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Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts

November 10, 2023May 18, 2022 by Raju

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts

ICSE Solutions Selina ICSE Solutions ML Aggarwal Solutions

APlusTopper.com provides step by step solutions for Selina Concise ICSE Solutions for Class 6 Mathematics. You can download the Selina Concise Mathematics ICSE Solutions for Class 6 with Free PDF download option. Selina Publishers Concise Mathematics for Class 6 ICSE Solutions all questions are solved and explained by expert mathematic teachers as per ICSE board guidelines.

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IMPORTANT POINTS

Algebra : Algebra is a generalized form of Arithmetic. In Arithmetic, we use numbers, such as : 3, – 8, 0.63, etc., each of which has one definite value ; whereas in Algebra, we use letters along with numbers.
For Example : 5x, 3x – 4, 7a + b, 3y – 5x, x + 3y – 9z, etc.
The letters used in Algebra are called variables or literal numbers or simply literals.
Signs and Symbols : In Algebra, the signs +, -, x and ÷ are used with the same meaning as in Arithmetic.
Following sign and symbols are frequently used in algebra and have the same meanings as they have in any other branch of Mathematics.
= means, “is equal to”
≠ means, “is not equal to”
< means, “is less than” > means, “is greater than”
\(\nless\) means, “is not less than”
\(\ngtr\) means, “is not greater than”
∴ means, “therefore”
∵ means, “because” or “since”
~ means, “difference between”
⇒ means, “implies that”.
To Write a Given Statement in Algebraic Form

Fundamental Concepts Exercise 18A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in algebraic form :
(i) The sum of 8 and x is equal to y.
(ii) x decreased by 5 is equal to y.
(iii) The sum of 2 and x is greater than y.
(iv) The sum of x and y is less than 24.
(v) 15 multiplied by m gives 3n.
(vi) Product of 8 and y is equal to 3x.
(vii) 30 divided by b is equal to p.
(viii) z decreased by 3x is equal to y.
(ix) 12 times of x is equal to 5z.
(x) 12 times of x is greater than 5z.
(xi) 12 times of x is less than 5z.
(xii) 3z subtracted from 45 is equal to y.
(xiii) 8x divided by y is equal to 2z.
(xiv) 7y subtracted from 5x gives 8z.
(xv) 7y decreased by 5x gives 8z.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 2

Question 2.
For each of the following algebraic expressions, write a suitable statement in words:
(i) 3x + 8=15
(ii) 7 – y > x
(iii) 2y – x < 12
(iv) 5 ÷ z = 5
(v) a + 2b > 18
(vi) 2x – 3y= 16
(vii) 3a – 4b > 14
(viii) b + 7a < 21
(ix) (16 + 2a) – x > 25
(x) (3x + 12) – y < 3a
Solution:
(i) 3x plus 8 is equal to 15
(ii) 1 decreased by y is greater than x
(iii) 2y decreased by x is less than 12
(iv) 5 divided by z is equal to 5
(v) a increased by 2b is greater than 18
(vi) 2x decreased by 3y is equal to 16
(vii) 3a decreased by 4b is greater than 14
(viii) b increased la is less than 21
(ix) The sum of 16 and 2a decreased by x is greater than 25
(x) The sum of 3x and 12 decreased by y is less than 3a.

Fundamental Concepts Exercise 18B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Separate the constants and the variables from each of the following:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 3
Solution:

Question 2.
Group the like terms together :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 5
Solution:

Question 3.
State whether true or false :
(i) 16 is a constant and y is a variable but 16y is variable.
(ii) 5x has two terms 5 and x.
(iii) The expression 5 + x has two terms 5 and x
(iv) The expression 2x² + x is a trinomial.
(v) ax² + bx + c is a trinomial.
(vi) 8 x ab is a binomial.
(vii) 8 + ab is a binomial.
(viii) x³ – 5xy + 6x + 7 is a polynomial.
(ix) x³ – 5xy + 6x + 7 is a multinomial.
(x) The coefficient of x in 5x is 5x.
(xi) The coefficient of ab in – ab is – 1.
(xii) The coefficient of y in – 3xy is – 3
Solution:
(i) True
(ii) False
(iii) True
(iv) False
(v) True
(vi) False
(vii) True
(viii) True
(ix) True
(x) False
(xi) True
(xii) False

