9ab + 15ba = ……………..
(vi) 25 – 7 – 9 = and 25xy – 7xy – 9yx = ……………
(vii) – 4 – 6 – 5 = …………. and – 4ax – 6ax – 5ay = …………….
Solution:
(i) The sum of – 2 and – 5 = – 7 and the sum of – 2x and – 5x = -7x
(ii) The sum of 8 and -3 = 5 and the sum of 8ab and – 3ab = 5ab
(iii) The sum of – 15 and – 4 = – 19 and the sum of – 15x and – 4y = – 15x – 4y
(iv) 15 + 8 + 3 = 26 and 15x + 8y + 3x = 18x + 8y
(v) 12 – 9 + 15 = 18 and 12ab – 9ab + 15ba = 18ab
(vi) 25 – 7 – 9 = 9 and 25xy – 7xy – 9yx = 9xy
(vii) – 4 – 6 – 5 = – 15 and – 4ax – 6ax – 5ay = – 10ax – 5ay
Question 3.
Add:
(i) 8xy and 3xy
(ii) 2xyz, xyz and 6xyz
(iii) 2a, 3a and 4b
(iv) 3x and 2y
(v) 5m, 3n and 4p
(vi) 6a, 3a and 9ab
(vii) 3p, 4q and 9q
(viii) 5ab, 4ba and 6b
(ix) 50pq, 30pq and 10pr
(x) – 2y, – y and – 3y
(xi) – 3b and – b
(xii) 5b, – 4b and – 10b
(xiii) – 2c, – c and – 5c
Solution:
(i) 8xy + 3xy = 11xy
(ii) 2xyz + xyz + 6xyz = (2 + 1 + 6) xyz = 9xyz
Question 4.
Evaluate :
Solution:
(i) 6a – a – 5a – 2a = 6a – (1 + 5 + 2).a
Question 5.
Evaluate :
Solution:
Question 6.
Subtract the first term from the second :
Page 5
IMPORTANT POINTS
1. Fundamental Operations : In mathematics, the operations : addition (+),
subtraction (-), multiplication (x) and division (÷) are called the four fundamental
operations.
2. Addition and Subtraction :
? Addition of Like Terms :
? When all the terms are positive, add their coefficients.
? When all the terms are negative, add their coefficients without
considering their negative signs and then prefix the minus sign to the
sum.
? Addition of Unlike Terms : As discussed above, the sum of two or more
like terms is a single like term ; but the two unlike terms cannot be added
together to get a single term.
? Subtraction of Like Terms : The same rules, as those for subtraction of
integers, are applied for the subraction of like terms. The result of
subtraction of two like terms is also a like term.
Add the positive terms together and negative terms separately together. Then, find the
result of two terms obtained.
EXERCISE 19(A)
Question 1.
Fill in the blanks :
(i) 5 + 4 = ………… and 5x + 4x = ………….
(ii) 12 + 18 = ………… and 12x
2
y + 18x
2
y = ………….
(iii) 7 + 16 = ………….. and 7a + 16b = …………
(iv) 1 + 3 = ………… and x
2
y + 3xy
2
= ………..
(v) 7 – 4 = …………… and 7ab – 4ab = …………..
(vi) 12 – 5 = ………… and 12x – 5y = ……………
(vii) 35 – 16 = ………….. and 35ab – 16ba = ………….
(viii) 28 – 13 = …………. and 28ax
2
– 13a
2
x = ………….
Solution:
(i) 5 + 4 = 9 and 5x + 4x = 9x
(ii) 12 + 18 = 30 and 12x
2
y + 18x
2
y = 30x
2
y
(iii) 7 + 16 = 23 and 7a + 16 b = 7a + 16b
(iv) 1 + 3 = 4 and x
2
y + 3xy
2
= x
2
y + 3xy
2
(v) 7 – 4 = 3 and 7ab – 4ab = 3ab
(vi) 12 – 5 = 7 and 12x – 5y = 12x – 5y
(vii) 35 – 16 = 19 and 35ab – 16ba = 19ab
(viii) 28 – 13 = 15 and 28ax
2
– 13a
2
x = 28ax
2
– 13a
2
x
Question 2.
Fill in the blanks :
(i) The sum of – 2 and – 5 = …………. and the sum of – 2x and – 5x = …………….
(ii) The sum of 8 and – 3 = ………….. and the sum of 8ab and – 3ab = ………….
(iii) The sum of – 15 and – 4 = …………….. and the sum of – 15x and -4y =
………………
(iv) 15 + 8 + 3 = ……….. and 15x + 8y + 3x = …………….
(v) 12 – 9 + 15 = …………… and 12ab – 9ab + 15ba = ……………..
(vi) 25 – 7 – 9 = and 25xy – 7xy – 9yx = ……………
(vii) – 4 – 6 – 5 = …………. and – 4ax – 6ax – 5ay = …………….
Solution:
(i) The sum of – 2 and – 5 = – 7 and the sum of – 2x and – 5x = -7x
(ii) The sum of 8 and -3 = 5 and the sum of 8ab and – 3ab = 5ab
(iii) The sum of – 15 and – 4 = – 19 and the sum of – 15x and – 4y = – 15x – 4y
(iv) 15 + 8 + 3 = 26 and 15x + 8y + 3x = 18x + 8y
(v) 12 – 9 + 15 = 18 and 12ab – 9ab + 15ba = 18ab
(vi) 25 – 7 – 9 = 9 and 25xy – 7xy – 9yx = 9xy
(vii) – 4 – 6 – 5 = – 15 and – 4ax – 6ax – 5ay = – 10ax – 5ay
Question 3.
Add:
(i) 8xy and 3xy
(ii) 2xyz, xyz and 6xyz
(iii) 2a, 3a and 4b
(iv) 3x and 2y
(v) 5m, 3n and 4p
(vi) 6a, 3a and 9ab
(vii) 3p, 4q and 9q
(viii) 5ab, 4ba and 6b
(ix) 50pq, 30pq and 10pr
(x) – 2y, – y and – 3y
(xi) – 3b and – b
(xii) 5b, – 4b and – 10b
(xiii) – 2c, – c and – 5c
Solution:
(i) 8xy + 3xy = 11xy
(ii) 2xyz + xyz + 6xyz = (2 + 1 + 6) xyz = 9xyz
Question 4.
Evaluate :
Solution:
(i) 6a – a – 5a – 2a = 6a – (1 + 5 + 2).a
Question 5.
Evaluate :
Solution:
Question 6.
Subtract the first term from the second :
Solution:
Question 7.
Simplify :
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