#### Chapters

Chapter 2: Rational Numbers

Chapter 3: Fractions (Including Problems)

Chapter 4: Decimal Fractions (Decimals)

Chapter 5: Exponents (Including Laws of Exponents)

Chapter 6: Ratio and Proportion (Including Sharing in a Ratio)

Chapter 7: Unitary Method (Including Time and Work)

Chapter 8: Percent and Percentage

Chapter 9: Profit, Loss and Discount

Chapter 10: Simple Interest

Chapter 11: Fundamental Concepts (Including Fundamental Operations)

Chapter 12: Simple Linear Equations (Including Word Problems)

Chapter 13: Set Concepts (Some Simple Divisions by Vedic Method)

Chapter 14: Lines and Angles (Including Construction of angles)

Chapter 15: Triangles

Chapter 16: Pythagoras Theorem

Chapter 17: Symmetry (Including Reflection and Rotation)

Chapter 18: Recognition of Solids (Representing 3-D in 2-D)

Chapter 19: Congruency: Congruent Triangles

Chapter 20: Mensuration

Chapter 21: Data Handling

Chapter 22: Probability

## Chapter 11: Fundamental Concepts (Including Fundamental Operations)

### Selina solutions for Concise Mathematics Class 7 ICSE Chapter 11 Fundamental Concepts (Including Fundamental Operations) Exercise 11 (A)

Separate constant terms and variable terms from tile following:

8, x, 6xy, 6 + x, - 5xy^{2} , 15az^{2} , `(32"z")/"xy", "y"^2/"3x"`

Constant is only 8 other is variable 2x ÷ 15

Constant is only 8 other is variable ax + 9

Constant is only 8 other is variable 3x^{2} × 5x

Constant is only 8 other is variable 5 + 2a - 3b

Constant is only 8 other is variable 2y –`7/3` z ÷ x

Constant is only 8 other is variable 3p x q ÷ z

Constant is only 8 other is variable 12z ÷ 5x + 4

Constant is only 8 other is variable 12 – 5 z – 4

Constant is only 8 other is variable a^{3} – 3ab^{2} x c

Write the coefficient of: xy in – 3axy

Write the coefficient of: z^{2} in p^{2}yz

Write the coefficient of: mn in -mn

Write the coefficient of: 15 in – 15p^{2}

For the following monomials, write its degree: 7y

For the following monomials, write its degree: – x^{2}y

For the following monomials, write its degree: xy^{2}z

For the following monomials, write its degree: – 9y^{2}z^{3}

For the following monomials, write its degree: 3m^{3}n^{4}

For the following monomials, write its degree: – 2p^{2}q^{3}r^{4}

Write the degree of the following polynomial: 3y^{3} -x^{2}y^{2} + 4x

Write the degree of the following polynomial: p^{3}q^{2} – 6p^{2}q^{5} + p^{4}q^{4}

Write the degree of the following polynomial: – 8mn^{6}+ 5m^{3}n

Write the degree of the following polynomial: 7 – 3x^{2}y + y^{2}

Write the degree of the following polynomial: 3x – 15

Write the degree of the following polynomial: 2y^{2}z + 9yz^{3}

Group the like term together: 9x^{2}, xy, – 3x^{2}, x^{2} and – 2xy

Group the like term together: ab, – a^{2}b, – 3ab, 5a^{2}b and – 8a^{2}b

Group the like term together: 7p, 8pq, – 5pq – 2p and 3p

Write numerical co-efficient of the following: y

Write numerical co-efficient of the following: - y

Write numerical co-efficient of the following: 2 x^{2}y

Write numerical co-efficient of the following: – 8xy^{3}

Write numerical co-efficient of the following: 3py^{2}

Write numerical co-efficient of the following: – 9a^{2}b^{3}

In -5x^{3}y^{2}z^{4} ; write the coefficient of: z^{2} Also, write the degree of the given algebraic expression.

In -5x^{3}y^{2}z^{4} ; write the coefficient of y^{2} Also, write the degree of the given algebraic expression.

In -5x^{3}y^{2}z^{4} ; write the coefficient of yz^{2}. Also, write the degree of the given algebraic expression.

In -5x^{3}y^{2}z^{4} ; write the coefficient of x^{3}y. Also, write the degree of the given algebraic expression.