Question 4.
State the number of terms in each of the following expressions :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 8
Solution:
(i) 2 terms
(ii) 2 terms
(iii) 2 terms
(iv) 2 terms
(v) 3 terms
(vi) 2 term
(vii) 2 terms
(viii) 3 terms
(ix) 3 terms

Question 5.
State whether true or false:
(i) xy and – yx are like terms.
(ii) x²y and – y²x are like terms.
(iii) a and – a are like terms.
(iv) – ba and 2ab are unlike terms.
(v) 5 and 5x are like terms.
(vi) 3xy and 4xyz are unlike terms.
Solution:
(i) True
(ii) False
(iii) True
(iv) False
(v) False
(vi) True

Question 6.
For each expression, given below, state whether it is a monomial, or a binomial or a trinomial.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 9
Solution:
(i) Monomial
(ii) Binomial
(iii) Monomial
(iv) Monomial
(v) Trinomial
(vi) Binomial
(vii) Trinomial
(viii) Binomial
(ix) Trinomial

Question 7.
Write down the coefficient of x in the following monomial :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 10
Solution:

Question 8.
Write the coefficient of :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 12
Solution:

Question 9.
State the numeral coefficient of the following monomials :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 14
(vii) – 7x ÷ y
(viii) – 3x ÷ (2y)
Solution:

Question 10.
Write the degree of each of the following polynomials :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 16
Solution:
(i) 2
(ii) 2
(iii) 10
(iv) 20
(v) 3

Fundamental Concepts Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in algebraic form :
(i) The sum of 3x and 4y is 8.
(ii) 5x decreased by 7 gives y.
(iii) 31 added to 4x gives 6x.
(iv) 3x subtracted from 89 gives 44.
Solution:
(i) 3x + 4y = 8
(ii) 5x – 7 = y
(iii) 4x + 37 = 6x
(iv) 89 – 3x = 44

Question 2.
Group the like terms :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 18
Solution:

Question 3.
Write the number of terms in each of the following polynomials :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 20
Solution:
(i) 2 terms
(ii) 3 terms
(iii) 3 terms
(iv) 4 terms
(v) 3 terms

Question 4.
For each expression, given below, state whether it is a monomial, or a binomial or a trinomial:
(i) x + y
(ii) 5x – 4y
(iii) 7x² + 5x + 8
(iv) 64 + 3 ÷ 6
(v) 9 ÷ a x b
(vi) 8a ÷ b
Solution:
(i) binomial
(ii) binomial
(iii) trinomial
(iv) 6a + 3 ÷ b = 6a + \(\frac { 3 }{ b }\)
It has two terms
It is binomial
(v) 9 ÷ a x b = \(\frac { 9b }{ a }\)
It has one term
It is monomial.
(vi) monomial

Question 5.
Write the coefficient of x2y in :
(i) -7x²yz
(ii) 8abx²y
(iii) – x²y
Solution:
(i) – 7z
(ii) 8ab
(iii) -1

Question 6.
Write the coefficient of :
(i) x² in – 8x²y
(ii) y in -4y
(iii) x in – xy²
Solution:
(i) – 8y
(ii) – 4
(iii) – y²

Question 7.
Write the numeral coefficient in :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 21
Solution:

Question 8.
Write the degree of each of the following polynomials :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 23
Solution:
(i) 8
(ii) 4
(iii) 2
(iv) 1
(v) 3

Question 9.
Write each statement, given below in algebraic form :
(i) 28 more than twice of x is equal to 45.
(ii) 3y reduced by 5z is greater than 8x.
(iii) 6x divided by 13y is less than 17.
(iv) 9 multiplied by 5x is equal to 2y.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts image - 26

Question 10.
State whether true or false :
(i) If 23 is a constant and x is a variable, 23 + x is constant.
(ii) If 23 is a constant and x is a variable, 23x is a variable.
(iii) If y is a variable and 57 is a constant, y – 57 is a variable.
(iv) If 3x and 2y are variable; each of 3x + 2y, 3x – 2y, 3x ÷ 2y and 3x x 2y is a variable.
Solution:
(i) False
Sum of a constant and a variable is also variable.
(ii) True
Product of a constant and a variable is variable.
(iii) True
Constant subtracted from a variable is also variable.
(iv) True
Sum, difference product or quotient of two variables is also variable.

