Selina solutions for Mathematics [English] Class 6 chapter 18 - Fundamental Concepts of algebra [Latest edition]

Express the following statement in algebraic form:

The sum of 8 and x is equal to y.

Express the following statement in algebraic form:

x decreased by 5 is equal to y.

Express the following statement in algebraic form:

The sum of 2 and x is greater than y.

Express the following statement in algebraic form:

The sum of x and y is less than 24.

Express the following statement in algebraic form:

15 multiplied by m gives 3n.

Express the following statement in algebraic form:

Product of 8 and y is equal to 3x.

Express the following statement in algebraic form:

30 divided by b is equal to p.

Express the following statement in algebraic form:

z decreased by 3x is equal to y.

Express the following statement in algebraic form:

12 times of x is equal to 5z.

Express the following statement in algebraic form:

12 times of x is greater than 5z.

Express the following statement in algebraic form:

12 times of x is less than 5z.

Express the following statement in algebraic form:

3z subtracted from 45 is equal to y.

Express the following statement in algebraic form:

8x divided by y is equal to 2z.

Express the following statement in algebraic form:

7y subtracted from 5x gives 8z.

Express the following statement in algebraic form:

7y decreased by 5x gives 8z.

For the following algebraic expression, write a suitable statement in words:

3x + 8=15

For the following algebraic expression, write a suitable statement in words:

7 – y > x

For the following algebraic expression, write a suitable statement in words:

2y – x < 12

For the following algebraic expression, write a suitable statement in words:

5 ÷ z = 5

For the following algebraic expression, write a suitable statement in words:

a + 2b > 18

For the following algebraic expression, write a suitable statement in words:

2x – 3y= 16

For the following algebraic expression, write a suitable statement in words:

3a – 4b > 14

For the following algebraic expression, write a suitable statement in words:

b + 7a < 21

For the following algebraic expression, write a suitable statement in words:

(16 + 2a) – x > 25

For the following algebraic expression, write a suitable statement in words:

(3x + 12) – y < 3a

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

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

Group the like term together:

`4"x",-3"y",-"x",2/3"x",4/5"y"` and y.

Group the like term together:

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

Group the like term together:

− ab², b²a², 7b²a, − 3a²b² and 2ab²

Group the like term together:

5ax, − 5by, `"by"/7`, 7xa and `(2"ax")/3`.

State whether true or false:

16 is a constant and y is a variable but 16y is variable.

State whether true or false:

5x has two terms 5 and x.

State whether true or false:

The expression 5 + x has two terms 5 and x

State whether true or false:

The expression 2x² + x is a trinomial.

State whether true or false:

ax² + bx + c is a trinomial.

State whether true or false:

8 × ab is a binomial.

State whether true or false:

8 + ab is a binomial.

State whether true or false:

x³ – 5xy + 6x + 7 is a polynomial.

State whether true or false:

x³ – 5xy + 6x + 7 is a multinomial.

State whether true or false:

The coefficient of x in 5x is 5x.

State whether true or false:

The coefficient of ab in – ab is – 1.

State whether true or false:

The coefficient of y in – 3xy is – 3

State the number of the term of the following expression:

2a − b

State the number of the term of the following expression:

`3xx"x"+"a"/2`

State the number of the term of the following expression:

`3"x"-"x"/"p"`

State the number of the term of the following expression:

a ÷ x × b + c

State the number of the term of the following expression:

3x ÷ 2 + y + 4

State the number of the term of the following expression:

xy ÷ 2

State the number of the term of the following expression:

x + y ÷ a

State the number of the term of the following expression:

2x + y + 8 ÷ y

State the number of the term of the following expression:

2 × a + 3 ÷ b + 4

State whether true or false:

xy and – yx are like terms.

State whether true or false:

x²y and – y²x are like terms.

State whether true or false:

a and – a are like terms.

State whether true or false:

– ba and 2ab are unlike terms.

State whether true or false:

5 and 5x are like terms.

State whether true or false:

3xy and 4xyz are unlike terms.