In -5x^{3}y^{2}z^{4} ; write the coefficient of -xy^{2}. Also, write the degree of the given algebraic expression.

In -5x^{3}y^{2}z^{4} ; write the coefficient of -5xy^{2}z. Also, write the degree of the given algebraic expression.

### Selina solutions for Concise Mathematics Class 7 ICSE Chapter 11 Fundamental Concepts (Including Fundamental Operations) Exercise 11 (B)

**Fill in the blank: **

8x + 5x = ________

**Fill in the blank: **

8x - 5x = ________

**Fill in the blank: **

6xy^{2} + 9xy^{2} = _____.

**Fill in the blank: **

6xy^{2} – 9xy^{2} = ______

**Fill in the blank: **

The sum of 8a, 6a and 5b = _______.

**Fill in the blank: **

The addition of 5, 7xy, 6 and 3xy = _____

**Fill in the blank: **

4a + 3b – 7a + 4b = _____

**Fill in the blank: **

- 15x + 13x + 8 = ______

**Fill in the blank: **

6x^{2}y + 13xy^{2} – 4x^{2}y + 2xy^{2} = _______

**Fill in the blank: **

16x^{2} – 9x^{2} = and 25xy^{2} – 17xy^{2} = _______.

Add : - 9x, 3x and 4x

Add : 23y^{2} , 8y^{2} and – 12y^{2}

Add : 18pq – 15pq and 3pq

Simplify : 3m + 12m – 5m

Simplify: 7n^{2} – 9n^{2} + 3n^{2}

Simplify: 25zy—8zy—6zy

Simplify: -5ax^{2} + 7ax^{2} – 12ax^{2}

Simplify: – 16am + 4mx + 4am – 15mx + 5am

Add : a + b and 2a + 3b

Add : 2x + y and 3x – 4y

Add : - 3a + 2b and 3a + b

Add : 4 + x, 5 – 2x and 6x

Find the sum of: 3x + 8y + 7z, 6y + 4z- 2x and 3y – 4x + 6z

Find the sum of: 3a + 5b + 2c, 2a + 3b-c and a + b + c.

Find the sum of: 4x^{2}+ 8xy – 2y^{2} and 8xy – 5y^{2} + x^{2}

Find the sum of: 9x^{2} – 6x + 7, 5 – 4x and 6 – 3x^{2}

Find the sum of: 5x^{2} – 2xy + 3y^{2} and – 2x^{2} + 5xy + 9y^{2} and 3x^{2} -xy- 4y^{2}

Find the sum of: a^{2} + b^{2} + 2ab, 2b^{2} + c^{2} + 2bc and 4c^{2} -a^{2} + 2ac

Find the sum of: 9ax – 6bx + 8, 4ax + 8bx – 7 and – 6ax – 46x – 3

Find the sum of: abc + 2 ba + 3 ac, 4ca – 4ab + 2 bca and 2ab – 3abc – 6ac

Find the sum of: 4a^{2} + 5b^{2} – 6ab, 3ab, 6a^{2} – 2b^{2} and 4b^{2} – 5 ab

Find the sum of: x^{2} + x – 2, 2x – 3x^{2} + 5 and 2x^{2} – 5x + 7

Find the sum of: 4x^{3} + 2x^{2} – x + 1, 2x^{3} – 5x^{2} – 3x + 6, x2 + 8 and 5x^{3} – 7x

Find the sum of: x and 3y

Find the sum of: -2a and +5

Find the sum of: – 4x^{2} and +7x

Find the sum of: + 4a and -7b

Find the sum of: x^{3}+3x^{2}y and 2y^{2}

Find the sum of: 11 and -by

The sides of a triangle are 2x + 3y, x + 5y and 7x – 2y, find its perimeter.

The two adjacent sides of a rectangle are 6a + 96 and 8a- 46. Find its, perimeter.