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Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations

November 10, 2023May 18, 2022 by Raju

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations (Related to Algebraic Expressions)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations (Related to Algebraic Expressions)

ICSE Solutions Selina ICSE Solutions ML Aggarwal Solutions

Selina Class 6 Maths ICSE Solutions Physics Chemistry Biology Geography History & Civics

IMPORTANT POINTS

Fundamental Operations : In mathematics, the operations : addition (+), subtraction (-), multiplication (x) and division (÷) are called the four fundamental operations.
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.

Fundamental Operations Exercise 19A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) 5 + 4 = ………… and 5x + 4x = ………….
(ii) 12 + 18 = ………… and 12x²y + 18x²y = ………….
(iii) 7 + 16 = ………….. and 7a + 16b = …………
(iv) 1 + 3 = ………… and x²y + 3xy² = ………..
(v) 7 – 4 = …………… and 7ab – 4ab = …………..
(vi) 12 – 5 = ………… and 12x – 5y = ……………
(vii) 35 – 16 = ………….. and 35ab – 16ba = ………….
(viii) 28 – 13 = …………. and 28ax² – 13a²x = ………….
Solution:
(i) 5 + 4 = 9 and 5x + 4x = 9x
(ii) 12 + 18 = 30 and 12x²y + 18x²y = 30x²y
(iii) 7 + 16 = 23 and 7a + 16 b = 7a + 16b
(iv) 1 + 3 = 4 and x²y + 3xy² = x²y + 3xy²
(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 28ax² – 13a²x = 28ax² – 13a²x

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
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 1

Question 4.
Evaluate :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 3
Solution:
(i) 6a – a – 5a – 2a = 6a – (1 + 5 + 2).a

Question 5.
Evaluate :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 5
Solution:

Question 6.
Subtract the first term from the second :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 7
Solution:

Question 7.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 9

Solution:

Fundamental Operations Exercise 19B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the sum of :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 15
Solution:

Question 2.
Add the following expressions :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 19

Solution:

Question 3.
Evaluate :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 22
Solution:

Question 4.
Subtract :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 25
Solution:

Question 5.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 28
Solution:

Question 6.
From the sum of x + y – 2z and 2x – y + z subtract x + y + z.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 30

Question 7.
From the sum of 3a – 2b + 4c and 3b – 2c subtract a – b – c.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 31

Question 8.
Subtract x – 2y – z from the sum of 3x – y + z and x + y – 3z.
Solution:
(3x – y + z) + (x + y – 3 z) – (x – 2y – z)
= 3x – y + z + x + y – 3z – x + 2y + z
= 3x + x – x – y + y + 2y + z + z – 3z
= 3x + 2y – z

Question 9.
Subtract the sum of x + y and x – z from the sum of x – 2z and x + y + z
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 32

Question 10.
By how much should x + 2y – 3z be increased to get 3x ?
Solution:
3x – (x + 2y – 3z)
= 3x – x – 2y + 3z
= 2x – 2y + 3z

Question 11.
The sum of two expressions is 5x² – 3y². If one of them is 3x² + 4xy – y², find the other.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 33

Question 12.
The sum of two expressions is 3a² + 2ab – b². If one of them is 2a² + 3b², find the other.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 34

Fundamental Operations Exercise 19C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 35
Solution:
(i) 6 x 3 = 18 and 6x x 3x = 6 x 3x x x x = 18x²

Question 2.
Fill in the blanks :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 37
Solution:

Question 3.
Find the value of :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 40
Solution:

Question 4.
Multiply :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 42

Solution:

Question 5.
Multiply :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 45
Solution:

Question 6.
Multiply :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 48
Solution:

Question 7.
Multiply :
(i) x + 2 and x + 10
(ii) x + 5 and x – 3
(iii) x – 5 and x + 3
(iv) x – 5 and x – 3
(v) 2x+ y and x+ 3y
(vi) (3x – 5y) and (x + 6y)
(vii) (x + 9y) and (x – 5y)
(viii) (2x + 5y) and (2x + 5y)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 50

Question 8.
Multiply :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 52
Solution:

Question 9.
Find the product of :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 55
Solution:

Fundamental Operations Exercise 19D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Divide :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 59
Solution:

