Student Portal: student.smartindia.pro • Entrance App: entrance.smartindia.pro
Support Email: support@smartindia.pro
← Return to Early Excellence App (entrance.smartindia.pro)

Class 7 Mathematics: Integers

Addition, subtraction, multiplication, and division properties of integers, commutative, associative, and distributive properties, and sign rules.

Class 7 Mathematics 5 Generated Practice Exercises NCERT Exercise Solutions

⚡ Key Formulas & Core Relations for Integers

(-) × (-) = (+), (+) × (-) = (-)
Distributive Law: a × (b + c) = a × b + a × c
a ÷ 0 is UNDEFINED, 0 ÷ a = 0 (for a ≠ 0)
Additive Inverse of a is -a

NCERT Textbook Exercise Solutions

1 Solutions
Exercise 1.3 - Q5

Textbook Exercise Problem

Find the product using suitable properties: (a) 26 × (-48) + (-48) × (-36).

Step-by-Step Verified Solution:

  1. Step 1: Identify common term: (-48) is present in both products.
  2. Step 2: Apply Distributive Law: a × b + a × c = a × (b + c).
  3. Step 3: Factor out (-48): (-48) × [26 + (-36)].
  4. Step 4: Simplify inside brackets: 26 - 36 = -10.
  5. Step 5: Multiply: (-48) × (-10) = +480.
Final Answer: 480
Key Concept / Exam Strategy: Distributive property simplifies long arithmetic into basic single-digit calculations.

5 AI-Generated Chapter Exercises (Foundation to HOTS)

5 Problems with Full Steps
Generated Exercise #1 Foundation
Question: Evaluate: (-30) ÷ [(-13) + (-17)].
Core Concept Tested: BODMAS rules and integer division
Mentor Hint: Evaluate the bracket first.

Step-by-Step Solution:

  1. Step 1: Inside bracket: (-13) + (-17) = -30.
  2. Step 2: Division: (-30) ÷ (-30) = +1.
Verified Answer: 1
Generated Exercise #2 Intermediate
Question: In a test (+5) marks are given for every correct answer and (-2) marks for every incorrect answer. Radhika answered all questions and scored 30 marks though she got 10 correct answers. How many incorrect answers did she attempt?
Core Concept Tested: Sign-weighted integer scoring model
Mentor Hint: Marks from correct answers minus total score gives penalty marks.

Step-by-Step Solution:

  1. Step 1: Marks for 10 correct answers = 10 × 5 = 50 marks.
  2. Step 2: Let number of incorrect answers = x.
  3. Step 3: Total score = 50 + x(-2) = 30 => -2x = 30 - 50 = -20.
  4. Step 4: x = -20 / -2 = 10 incorrect answers.
Verified Answer: 10 incorrect answers
Generated Exercise #3 Intermediate
Question: Verify whether a - (-b) = a + b for a = 21, b = 18.
Core Concept Tested: Double negative subtraction identity
Mentor Hint: LHS has double negative which flips into addition.

Step-by-Step Solution:

  1. Step 1: LHS = 21 - (-18) = 21 + 18 = 39.
  2. Step 2: RHS = 21 + 18 = 39.
  3. Step 3: LHS = RHS = 39. Hence verified.
Verified Answer: LHS = RHS = 39 (Verified)
Generated Exercise #4 JEE-NEET Foundation
Question: An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach -350 m?
Core Concept Tested: Relative elevation distance with sign conventions
Mentor Hint: Total distance = 10 - (-350) = 360 m.

Step-by-Step Solution:

  1. Step 1: Initial position = +10 m, Final position = -350 m.
  2. Step 2: Total vertical distance = 10 - (-350) = 360 m.
  3. Step 3: Speed of descent = 6 m/min.
  4. Step 4: Time taken = Distance / Speed = 360 / 6 = 60 minutes = 1 hour.
Verified Answer: 60 minutes (1 hour)
Generated Exercise #5 Advanced HOTS
Question: Determine the sign of the product if we multiply 99 negative integers and 10 positive integers together.
Core Concept Tested: Parity of negative factors in integer multiplication
Mentor Hint: Negative count is 99 (odd number).

Step-by-Step Solution:

  1. Step 1: The product of any number of positive integers is always positive (+).
  2. Step 2: The product of an odd number of negative integers is always negative (-).
  3. Step 3: Since 99 is odd, product of negatives is (-).
  4. Step 4: (-) × (+) = (-). Therefore the overall product is negative.
Verified Answer: Negative (-)