**Subtract the second expression from the first:**

2a + b, a + b

**Subtract the second expression from the first:**

- 2b + 2c, b + 3c

**Subtract the second expression from the first:**

5a + b, - 6b + 2a

**Subtract the second expression from the first:**

a^{3} - 1 + a, 3a - 2a^{2 }

**Subtract the second expression from the first:**

p + 2, 1

**Subtract the second expression from the first:**

x + 2y + z, - x - y - 3z

**Subtract the second expression from the first:**

3a^{2} - 8ab - 2b^{2} , 3a^{2} - 4ab + 6b^{2}

**Subtract the second expression from the first:**

4pq - 6p^{2} - 2q^{2} , 9p^{2}

**Subtract the second expression from the first:**

10abc, 2a^{2} + 2abc - 4b^{2}

**Subtract the second expression from the first:**

a^{2} + ab + c^{2}, a^{2} - d^{2}

Subtract: 4x from 8 - x

Subtract: - 8c from c + 3d

Subtract: - 5a - 2b from b + 6c

Subtract: 4p + p^{2} from 3p^{2} - 8p

Subtract: 5a - 3b + 2c from 4a - b - 2c

Subtract: - xy + yz - zx from xy - yz - xz

Subtract: 2x^{2} - 7xy - y^{2} from 3x^{2} - 5xy + 3y^{2}

Subtract: a^{2} - 3ab - 6b^{2} from 2b^{2} - a^{2} + 2ab

Subtract: 4x^{2} - 5x^{2}y + y^{2} from - 3y^{2} + 5xy^{2} - 7x^{2} - 9x^{2}y

Subtract: 6m^{3} + 4m^{2} + 7m - 3 from 3m^{3} + 4

Subtract – 5a^{2} – 3a + 1 from the sum of 4a^{2} + 3 – 8a and 9a – 7.

By how much does 8x^{3} – 6x^{2} + 9x – 10 exceed 4x^{3} + 2x^{2} + 7x -3?

What must be added to 2a^{3} + 5a – a^{2} – 6 to get a^{2} – a – a^{3} + 1?

What must be subtracted from a^{2} + b^{2} + lab to get – 4ab + 2b^{2}?

Find the excess of 4m^{2} + 4n^{2} + 4p^{2} over m^{2}+ 3n^{2} – 5p^{2 }

By how much is 3x^{3 }– 2x^{2}y + xy^{2} -y^{3} less than 4x^{3} – 3x^{2}y – 7xy^{2} +2y^{3}

Subtract the sum of 3a^{2} – 2a + 5 and a^{2} – 5a – 7 from the sum of 5a^{2} -9a + 3 and 2a – a^{2} – 1

The perimeter of a rectangle is 28x^{3}+ 16x^{2} + 8x + 4. One of its sides is 8x^{2} + 4x. Find the other side

The perimeter of a triangle is 14a^{2} + 20a + 13. Two of its sides are 3a^{2} + 5a + 1 and a^{2} + 10a – 6. Find its third side.

If x = 4a^{2} + b^{2} - 6ab; y = 3b^{2} - 2a^{2} + 8ab and z = 6a^{2} + 8b^{2} - 6ab find: x + y + z

If x = 4a^{2} + b^{2} - 6ab; y = 3b^{2} - 2a^{2} + 8ab and z = 6a^{2} + 8b^{2} - 6ab find: x - y - z

If m = 9x^{2} - 4xy + 5y^{2} and n = - 3x^{2} + 2xy - y^{2} find: 2m - n

If m = 9x^{2} - 4xy + 5y^{2} and n = - 3x^{2} + 2xy - y^{2} find: m + 2n

If m = 9x^{2} - 4xy + 5y^{2} and n = - 3x^{2} + 2xy - y^{2} find: m - 3n

Simplify: 3x + 5(2x + 6) - 7x

Simplify: 3(4y - 10) 2(y - 1)

Simplify: - (7 + 6x) - 7(x + 2)

Simplify: x - (x - y) - y - (y - x)

Simplify: 4x + 7y - (5y - 8) - 2x

Simplify: - 2m + 5 + 4(m - 3)

Simplify: 2x - y + 5 - (x - y)

Simplify: 2(x - y) - (x - 8)

Simplify: 4(3x - 8) - 3(5x + 3) - 2(6x - 8)

Simplify: 5(x - 4) - 3(x - 4) + 7(x - 4)

### Selina solutions for Concise Mathematics Class 7 ICSE Chapter 11 Fundamental Concepts (Including Fundamental Operations) Exercise 11 (C)