Question 2.
Simplify :

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 62
Solution:

Question 3.
Divide :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 65

Solution:

Question 4.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 69
Solution:

Question 5.
Divide :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations image - 71

Solution:

Selina Class 6 Maths ICSE Solutions Physics Chemistry Biology Geography History & Civics

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution

November 10, 2023May 18, 2022 by Raju

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution (Including Use of Brackets as Grouping Symbols)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution (Including Use of Brackets as Grouping Symbols)

ICSE Solutions Selina ICSE Solutions ML Aggarwal Solutions

Selina Class 6 Maths ICSE Solutions Physics Chemistry Biology Geography History & Civics

IMPORTANT POINTS

Substitution : The value of an expression depends on the value of its variable (s).
Use of Brackets :
The Symbols —, ( ), { }, [ ] are called brackets.
If an expression is enclosed within a bracket, it is considered a single quantity, even if it is made up of many terms.
Keep in Mind :
- While simplifying an expression containing a bracket, first of all, the terms inside the bracket are operated (combined).
- ( ) is called a small bracket or Parenthesis.
- { } is called a middle bracket or Curly bracket.
- [ ] is called big or square bracket.
- If one more bracket is needed, then we use the bar bracket.
  i.e. a line ———— is drawn over a group of terms.
  Thus, in \(3x+\bar { 4y-5z }\), the line over 4y – 5z serves as the bar bracket and is called Vinculum.

Substitution Exercise 20A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the following blanks, when :
x = 3,y = 6, z = 18, a = 2, b = 8, c = 32 and d = 0.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 1

Solution:

Question 2.
Find the value of :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 5
Solution:

Question 3.
Find the value of :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 8
Solution:

Question 4.
If a = 3, b = 0, c = 2 and d = 1, find the value of :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 10
Solution:

Question 5.
Find the value of 5x² – 3x + 2, when x = 2.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 13

Question 6.
Find the value of 3x³ – 4x² + 5x – 6, when x = -1.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 14

Question 7.
Show that the value of x³ – 8x² + 12x – 5 is zero, when x = 1.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 15

Question 8.
State true and false :
(i) The value of x + 5 = 6, when x = 1
(ii) The value of 2x – 3 = 1, when x = 0
(iii) \(\frac { 2x-4 }{ x+1 }\) = -1,when x = 1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 16

Question 9.
If x = 2, y = 5 and z = 4, find the value of each of the following :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 18
Solution:

Question 10.
If a = 3, find the values of a² and 2^a.
Solution:
a² = (3)² = 3 x 3 = 9
2^a = (2)³ = 2 x 2 x 2 = 8

Question 11.
If m = 2, find the difference between the values of 4m³ and 3m⁴.
Solution:
4m³ = 4 (2)³ = 4 x 2 x 2 x 2 = 32
3m⁴ = 3 (2)⁴ = 3 x 2 x 2 x 2 x 2 = 48
Now, a difference 3m⁴ – 4m³ = 48 – 32 = 16

Substitution Exercise 20B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Evaluate :
(i) (23 – 15) + 4
(ii) 5x + (3x + 7x)
(iii) 6m – (4m – m)
(iv) (9a – 3a) + 4a
(v) 35b – (16b + 9b)
(vi) (3y + 8y) – 5y
Solution:
(i) (23 – 15) + 4 = 8 + 4 = 12
(ii) 5x + (3x + 7x) = 5x + 10x = 15x
(iii) 6m – (4m – m) = 6m – 3m = 3m
(iv) (9a – 3a) + 4a = 6a + 4a = 10a
(v) 35b – (16b + 9b)= 35b – 25b = 10b
(vi) (3y + 8y) – 5y = 11y – 5y = 6y

Question 2.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 20

Solution:

Question 3.
Simplify :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 25
Solution:

Substitution Exercise 20C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 28
Solution:

(viii) 2t + r – p – q + s = 2t + r – (p + q – s)

Question 2.
Insert the bracket as indicated :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 30
Solution:

Substitution Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the value of 3ab + 10bc – 2abc when a = 2, b = 5 and c = 8.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 32

Question 2.
If x = 2, = 3 and z = 4, find the value of 3x² – 4y² + 2z².
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 33

