Selina Solutions for Class 6, maths Chapter 18

Class 6: Maths Chapter 18 solutions. Complete Class 6 Maths Chapter 18 Notes.

Contents

1 Selina Class 6 ICSE Solutions Mathematics : Chapter 18- Fundamental Concepts
- 1.1 Exercise 18(A)
- 1.2 Exercise 18(B)
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3 Chapterwise Selina Publishers ICSE Solutions for Class 6 Mathematics :
4 About Selina Publishers ICSE

Selina Class 6 ICSE Solutions Mathematics : Chapter 18- Fundamental Concepts

Selina 6th Maths Chapter 18, Class 6 Maths Chapter 18 solutions

Exercise 18(A)

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:

(i) The sum of 8 and x is equal to y in algebraic form is written as,

8 + x = y

(ii) x decreased by 5 is equal to y in algebraic form is written as,

x – 5 = y

(iii) The sum of 2 and x is greater than y in algebraic form is written as,

2 + x > y

(iv) The sum of x and y is less than 24 in algebraic form is written as,

x + y < 24

(v) 15 multiplied by m gives 3n in algebraic form is written as,

15 × m = 3n

(vi) Product of 8 and y is equal to 3x in algebraic form is written as,

8 × y = 3x

(vii) 30 divided by b is equal to p in algebraic form is written as,

30 ÷ b = p

(viii) z decreased by 3x is equal to y in algebraic form is written as,

z – 3x = y

(ix) 12 times of x is equal to 5z in algebraic form is written as,

12 × x = 5z

(x) 12 times of x is greater than 5z in algebraic form is written as,

12 × x > 5z

(xi) 12 times of x is less than 5z in algebraic form is written as,

12 × x < 5z

(xii) 3z subtracted from 45 is equal to y in algebraic form is written as,

45 – 3z = y

(xiii) 8x divided by y is equal to 2z in algebraic form is written as,

8x ÷ y = 2z

(xiv) 7y subtracted from 5x gives 8z in algebraic form is written as,

5x – 7y = 8z

(xv) 7y decreased by 5x gives 8z in algebraic form is written as,

7y – 5x = 8z

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) The algebraic expression 3x + 8 = 15 in words is expressed as,

3x plus 8 is equal to 15

(ii) The algebraic expression 7 – y > x in words is expressed as,

7 decreased by y is greater than x

(iii) The algebraic expression 2y – x < 12 in words is expressed as,

2y decreased by x is less than 12

(iv) The algebraic expression 5 ÷ z = 5 in words is expressed as,

5 divided by z is equal to 5

(v) The algebraic expression a + 2b > 18 in words is expressed as,

a increased by 2b is greater than 18

(vi) The algebraic expression 2x – 3y = 16 in words is written as,

2x decreased by 3y is equal to 16

(vii) The algebraic expression 3a – 4b > 14 in words is written as,

3a decreased by 4b is greater than 14

(viii) The algebraic expression b + 7a < 21 in words is written as,

b increased by 7a is less than 21

(ix) The algebraic expression (16 + 2a) – x > 25 in words is written as,

The sum of 16 and 2a decreased by x is greater than 25

(x) The algebraic expression (3x + 12) – y < 3a in words is written as,

The sum of 3x and 12 decreased by y is less than 3a

Exercise 18(B)

1. Separate the constants and the variables from each of the following:

6, 4y, -3x, 5 / 4, (4 / 5)xy, az, 7p, 0, 9x / y, 3 / 4x, – xz / 3y

Solution:

6, 5 / 4and 0 are the constants

4y, -3x, (4 / 5)xy, az, 7p, 9x / y, 3 / 4x and – xz / 3y are the variables

2. Group the like terms together:

(i) 4x, -3y, -x, (2 / 3)x, (4 / 5)y and y.

(ii) (2 / 3) xy, -4yx, 2yz, (-2 / 3)yz, zy / 3 and yx.

