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#### Page No 68:

#### Question O1:

Which is the numerical co-efficient in 4*x*^{2}*y*?

#### Answer:

The numerical co-efficient in is 4.

#### Page No 68:

#### Question W1:

Classify the following into constants and variables.

#### Answer:

Constants: 5, π, 8, − 7,

Variables:

#### Page No 68:

#### Question O2:

Mention the absolute term in 3*x*^{2} − 6*x* −8.

#### Answer:

The absolute term in _{ }is −8.

[The constant term in an expression is called an absolute term.]

#### Page No 68:

#### Question O3:

Given an example for binomial expression.

#### Answer:

5*x*^{2} − 3*x*

Here, number of terms is two.

5*x*^{2} − 3*x* is a binomial expression.

#### Page No 69:

#### Question W2:

Write the numerical co-efficient of the following terms.

(1) −3*x*^{2}

(2)

(3) 4*y*

(4) 0.3*m*

(5) −1.5*p*

(6) *pqr*

#### Answer:

(1) Numeral coefficient = − 3

(2) Numeral coefficient =

(3) Numeral coefficient = 4

(4) Numeral coefficient = 0.3

(5) Numeral coefficient = −1.5

(6) Numeral coefficient = 1

#### Page No 69:

#### Question W3:

Write the co-efficient as indicated below:

1. In 27 *abc*

(a) The numerical co-efficient of *abc *________.

(b) Algebraic co-efficient of 27 *ab* ________.

(c) Algebraic co-efficient of 27 *ac* _______.

(d) Algebraic co-efficient of 27 *bc* _______.

(e) Algebraic co-efficient of 27 _______.

2. In

(a) Numerical co-efficient of *xy*^{2}*z* _______.

(b) Algebraic co-efficient of_______.

(c) Algebraic co-efficient of_______.

(d) Algebraic co-efficient of_______.

(e) Algebraic co-efficient of_______.

#### Answer:

(1)

(a) The numerical co-efficient of *abc *__ ____27 __.

(b) Algebraic co-efficient of 27 *ab* __ ____c ____ __.

(c) Algebraic co-efficient of 27 *ac *__ ____b____ __.

(d) Algebraic co-efficient of 27 *bc *__ ____a____ __.

(e) Algebraic co-efficient of 27 __ ____abc____ __.

(2)

(a) Numerical co-efficient of *xy*^{2}*z*.

(b) Algebraic co-efficient of__ ____z____ __.

(c) Algebraic co-efficient of__ ____y__^{2}__ __.

(d) Algebraic co-efficient of__ ____x____ __.

(e) Algebraic co-efficient of__ ____xy__^{2}__z____ __.

#### Page No 69:

#### Question W4:

Using the terms given below form the sets of like terms:

#### Answer:

Sets of like terms are given below:

(1)

(2)

(3)

(4)

#### Page No 69:

#### Question W5:

Write the least three sets containing 5 terms in each, by using the unlike terms given below:

#### Answer:

Sets containing 5 terms:

(1)

(2)

(3)

#### Page No 70:

#### Question W6:

Classify the following into monomial, binomial and trinomials.

(1) *a*^{2} + *a* − 2

(2) *x*^{2} + 2*y*^{2}

(3) 3*x*^{2} + 4*y* + 5*z*

(4) *ax*^{2} + *bx* + *c*

(5)* x *− 5

(6) 8*mn*^{3}

(7) *a*^{2} − *b*

(8)

(9) 7*k* + *l*

(10) 12*ab*

#### Answer:

(1) Trinomial

(2) Binomial

(3) Trinomial

(4) Trinomial

(5) Binomial

(6) Monomial

(7) Binomial

(8) Monomial

(9) Binomial

(10) Monomial

#### Page No 70:

#### Question W7:

Pickout and write the absolute term from the expression given below:

(1) *x*^{2} + 5*x* = 8

(2) 5*x*^{3} − 4*x*^{2} + 3*x* + 18

(3) 6*x*^{2}*y* + 8*y*^{2} + *xy* − 10

(4)

#### Answer:

(1) Absolute Term = 8

(2) Absolute Term = 18

(3) Absolute Term = − 10

(4) Absolute Term =

#### Page No 71:

#### Question W1:

Add:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

#### Answer:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

#### Page No 71:

#### Question O1:

What is the sum of 9*x* and 3*x*?