Question 3.
If x = 3, y = 2 and z = 1; find the value of:
(i) x^y
(ii) y^x
(iii) 3x² – 5y²
(iv) 2x – 3y + 4z + 5
(v) y² – x² + 6z²
(vi) xy + y²z – 4zx
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 34

Question 4.
If P = -12x² – 10xy + 5y², Q = 7x² + 6xy + 2y², and R = 5x² + 2xy + 4y² ; find :
(i) P – Q
(ii) Q + P
(iii) P – Q + R
(iv) P + Q + R
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 35

Question 5.
If x = a² – bc, y = b² – ca and z = c² – ab ; find the value of :
(i) ax + by + cz
(ii) ay – bx + cz
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution image - 37

Question 6.
Multiply and then evaluate :
(i) (4x + y) and (x – 2y); when x = 2 and y = 1.
(ii) (x² – y) and (xy – y²); when x = 1 and y = 2.
(iii) (x – 2y + z) and (x – 3z); when x = -2, y = -1 and z = 1.
Solution:

Question 7.
Simplify :
(i) 5 (x + 3y) – 2 (3x – 4y)
(ii) 3x – 8 (5x – 10)
(iii) 6 {3x – 8 (5x – 10)}
(iv) 3x – 6 {3x – 8 (5x – 10)}
(v) 2 (3x² – 4x – 8) – (3 – 5x – 2x²)
(vi) 8x – (3x – \(\bar { 2x-3 }\))
(vii) 12x² – (7x – \(\bar { 3x^{ 2 }+15 }\))
Solution:

Question 8.
If x = -3, find the value of : 2x³ + 8x² – 15.
Solution:

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Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions

November 10, 2023May 18, 2022 by Raju

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions (Including Evaluation)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions (Including Evaluation)

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Framing Algebraic Expressions Exercise 21 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write in the form of an algebraic expression :
(i) Perimeter (P) of a rectangle is two times the sum of its length (l) and its breadth (b).
(ii) Perimeter (P) of a square is four times its side.
(iii) Area of a square is square of its side.
(iv) Surface area of a cube is six times the square of its edge.
Solution:
(i) Let P be the perimeter and / be the length, and b be the breadth.
P = 2 (l + b)
(ii) Let P be the perimeter and a be the side of the square.
P = 4a
(iii) Let A be the area of the square and a be the sides of the square.
A = (a)²
(iv) Let S be the surface area and a be the edges of the cube.
S = 6a²

Question 2.
Express each of the following as an algebraic expression :
(i) The sum of x and y minus m.
(ii) The product of x and y divided by m.
(iii) The subtraction of 5m from 3n and then adding 9p to it.
(iv) The product of 12, x, y and z minus the product of 5, m and n.
(v) Sum of p and 2r – s minus sum of a and 3n + 4x.
Solution:
(i) x + y – m
(ii) \(\frac { xy }{ m }\)
(iii) 3n – 5m + 9p
(iv) 12xyz – 5mn
(v) p + 2r – s – (a + 3n + 4x)

Question 3.
Construct a formula for the following :
Total wages (₹ W) of a man whose basic wage is (₹ B) for t hours week plus (₹ R) per hour, if he Works a total of T hours.
Solution:
Wages for t hours = ₹ B
Wages for overtime = R(T – t)
=> Total wages = Wages for t hours + wages for overtime of (T – t) hours
=> ₹ W = ₹ B + ₹ R (T – t)

Question 4.
If x = 4, evaluate :
(i) 3x + 8
(ii) x² – 2x
(iii) \(\frac { { x }^{ 2 } }{ 2 }\)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 1

Question 5.
If m – 6, evaluate :
(i) 5m – 6
(ii) 2m² + 3m
(iii) (2m)²
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 2

Question 6.
If x = 4, evaluate :
(i) 12x + 7
(ii) 5x² + 4x
(iii) \(\frac { { x }^{ 2 } }{ 8 }\)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 3

Question 7.
If m = 2, evaluate :
(i) 16m – 7
(ii) 15m² – 10m
(iii) \(\frac { 1 }{ 4 } \times { m }^{ 3 }\)
Solution:
16m – 7
= (16 x 2) – 7
= 32 – 7 = 25
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 4

Question 8.
If x = 10, evaluate :
(i) 100x + 225
(ii) 6x² – 25x
(iii) \(\frac { 1 }{ 50 } \times { x }^{ 3 }\)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 5