(iii) –ab², b²a², 7b²a, -3a²b² and 2ab²

(iv) 5ax, -5by, by / 7, 7xa and 2ax / 3

Solution:

(i) 4x, -3y, -x, (2 / 3)x, (4 / 5)y and y.

Here, the like term are as follows

4x, -x, (2 / 3)x and -3y, (4 / 5)y, y

(ii) (2 / 3) xy, -4yx, 2yz, (-2 / 3)yz, zy / 3 and yx.

Here, the like terms are as follows

(2 / 3) xy, -4yx, yx and 2yz, (-2 / 3)yz, zy / 3

(iii) –ab², b²a², 7b²a, -3a²b² and 2ab²

Here, the like terms are as follows

-ab², 7b²a, 2ab² and b²a², -3a²b²

(iv) 5ax, -5by, by / 7, 7xa and 2ax / 3

Here, the like terms are as follows

5ax, 7xa, 2ax / 3 and – 5by, by / 7

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 × 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) 16 is a constant and y is a variable but 16y is variable

The given statement is true

(ii) 5x has two terms 5 and x

The given statement is false

(iii) The expression 5 + x has two terms 5 and x

The given statement is true

(iv) The expression 2x² + x is a trinomial

The given statement is false

(v) ax² + bx + c is a trinomial

The given statement is true

(vi) 8 × ab is a binomial

The given statement is false

(vii) 8 + ab is a binomial

The given statement is true

(viii) x³ – 5xy + 6x + 7 is a polynomial

The given statement is true

(ix) x³ – 5xy + 6x + 7 is a multinomial

The given statement is true

(x) The coefficient of x in 5x is 5x

The given statement is false

(xi) The coefficient of ab in –ab is -1

The given statement is true

(xii) The coefficient of y in -3xy is -3

The given statement is false

4. State the number of terms in each of the following expressions:

(i) 2a – b

(ii) 3 × x + a / 2

(iii) 3x – x / p

(iv) a ÷ x × b + c

(v) 3x ÷ 2 + y + 4

(vi) xy ÷ 2

(vii) x + y ÷ a

(viii) 2x + y + 8 ÷ y

(ix) 2 × a + 3 ÷ b + 4

Solution:

(i) 2a – b

The number of terms in given expression is two

(ii) 3 × x + a / 2

The number of terms in given expression is two

(iii) 3x – x / p

The number of terms in given expression is two

(iv) a ÷ x × b + c

The number of terms in given expression is two

(v) 3x ÷ 2 + y + 4

The number of terms in given expression is three

(vi) xy ÷ 2

The number of terms in given expression is one

(vii) x + y ÷ a

The number of terms in given expression is two

(viii) 2x + y + 8 ÷ y

The number of terms in given expression is three

(ix) 2 × a + 3 ÷ b + 4

The number of terms in given expression is three

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) xy and –yx are like terms

Yes, xy and –yx are like terms. Hence, the given statement is true

(ii) x²y and –y²x are like terms

No, x²y and –y²x are not like terms. Hence, the given statement is false

(iii) a and –a are like terms.

Yes, a and –a are like terms. Hence, the given statement is true

(iv) –ba and 2ab are unlike terms.

No, –ba and 2ab are like terms. Hence, the given statement is false

(v) 5 and 5x are like terms.

No, 5 and 5x are not like terms. Hence, the given statement is false

(vi) 3xy and 4xyz are unlike terms.