Multiply: 3x, 5x^{2}y and 2y

Multiply: 5, 3a and 2ab^{2}

Multiply: 5x + 2y and 3xy

Multiply: 6a - 5b and - 2a

Multiply: 4a + 5b and 4a - 5b

Multiply: 9xy + 2y^{2} and 2x - 3y

Multiply: - 3m^{2}n + 5mn - 4mn^{2} and 6m^{2}n

Multiply: 6xy^{2} - 7x^{2}y^{2} + 10x^{3} and - 3x^{2}y^{3}

**Copy and complete the following multi-plication:**

3a + 2b

× - 3xy

**Copy and complete the following multi-plication:**

9x + 5y

× - 3xy

**Copy and complete the following multi-plication:**

3xy - 2x^{2} - 6x

× -5x^{2}y

**Copy and complete the following multi-plication:**

a + b

× a + b

**Copy and complete the following multi-plication:**

ax - b

× 2ax + 2b^{2}

**Copy and complete the following multi-plication:**

2a - b + 3c

× 2a - 4b

**Copy and complete the following multi-plication:**

3m^{2} + 6m - 2n

× 5n - 3m

**Copy and complete the following multi-plication:**

6 - 3x + 2x^{2}

× 1 + 5x - x^{2}

**Copy and complete the following multi-plication:**

4x^{3} - 10x^{2} + 6x - 8

× 3 + 2x - x^{2}

Evaluate: (c + 5)(c - 3)

Evaluate: (3c - 5d)(4c - 6d)

Evaluate: `(1/2 "a" + 1/2 "b") (1/2 "a" - 1/2 "b")`

Evaluate: (a^{2} + 2ab + b^{2})(a + b)

Evaluate: (3x - 1)(4x^{3} - 2x^{2} + 6x - 3)

Evaluate: (4m - 2)(m^{2} + 5m - 6)

Evaluate: (8 - 12x + 7x^{2} - 6x^{3})(5 - 2x)

Evaluate: (4x^{2} - 4x + 1)(2x^{3} - 3x^{2} + 2)

Evaluate: (6p^{2} - 8pq + 2q^{2}) (- 5p)

Evaluate: - 4y (15 + 12y - 8z) (x - 2y)

Evaluate: (a^{2} + b^{2} + c^{2} - ab - bc - ca)(a + b + c)

Evaluate:

(i) (a + b)(a - b)

(ii) (a^{2} + b^{2})(a + b)(a - b); using the result of (i).

(iii) (a^{4} + b^{4})(a^{2} + b^{2})(a + b)(a - b); using the result of (ii).

Evaluate: (3x - 2y)(4x + 3y)

Evaluate: (3x - 2y)(4x + 3y) (8x - 5y)

Evaluate: (a + 5)(3a - 2)(5a + 1)

Evaluate: (a + 1)(a^{2} - a + 1) and (a - 1)(a^{2} + a + 1)

Evaluate: (5m - 2n)(5m + 2n)(25m^{2} + 4n^{2})

Multiply: mn^{4}, m^{3}n and 5m^{2}n^{3}

Multiply: 2mnpq, 4mnpq and 5 mnpq

Multiply: pq - pm and p^{2}m

Multiply: x^{3} - 3y^{3} and 4x^{2}y^{2}

Multiply: a^{3} - 4ab and 2a^{2}b

Multiply: x^{2} + 5yx - 3y^{2} and 2x^{2}y

Multiply: (2x + 3y)(2x + 3y)

Multiply: (2x - 3y)(2x + 3y)

Multiply: (2x + 3y)(2x - 3y)

Multiply: (2x - 3y)(2x - 3y)

Multiply: (-2x + 3y)(2x - 3y)

Multiply: (xy + 2b)(xy - 2b)

Multiply: (x - a)(x + 3b)

Multiply: (2x + 5y + 6)(3x + y - 8)

Multiply: (3x - 5y + 2)(5x - 4y - 3)

Multiply: (6x - 2y)(3x - y)

Multiply: (1 + 6x^{2} - 4x^{3})(-1 + 3x - 3x^{2})

### Selina solutions for Concise Mathematics Class 7 ICSE Chapter 11 Fundamental Concepts (Including Fundamental Operations) Exercise 11 (D)