#### Answer:

The sum of 9*x* and 3*x* is .

#### Page No 71:

#### Question O2:

What do you get when −2*m* is added to −4*m*?

#### Answer:

On adding −2*m* and −4*m*, we get.

#### Page No 72:

#### Question W2:

Find the perimeter of the figures given below.

(1)

(2)

(3)

(4)

#### Answer:

(1) Perimeter

(2) Perimeter

(3) Perimeter

(4) Perimeter

#### Page No 73:

#### Question W1:

Find the sum of:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

#### Answer:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

#### Page No 73:

#### Question O1:

What is the sum of +4*xy* and −7*xy*?

#### Answer:

−3*xy*

#### Page No 73:

#### Question O2:

_{What is the sum of −6}_{a}_{, + 2}_{a}_{ and −5}_{a}_{?}

#### Answer:

−9*a*

#### Page No 74:

#### Question O1:

What do you get when 3*q* is added to 4*p*?

#### Answer:

On adding 3*q* to 4*q*, we get .

#### Page No 74:

#### Question W1:

Find the sum of the following.

(1) 3*b* and −2*a*

(2) −7*x* and 3*y*

(3) 5*a* and 2*b*

(4) 7*m* and −5*n*

(5) 15*xy* and 5*pq*

(6) 4*x*^{2} and *b*^{2}

(7) 5*mn*^{2} and 9*m*^{2}*n*

(8) 6*a*^{2}*bc* and 4*x*^{2}*yz*

#### Answer:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

#### Page No 74:

#### Question O2:

What is the sum of 5*p*, 6*q* and 7*r*?

#### Answer:

On adding 5*p*, 6*q* and 7*r*, we get .

#### Page No 74:

#### Question W2:

Simplify:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

#### Answer:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

#### Page No 75:

#### Question W3.1:

If the number of students in four classes of a school are 8*x*, 10*x*, 15*x* and 25*x* respectively, how many students are there altogether in the school?

#### Answer:

Total number of students

#### Page No 75:

#### Question W3.2:

If the number of benches and chairs in a school are 4*b* and 5*c* respectively, what is the total number of chairs and benches?

#### Answer:

Total number of chairs and benches

#### Page No 75:

#### Question W3.3:

If there are ‘12*b*’ bananas, ‘9*a*’ apples and ‘5*p*’ papayas in the basket of Kenchappa the fruit seller, find the total number of fruits.

#### Answer:

Total number of fruits

#### Page No 75:

#### Question W3.4:

Thimmakka has planted ‘8g’ sapling in a year. She planted ‘10g’ sapling next year. How many sapling did she plant altogether?

#### Answer:

Total number of saplings planted

#### Page No 77:

#### Question O1:

What do you get when 10*p* is subtracted from 6*p*?

#### Answer:

−4*p*

#### Page No 77:

#### Question W1:

Subtract:

(1) 5*a* from 3*a*

(2) −3*b* from 2*b*

(3) 3*x*^{2} from (−8*x*^{2})

(4) −11*xyz* from −7*xyz*

(5) 7*xy* from 14*xy*

(6) What should be added to 8*ab* to get 15*ab*?

#### Answer:

(1)

(2)

(3)

(4)

(5)

(6)

Thus, should be added to to get.

#### Page No 77:

#### Question O2:

What do you get when 5*n* is subtracted from 3*m*?

#### Answer:

#### Page No 77:

#### Question W2:

Subtract:

(1) 5*y* from 4*x*

(2) −2*a* from 3*b*

(3) 5*p* from −12*p*

(4) −4*c* from −7*d*

(5) 5*pq* from 7*mn*

#### Answer:

(1)

(2)

(3)

(4)

(5)

#### Page No 77:

#### Question W3:

(1) Subtract the sum of 3*a* and 4*a* from 9*a*

(2) Subtract (−5*xy* + 9*yz*) from (3*xy* − 4*yz*)

(3) Subtract (7*m*^{2} − 2*m*) from (−4*m* − 7*m*^{2})

(4) Subtract (6*a* − 4*b* + *c*) from (−*a* + 3*b* − 5*c*)

(5) Subtract (−4*x* − 8*y* + 7) from (3*y* − 7*x* + 1)

(6) How much should be added to (5*x* − 3*y*) to get (3*x* − 5*y*)?

#### Answer:

(1)

(2)

(3)

(4)

(5)

(6)

Thus, should be added to to get.