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

xy

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

xy + x

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

2x ÷ y

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

− a

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

ax² − x + 5

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

− 3bc + d

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

1 + x + y

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

1 + x ÷ y

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

x + xy − y²

Write down the coefficient of x in the following monomial:

x

Write down the coefficient of x in the following monomial:

− x

Write down the coefficient of x in the following monomial:

− 3x

Write down the coefficient of x in the following monomial:

− 5ax

Write down the coefficient of x in the following monomial:

`3/2`xy

Write down the coefficient of x in the following monomial:

`"ax"/"y"`

Write the coefficient of x in − 3xy²

Write the coefficient of x in − ax

Write the coefficient of y in − y

Write the coefficient of y in `2/"a""y"`

Write the coefficient of xy in − 2xyz

Write the coefficient of ax in − axy²

Write the coefficient of x²y in − 3ax²y

Write the coefficient of xy² in 5axy²

State the numeral coefficient of the following monomial:

5xy

State the numeral coefficient of the following monomial:

abc

State the numeral coefficient of the following monomial:

5pqr

State the numeral coefficient of the following monomial:

`(-2"x")/"y"`

State the numeral coefficient of the following monomial:

`2/3"xy"^2`

State the numeral coefficient of the following monomial:

`(-15"xy")/(2"z")`

State the numeral coefficient of the following monomial:

– 7x ÷ y

State the numeral coefficient of the following monomial:

– 3x ÷ (2y)

Write the degree of the following polynomial:

x + x²

Write the degree of the following polynomial:

5x² − 7x + 2

Write the degree of the following polynomial:

x³ − x⁸ + x¹⁰

Write the degree of the following polynomial:

1 − 100x²⁰

Write the degree of the following polynomial:

4 + 4x − 4x³

Write the degree of the following polynomial:

8x²y − 3y² + x²y⁵

Write the degree of the following polynomial:

8z³ − 8y²z³ + 7yz⁵

Write the degree of the following polynomial:

4y² − 3x³ + y²x⁷

Express the following statement in algebraic form:

The sum of 3x and 4y is 8.

Express the following statement in algebraic form:

5x decreased by 7 gives y.

Express the following statement in algebraic form:

31 added to 4x gives 6x.

Express the following statement in algebraic form:

3x subtracted from 89 gives 44.

Group the like term:

7y, 3x, − 8y, − x and `"x"/5`

Group the like term:

3x², − 5x³, − x², 5x² and 8x³

Group the like term:

x²y³, − 5x³y², 8x³y², − 4x²y³ and − x²y³

Write the number of the term of the following polynomial:

5 + 4x ÷ 2

Write the number of the term of the following polynomial:

5 + 4x + 2y

Write the number of the term of the following polynomial:

8x² − 4x + 7

Write the number of the term of the following polynomial:

`"x"/5+"x"^2/7-"x"^3/8-1/4`

Write the number of the term of the following polynomial:

6x² ÷ x − 18 ÷ 9 + x²

For expression given below, state whether it is a monomial, or a binomial or a trinomial:

x + y

For expression given below, state whether it is a monomial, or a binomial or a trinomial:

5x – 4y

For expression given below, state whether it is a monomial, or a binomial or a trinomial:

7x² + 5x + 8

For expression given below, state whether it is a monomial, or a binomial or a trinomial:

6a + 3 ÷ b

For expression given below, state whether it is a monomial, or a binomial or a trinomial:

9 ÷ a × b

For expression given below, state whether it is a monomial, or a binomial or a trinomial:

8a ÷ b

Write the coefficient of x²y in:

− 7x²yz

Write the coefficient of x²y in:

8abx²y

Write the coefficient of x²y in:

– x²y

Write the coefficient of x² in – 8x²y

Write the coefficient of y in − 4y

Write the coefficient of x in – xy²

Write the numeral coefficient in 7x²y

Write the numeral coefficient in `(2"x")/3`

Write the numeral coefficient in `-5/4"xy"^2"z"`

Write the degree of the following polynomial:

x⁵ − 6x⁸ + x

Write the degree of the following polynomial:

4x³ − x⁴

Write the degree of the following polynomial:

4 − x²

Write the degree of the following polynomial:

x − 1

Write the degree of the following polynomial:

x² + x − x³

Write the degree of the following polynomial:

x³ − 8xy² + x³y³

Write the degree of the following polynomial:

x⁷ − 6y⁴

Write the degree of the following polynomial:

3y³ − 2y²z⁴

Write the degree of the following polynomial:

100x⁸ − 8x¹⁰⁰

Write the statement given below in algebraic form:

28 more than twice of x is equal to 45.

Write the statement given below in algebraic form:

3y reduced by 5z is greater than 8x.

Write the statement given below in algebraic form:

6x divided by 13y is less than 17.

Write the statement given below in algebraic form:

9 multiplied by 5x is equal to 2y.

State whether true or false:

If 23 is a constant and x is a variable, 23 + x is constant.

State whether true or false:

If 23 is a constant and x is a variable, 23x is a variable.

State whether true or false:

If y is a variable and 57 is a constant, y – 57 is a variable.

State whether true or false:

If 3x and 2y are variable; each of 3x + 2y, 3x – 2y, 3x ÷ 2y and 3x x 2y is a variable.