Divide: - 16ab^{2}c by 6abc

Divide: 25x^{2}y by - 5y^{2}

Divide: 8x + 24 by 4

Divide: 4a^{2} - a by - a

Divide: 8m - 16 by - 8

Divide: - 50 + 40p by 10p

Divide: 4x^{3} - 2x^{2} by - x

Divide: 10a^{3} - 15a^{2}b by - 5a^{2}

Divide: 12x^{3}y - 8x^{2}y^{2} + 4x^{2}y^{3} by 4xy

Divide: 9a^{4}b - 15a^{3}b^{2} + 12a^{2}b^{3} by - 3a^{2}b

Divide: n^{2} - 2n + 1 by n - 1

Divide: m^{2} - 2mn + n^{2} by m - n

Divide: 4a^{2} + 4a + 1 by 2a + 1

Divide: p^{2} + 4p + 4 by p + 2

Divide: x^{2} + 4xy + 4y^{2} by x + 2y

Divide: 2a^{2} - 11a + 12 by a - 4

Divide: 6x^{2} + 5x - 6 by 2x + 3

Divide: 8a^{2} + 4a - 60 by 2a - 5

Divide: 9x^{2} - 24xy + 16y^{2} by 3x- 4y

Divide: 15x^{2} + 31xy + 14y^{2} by 5x + 7y

Divide: 35a^{3} + 3a^{2}b - 2ab^{2} by 5a - b

Divide: 6x^{3} + 5x^{2} - 21x + 10 by 3x - 2

The area of a rectangle is 6x^{2} – 4xy – 10y^{2} square unit and its length is 2x + 2y unit. Find its breadth.

The area of a rectangular field is 25x2 + 20xy + 3y2 square unit. If its length is 5x + 3y unit, find its breadth, Hence find its perimeter.

Divide: 2m^{3}n^{5} by - mn

Divide: 5x^{2} - 3x by x

Divide: 10x^{3}y - 9xy^{2} - 4x^{2}y^{2} by xy

Divide: 3y^{3} - 9ay^{2} - 6ab^{2}y by -3y

Divide: x^{5} - 15x^{4} - 10x^{2} by -5x^{2}

Divide: 12a^{2} + ax - 6x^{2} by 3a - 2x

Divide: 6x^{2} - xy - 35y^{2} by 2x - 5y

Divide: x^{3} - 6x^{2} + 11x - 6 by x^{2} - 4x + 3

Divide: m^{3} - 4m^{2} + m + 6 by m^{2} - m - 2

### Selina solutions for Concise Mathematics Class 7 ICSE Chapter 11 Fundamental Concepts (Including Fundamental Operations) Exercise 11 (E)

Simplify: `"x"/2+"x"/4`

Simplify: `"a"/10+"2a"/5`

Simplify: `"y"/4 +"3y"/5`

Simplify: `"x"/2 -"x"/8`

Simplify: `"3y"/4 -"y"/5`

Simplify: `"2p"/3 -"3p"/5`

Simplify: `"k"/2 + "k"/3 + "2k"/5`

Simplify: `"2x"/5 + "3x"/4 - "3x"/5`

Simplify: `"4a"/7 + "2a"/3 - "a"/7`

Simplify: `"2b"/5 - "7b"/15 + "13b"/3`

Simplify: `"6k"/7 - ("8k"/9 - "k"/3)`

Simplify: `"3a"/8 + "4a"/5 - ("a"/2 + "2a"/5)`

Simplify: `"x" + "x"/2 + "x"/3`

Simplify: `"y"/5 + "y" - "19y"/15`

Simplify: `"x"/5 + "x + 1"/2`

Simplify: `"x" + "x + 2"/3`

Simplify: `"3y"/5 - "y + 2"/2`

Simplify: `"2a + 1"/3 + "3a - 1"/2`

Simplify: `"k + 1"/2 + "2k - 1"/3 - "k + 3"/4`

Simplify: `"m"/5 - "m - 2"/3 + "m"`

Simplify: `(5 ("x" - 4))/3 + (2(5x - 3))/5 + (6(x - 4))/7`

Simplify: `("p" + "p"/3)("2p" + "p"/2)("3p" - "2p"/3)`

Simplify: `7/30 "of" ("p"/3 + "7p"/15)`

Simplify: `(2"p" + "p"/7) div ("9p"/10 + "4p")`

Simplify: `("5k"/8 - "3k"/5) div "k"/4`

Simplify: `("y"/6 + "2y"/3) div ("y" + ("2y" - 1)/3)`

### Selina solutions for Concise Mathematics Class 7 ICSE Chapter 11 Fundamental Concepts (Including Fundamental Operations) Exercise 11 (F)

**Enclose the given term in bracket as required:**

x – y – z = x - {…….)

