NCERT Solutions Class 7 Maths Chapter 4 — Algebraic Expressions

Solution:

Step 1: A variable is a symbol, usually a letter, that represents an unknown quantity or a quantity that can change.

Step 2: Unlike a constant, which has a fixed value, a variable's value can vary.

Solution:

Step 1: Cost of 5 apples = 5 × a = 5a.

Step 2: Cost of 3 bananas = 3 × b = 3b.

Step 3: Total cost = Cost of 5 apples + Cost of 3 bananas.

Step 4: Total cost = 5a + 3b.

Solution:

Step 1: An algebraic expression consists of terms. In the given expression, the terms are 7x²y, -4xy, and 9.

Step 2: For the term '-4xy', the variable part is 'xy'.

Step 3: The numerical factor multiplying 'xy' is -4. Therefore, -4 is the coefficient of 'xy'.

Solution:

Step 1: Like terms are terms that have the same variables raised to the same powers.

Step 2: For option A (6x, 6y), the variables are different (x and y).

Step 3: For option B (9ab, 4ba), the variables are 'a' and 'b' for both terms. Since 'ab' is the same as 'ba' (due to commutative property of multiplication), these are like terms.

Step 4: For option C (3p², 3p), the powers of 'p' are different (p² and p).

Step 5: For option D (2m, 2mn), the variables are different (m and mn).

Solution:

Step 1: Group the like terms: (7x - 3x) + (2y + 5y).

Step 2: Combine the 'x' terms: 7x - 3x = 4x.

Step 3: Combine the 'y' terms: 2y + 5y = 7y.

Step 4: The simplified expression is 4x + 7y.