#### Page No 78:

#### Question W4:

(1) Krishna buys ‘8*a*’ bananas and sells ‘3*a*’ bananas out of them. How many bananas are left with him?

(2) Joseph has Rs 30*x* with him. In that if he spend Rs 7*x* for books and Rs 5*x *for sweets, how much money is left with him?

#### Answer:

(1)

Therefore, bananas are left with Krishna.

(2)

Rs. is left with Joseph.

#### Page No 79:

#### Question W1:

Fill in the blanks with appropriate answers in the following:

(1)

(2)

(3)

(4)

(5)

(6)

#### Answer:

(1)

(2)

(3)

(4)

(5)

(6)

#### Page No 79:

#### Question O1:

Give an example for commutative property of addition.

#### Answer:

An example in which commutative property of addition is used is .

#### Page No 79:

#### Question W2:

Mention the value of the variable in each of the following:

(1)

(2)

(3)

(4)

(5)

#### Answer:

(1)

(2)

(3)

(4)

(5)

#### Page No 79:

#### Question O2:

Identify he property used in

(*m* + *n*) + *p* = *m* + (*n* + *p*)

#### Answer:

The property used in is the associative law of addition.

#### Page No 81:

#### Question W1:

Multiply:

(1) 3*x* by 4*y*

(2) 2*y* by 4*y*

(3) 8*a* by 4*m*

(4) −4*x* by 8*x*

(5) −5*a *by −8*b*

(6) −6*p* by 4*pq*

(7) 2*a*^{2} by 5*a*^{2}

(8) 3*x*^{2}*b*^{2} by 5*x*

(9) −7*m*^{2}*n*^{2} by 4*m*

(10) −5*a*^{2}*b* by −7*ab*^{2}

#### Answer:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

#### Page No 81:

#### Question O1:

What is the product of 2*x* and 5*x*?

#### Answer:

The product of 2*x* and 5*x* is.

#### Page No 81:

#### Question O2:

How many marbles are there in 5*n* boxes, each containing 3*m* marbles?

#### Answer:

15*mn*

**Explanation:** To find the required number of marbles in the boxes, we need to multiply the number of the boxes to the number of the marbles in each. Thus, the number of the boxes is

.

#### Page No 81:

#### Question W2.1:

If the side of a square is 8a cm, what is its area?

#### Answer:

Side of a square

∴ Area of square

#### Page No 81:

#### Question W2.2:

The length of a rectangle is 3*x* cm and its breadth is 5*y* cm. What is the area of the rectangle?

#### Answer:

Area of rectangle

#### Page No 84:

#### Question O1:

Give an example for commutative property of multiplication.

#### Answer:

An example of commutative property of multiplication is .

#### Page No 84:

#### Question W1:

Fill in the blanks is the following and also mention the law which is used.

(1)

(2)

(3)

(4)

(5)

(6) ** **

#### Answer:

(1)

Here, commutative law of multiplication is used.

(2)

Here, associative law of multiplication is used.

(3)

Here, commutative law of multiplication is used.

(4)

Here, distributive law of multiplication is used.

(5)

Here, distributive law of multiplication is used.

(6)

Here, associative law of multiplication is used.

#### Page No 84:

#### Question O2:

Identify the property used in.

#### Answer:

The property used in is the associative law of multiplication.

#### Page No 84:

#### Question O3:

Identify the property used in the equation.

#### Answer:

The property used in _{ }is the distributive law of multiplication.

#### Page No 85:

#### Question W2:

If *a* = 1, *b* = 2 and *c* = −3, put the values in the given equations and mention the law which they prove.

(1) [2*a* + (−3*b*)] *c* = 2*ac* − 3*bc*

(2) *a* × (2*b* × 3*c*) = (*a* × 2*b*) × 3*c*

#### Answer:

(1)

The equation proves the distributive law.

(2)

∴ LHS = RHS

The equation proves the associative law.

#### Page No 85:

#### Question O1:

What is the product of 2*b* and (3*a* − 4*c*)?

#### Answer:

#### Page No 85:

#### Question O2:

What is the product of (6*x* + 7*y*) and 3*x*?

#### Answer:

#### Page No 86:

#### Question W1:

Multiply:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

#### Answer:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

#### Page No 87:

#### Question 1:

Find the product of the following:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

#### Answer:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

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