Question 9.
If a = – 10, evaluate :
(i) 5a
(ii) a²
(iii) a³
Solution:
(i)5a
= 5 x (-10) = -50
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 6

Question 10.
If x = – 6, evaluate :
(i) 11x
(ii) 4x²
(iii) 2x³
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 7

Question 11.
If m = – 7, evaluate :
(i) 12m
(ii) 2m²
(iii) 2m³
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 8

Question 12.
Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7 ; find the value of s.
Solution:
Given, average of four quantities (A) = 6
and p = 3,q = 5, r = 7 and s = ?
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 9

Question 13.
If a = 5 and b = 6, evaluate :
(i) 3ab
(ii) 6a²b
(iii) 2b²
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 10

Question 14.
If x = 8 and y = 2, evaluate :
(i) 9xy
(ii) 5x²y
(iii) (4y)²
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 11

Question 15.
If x = 5 and y = 4, evaluate :
(i) 8xy
(ii) 3x²y
(iii) 3y²
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 13

Question 16.
If y = 5 and z = 2, evaluate :
(i) 100yz
(ii) 9y²z
(iii) 5y²
(iv) (5z)³
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 14

Question 17.
If x = 2 and y = 10, evaluate :
(i) 30xy
(ii) 50xy²
(iii) (10x)²
(iv) 5y²
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 15

Question 18.
If m = 3 and n = 7, evaluate :
(i) 12mn
(ii) 5mn²
(iii) (10m)²
(iv) 4n²
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 16

Question 19.
If a = -10, evaluate :
(i) 3a – 2
(ii) a² + 8a
(iii) \(\frac { 1 }{ 5 }\) x a2
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 17

Question 20.
If x = -6, evaluate :
(i) 4x – 9
(ii) 3x² + 8x
(iii) \(\frac { { x }^{ 2 } }{ 2 }\)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 18

Question 21.
If m = -8, evaluate :
(i) 2m + 21
(ii) m² + 9m
(iii) \(\frac { { m }^{ 2 } }{ 4 }\)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 20

Question 22.
If p = -10, evaluate :
(i) 6p + 50
(ii) 3p² – 20p
(iii) \(\frac { { p }^{ 2 } }{ 50 }\)
Solution:
(i) 6p + 50
= (6 x p) + 50
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 21

Question 23.
If y = -8, evaluate :
(i) 6y + 53
(ii) y²+ 12y
(iii) \(\frac { { y }^{ 3 } }{ 4 }\)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 22

Question 24.
If x = 2 and 7 = -4, evaluate :
(i) 11xy
(ii) 5x²y
(iii) (5y)²
(iv) 8x²
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 24

Question 25.
If m = 9 and n = -2, evaluate
(i) 4mn
(ii) 2m²n
(iii) (2n)³
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 25

Question 26.
If m = -8 and n = -2, evaluate :
(i) 12mn
(ii) 3m²n
(iii) (4n)²
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 27

Question 27.
If x = -5 and y = -8, evaluate :
(i) 4xy
(ii) 2xy²
(iii) 4x²
(iv) 3y²
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions image - 28

Question 28.
Find T, if T = 2a – b, a = 7 and b = 3.
Solution:
T = 2a – b, a = 1 and b = 3
Put the value of a = 1, and b = 3 in above equation
T = (2 x 7) -3
T = 14 – 3 = 11
T = 11

Question 29.
From the formula B = 2a² – b², calculate the value of B when a = 3 and b = -1.
Solution:
B = 2a² – b²
Put the values of a = 3 and b = -1 in above equation
B = 2 x (3)² – (-1)²
B = 18 – 1
B = 17
Value of B is = 17

Question 30.
The wages ₹ W of a man earning ₹ x per hour for t hours are given by the formula W = xt. Find his wages for working 40 hours at a rate of ₹ 39.45 per hour.
Solution:
T = 40 hours
x = ₹ 39.45
W = xt = 40 x 39.45
W = ₹ 1578

Question 31.
The temperature in Fahrenhiet scale is represented by F and the tempera¬ture in Celsius scale is represented by C. If F = \(\frac { 9 }{ 5 }\) x C + 32, find F when C = 40.
Solution:
F = \(\frac { 9 }{ 5 }\) x C + 32
Given, C = 40
F = \(\frac { 9 }{ 5 }\) x 40 + 32 = 9 x 8 + 32
F = 104°