**Enclose the given term in bracket as required:**

x^{2} – xy^{2} – 2xy – y^{2} = x^{2} – (……..)

**Enclose the given term in bracket as required:**

4a – 9 + 2b – 6 = 4a – (……..)

**Enclose the given term in bracket as required:**

x^{2} -y^{2} + z^{2} + 3x – 2y = x^{2} – (……..)

**Enclose the given term in bracket as required:**

– 2a^{2} + 4ab – 6a^{2}b^{2} + 8ab^{2} = – 2a (………)

Simplify: 2x – (x + 2y- z)

Simplify: p + q – (p – q) + (2p – 3q)

Simplify: 9x – (- 4x + 5)

Simplify: 6a – (- 5a – 8b) + (3a + b)

Simplify: (p – 2q) – (3q – r)

Simplify: 9a (2b – 3a + 7c)

Simplify: -5m (-2m + 3n – 7p)

Simplify: - 2x (x + y) + x^{2}

Simplify: `"b"("2b" - 1/"b") - "2b"("b" - 1/"b")`

Simplify: 8 (2a + 3b – c) – 10 (a + 2b + 3c)

Simplify: `"a"("a" + 1/"a") - "b"("b" - 1/"b") -"c"("c" + 1/"c")`

Simplify: 5 x (2x + 3y) – 2x (x – 9y)

Simplify: a + (b + c – d)

Simplify: 5 – 8x – 6 – x

Simplify: `2"a" +(6 - bar("a" - "b"))`

Simplify: 3x + [4x – (6x – 3)]

Simplify: 5b – {6a + (8 – b – a)}

Simplify: 2x-[5y- (3x -y) + x]

Simplify: 6a – 3 (a + b – 2)

Simplify: 8 [m + 2n-p – 7 (2m -n + 3p)]

Simplify: {9 – (4p – 6q)} – {3q – (5p – 10)}

Simplify: 2 [a – 3 {a + 5 {a – 2) + 7}]

Simplify: 5a – [6a – {9a – (10a – `bar("4a" - "3a"))}]`

Simplify: 9x + 5 – [4x – {3x – 2 (4x – 3)}]

Simplify: (x + y – z)x + (z + x – y)y – (x + y – z)z

Simplify: -1 [a - 3 {b - 4 (a - b - 8) + 4a} + 10]

Simplify: `"p"^2 - ["x"^2 - {"x"^2 - ("q"^2 - bar("x"^2 - "q"^2)) - "2y"^2}]`

Simplify: `10 – {4"a" – (7 – bar ("a" - 5) - (5"a" - bar(1 + "a")))`

Simplify: `7"a" ["8a" - (11"a" - (12"a" - bar"6a - 5a"))]`

Simplify: `8"x" - ["4y" - {"4x" + ("2x" - bar"2y - 2x")}]`

Simplify: `"x" - ("3y" - bar"4x - 3x" + 2z - bar"5y - 7x")`

## Chapter 11: Fundamental Concepts (Including Fundamental Operations)

## Selina solutions for Concise Mathematics Class 7 ICSE chapter 11 - Fundamental Concepts (Including Fundamental Operations)

Selina solutions for Concise Mathematics Class 7 ICSE chapter 11 (Fundamental Concepts (Including Fundamental Operations)) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Concise Mathematics Class 7 ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Concise Mathematics Class 7 ICSE chapter 11 Fundamental Concepts (Including Fundamental Operations) are Fundamental Concepts, Performs Operations (Addition and Subtraction) on Algebraic Expressions with Integral Coefficients Only., Terms, Factors and Coefficients of Expression, Algebraic Expressions.

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