Yes, 3xy and 4xyz are unlike terms. Hence, the given statement is true

6. For each expression, given below, state whether it is a monomial, or a binomial or a trinomial.

(i) xy

(ii) xy + x

(iii) 2x ÷ y

(iv) –a

(v) ax² – x + 5

(vi) -3bc + d

(vii) 1 + x + y

(viii) 1 + x ÷ y

(ix) x + xy – y²

Solution:

(i) xy

Here xy has one term

Therefore, xy is a monomial

(ii) xy + x

Here xy + x has two terms

Therefore, xy + x is a binomial

(iii) 2x ÷ y

Here 2x ÷ y has one term

Therefore, 2x ÷ y is monomial

(iv) –a

Here –a has one term

Therefore, –a is a monomial

(v) ax² – x + 5

Here ax² – x + 5 has three terms

Therefore, ax² – x + 5 is a trinomial

(vi) -3bc + d

Here -3bc + d has two terms

Therefore, -3bc + d is a binomial

(vii) 1 + x + y

Here 1 + x + y has three terms

Therefore, 1 + x + y is a trinomial

(viii) 1 + x ÷ y

Here 1 + x ÷ y has two terms

Therefore, 1 + x ÷ y is a binomial

(ix) x + xy – y²

Here x + xy – y² has three terms

Therefore, x + xy – y² is a trinomial

7. Write down the coefficient of x in the following monomial:

(i) x

(ii) –x

(iii) -3x

(iv) -5ax

(v) 3 / 2 xy

(vi) ax / y

Solution:

(i) x

The coefficient of x in the given monomial x is 1

(ii) – x

The coefficient of x in the given monomial –x is -1

(iii) -3x

The coefficient of x in the given monomial -3x is -3

(iv) -5ax

The coefficient of x in the given monomial -5ax is -5a

(v) 3 / 2 xy

The coefficient of x in the given monomial is (3 / 2)y

(vi) ax / y

The coefficient of x in the given monomial is (a / y)

8. Write the coefficient of:

(i) x in -3xy²

(ii) x in –ax

(iii) y in –y

(iv) y in (2 / a)y

(v) xy in -2xyz

(vi) ax in –axy²

(vii) x²y in -3ax²y

(viii) xy² in 5axy²

Solution:

(i) x in -3xy²

– 3y² is the coefficient of x in -3xy²

(ii) x in –ax

– a is the coefficient of x in –ax

(iii) y in –y

-1 is the coefficient of y in –y

(iv) y in (2 / a)y

(2 / a) is the coefficient of y in (2 / a)y

(v) xy in -2xyz

– 2z is the coefficient of xy in -2xyz

(vi) ax in –axy²

– y² is the coefficient of ax in –axy²

(vii) x²y in -3ax²y

– 3a is the coefficient of x²y in -3ax²y

(viii) xy² in 5axy²

5a is the coefficient of xy² in 5axy²

9. State the numeral coefficient of the following monomials:

(i) 5xy

(ii) abc

(iii) 5pqr

(iv) -2x / y

(v) (2 / 3) xy²

(vi) -15xy / 2z

(vii) -7x ÷ y

(viii) -3x ÷ (2y)

Solution:

(i) 5xy

The numeral coefficient of the given monomial is 5

(ii) abc

The numeral coefficient of the given monomial is 1

(iii) 5pqr

The numeral coefficient of the given monomial is 5

(iv) -2x / y

The numeral coefficient of the given monomial is -2

(v) (2 / 3) xy²

The numeral coefficient of the given monomial is (2 / 3)

(vi) -15xy / 2z

The numeral coefficient of the given monomial is (-15 / 2)

(vii) -7x ÷ y

The numeral coefficient of the given monomial is -7 ÷ 1 = -7

(viii) -3x ÷ (2y)

The numeral coefficient of the given monomial is -3 ÷ 2 i.e. (-3 / 2)

10. Write the degree of each of the following polynomials:

(i) x + x²

(ii) 5x² – 7x + 2

(iii) x³ – x⁸ + x¹⁰

(iv) 1 – 100x²⁰

(v) 4 + 4x – 4x³

(vi) 8x²y – 3y² + x²y⁵

(vii) 8z³ – 8y²z³ + 7yz⁵

(viii) 4y² – 3x³ + y²x⁷

Solution:

(i) x + x²