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Selina Concise Mathematics Class 6 ICSE Solutions Chapter 3 Numbers in India and International System

November 10, 2023May 16, 2022 by Raju

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 3 Numbers in India and International System (With Comparison)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 3 Numbers in India and International System (With Comparison)

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IMPORTANT POINTS

Place -Value (Local Value) : The place – value (Local-value) of a digit depends upon the position, it occupies in the number:
For example :
In the number 6453 the place value of 6 is 6 thousand = 6 x 1000 = 6000
the place value of 4 is 4 hundred = 4 x 100 = 400
the place value of 5 is 5 ten = 5 x 10 = 50
the place value of 3 is 3 one = 3 x 1=3
Face -Value (True-Value) : Each digit in a number has a fixed value, regardless to its position in the number
For Example :
In the above number 6453
Face of value of 6 is 6, 4 is 4, 5 is 5 and 3 is 3
An Abstract Number : Which does not refer to any particular unit e.g., 3, 5, 9.
A Concrete Number : Which refers to particular unit e.g., 3 boys, 5 girls, 9 rooms etc.
The smallest (least) one digit Number is 1.
The largest (greatest) one digit number is 9.

Numbers in India and International System Exercise 3 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write the following numerals using Indian System words or International system (as required in words) :
(i) 4, 35, 342 = …………..
(ii) 36, 71, 430 = …………..
(iii) 4, 28, 30, 004 = …………..
(iv) 75, 132, 684 = ……………
(v) 815, 906 = …………….
(vi) 5, 420, 700 = ……………..
Solution:
(i) 4, 35, 342 = four lakh, thirty five thousand, three hundred forty two
(ii) 36, 71, 430 = Thirty six lakh, seventy one thousand four hundred thirty
(iii) 4, 28, 30, 004 = four crore, twenty eight lakh, thirty thousand four
(iv) 75, 132, 684 = Seventy five million, one hundred thirty two thousand, six hundred eighty four
(v) 815, 906 = Eight hundred fifteen thousand, nine hundred six
(vi) 5, 420, 700 = Five million, four hundred twenty thousand, seven hundred

Question 2.
Write the following numbers, placing the commas, according to Indian system :
(i) 835629 = …………
(ii) 35640254 = …………
(iii) 2826040 = ………
Solution:
(i) 835629 = 8, 35, 629
(ii) 35640254 = 3, 56, 40, 254
(iii) 2826040 = 28, 26, 041

Question 3.
Write the following numbers, by placing the commas, according to International system :
(i) 6509820 = ………..
(ii) 428140584 = …………
(iii) 63560981 = ……….
Solution:
(i) 6509820 = 6, 509, 820
(ii) 428140584 = 428, 140, 584
(iii) 63560981 = 63, 560, 981

Question 4.
Fill in the blanks :
(i) Four lakh sixty seven thousand three hundred six.
= ……………… (In numeral form)
= …………… (In International System)
= ……………. (In International numeration)
(ii) Thirteen lakh forty five.
= ……………. (In numeral form)
= ……………. (In International System)
= ……………. (In International numerals)
Solution:
(i) Four lakh sixty seven thousand three hundred six
= 4, 67, 306
= 467, 306
= Four hundred sixty seven thousand three hundred six
(ii) Thirteen lakh forty five
= 13, 00, 45
= 130, 045
= One hundred thirty thousand forty five

Question 5.
Fill in the blanks :
(i) Six hundred four thousand eight hundred forty seven.
= ……………. (In numeral form)
= ……………. (In Indian System)
= ……………… (Number name in Indian System)
(ii) Two million three hundred ten thousand one hundred four
= …………….. (In numeral form)
= …………… (In Indian System)
= ……………. (In Indian numeration)
= …………….. (In international numerals)
Solution:
(i) Six hundred four thousand eight hundred forty seven
= 6, 04, 847
= 604, 847
= Six lakh four thousand eight hundred forty seven
(ii) Two million three hundred ten thousand one hundred four
= 2, 310, 104
= 23, 10, 104
= Twenty three lakh ten thousand one hundred four
= 2, 310, 104

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