7 th maths chapter 3 ||3.1

7th Standard Mathematics — Chapter 3: Algebra

Exercise 3.1 Solutions

1. Fill in the blanks

1. The variable in the expression 16x - 7 is x.
2. The constant term of the expression 2y - 6 is -6.
3. In the expression 25m + 14n, the type of the terms are unlike terms.
4. The number of terms in the expression 3ab + 4c - 9 is 3.
5. The numerical co-efficient of the term -xy is -1.

2. Say True or False

1. x + (-x) = 0
   Answer: True
   Reason: Adding a variable and its additive inverse results in 0.
2. The co-efficient of ab in the term 15abc is 15.
   Answer: False
   Reason: The coefficient of ab in 15abc is 15c. (The numerical coefficient is 15).
3. 2pq and -7qp are like terms
   Answer: True
   Reason: Both terms contain the exact same variables p and q, since pq = qp.
4. When y = -1, the value of the expression 2y - 1 is 3
   Answer: False
   Reason: 2(-1) - 1 = -2 - 1 = -3, not 3.

3. Find the numerical coefficient in each of the following terms

Numerical coefficients for the given terms:

• -3yx ⇒ Numerical Coefficient = -3
• 12k ⇒ Numerical Coefficient = 12
• y ⇒ Numerical Coefficient = 1
• 121bc ⇒ Numerical Coefficient = 121
• -x ⇒ Numerical Coefficient = -1
• 9pq ⇒ Numerical Coefficient = 9
• 2ab ⇒ Numerical Coefficient = 2

4. Write the variables, constants and terms of the following expressions

S.No.	Expression	Variables	Constants	Terms
(i)	18 + x - y	x, y	18	18, x, -y
(ii)	7p - 4q + 5	p, q	5	7p, -4q, 5
(iii)	29x + 13y	x, y	None (0)	29x, 13y
(iv)	b + 2	b	2	b, 2

5. Identify the like terms among the following

Given terms: 7x, 5y, -8x, 12y, 6z, z, -12x, -9y, 11z

Like terms grouped together:

• Terms with variable 'x': 7x, -8x, -12x
• Terms with variable 'y': 5y, 12y, -9y
• Terms with variable 'z': 6z, z, 11z

6. Find the value of the expressions (If x = 2 and y = 3)

Substitute x = 2 and y = 3 into each expression:

1. 2x - 3y
   = 2(2) - 3(3) = 4 - 9 = -5
2. x + y
   = 2 + 3 = 5
3. 4y - x
   = 4(3) - 2 = 12 - 2 = 10
4. x + 1 - y
   = 2 + 1 - 3 = 3 - 3 = 0