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About Integers — Class 7 ICSE

Deepen understanding of integer operations including multiplication and division of negative numbers. This topic is part of the ICSE Class 7 mathematics syllabus (chapter: Chapter 1). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Integers

  • What are Integers?
  • Addition and Subtraction of Integers
  • Multiplication of Integers
  • Division of Integers
  • Properties of Integers & Review

Interactive lesson · about 20 minutes · checkpoint question after every unit

Integers — solved examples for Class 7 ICSE

Example 1easy

What is (-5) + 8?
  1. A)3
  2. B)-3
  3. C)13
  4. D)-13

Step-by-step solution

  1. We have (-5) + 8.
  2. Since |8| > |-5|, subtract: 8 - 5 = 3. The result is positive.
    (−5)+8=3(-5) + 8 = 3

Answer: 3

Example 2medium

Evaluate: (-12) + 7 + (-3) + 8
  1. A)0
  2. B)2
  3. C)-2
  4. D)30

Step-by-step solution

  1. Positive numbers: 7 + 8 = 15
  2. Negative numbers: (-12) + (-3) = -15
  3. Combine:
    15+(−15)=015 + (-15) = 0

Answer: 0

Example 3hard

Evaluate: (-2)³ × (-3)² + (-1)⁵
  1. A)-73
  2. B)73
  3. C)-71
  4. D)71

Step-by-step solution

  1. (-2)³ = -8 (odd power, negative)
  2. (-3)² = 9 (even power, positive)
  3. (-1)⁵ = -1 (odd power, negative)
  4. Combine:
    −8×9+(−1)=−72+(−1)=−73-8 × 9 + (-1) = -72 + (-1) = -73

Answer: -73

Practice questions on Integers

  1. Q1.easy

    What is (-3) - (-7)?
    1. A)4
    2. B)-4
    3. C)10
    4. D)-10
    Show answer

    Answer: 4

    Hint: Subtracting a negative number is the same as adding its positive.

  2. Q2.easy

    What is (-6) × 4?
    1. A)-24
    2. B)24
    3. C)-10
    4. D)10
    Show answer

    Answer: -24

    Hint: A negative number multiplied by a positive number gives a negative result.

  3. Q3.easy

    What is (-18) ÷ (-3)?
    1. A)6
    2. B)-6
    3. C)15
    4. D)-15
    Show answer

    Answer: 6

    Hint: When dividing two negative numbers, the result is positive.

  4. Q4.medium

    Find the product: (-3) × (-2) × (-4)
    1. A)-24
    2. B)24
    3. C)-9
    4. D)9
    Show answer

    Answer: -24

    Hint: Multiply step by step. Count the negative signs to determine the final sign.

  5. Q5.medium

    Verify the distributive property: (-5) × (3 + 7) = (-5) × 3 + (-5) × 7. What is the value of each side?
    1. A)-50
    2. B)50
    3. C)-35
    4. D)35
    Show answer

    Answer: -50

    Hint: Compute both sides and check they are equal.

  6. Q6.medium

    A submarine is at -120 m depth. It ascends 45 m, then descends 30 m. What is its final depth?
    1. A)-105 m
    2. B)-95 m
    3. C)-135 m
    4. D)-150 m
    Show answer

    Answer: -105 m

    Hint: Ascending means moving toward the surface (adding), descending means going deeper (subtracting).

  7. Q7.hard

    Find the value of x if: 5x - 3(-2x + 4) = -23
    1. A)-1
    2. B)1
    3. C)-11
    4. D)11
    Show answer

    Answer: -1

    Hint: First expand the brackets, then collect like terms and solve for x.

  8. Q8.hard

    The product of three consecutive negative integers is -120. Find the smallest of the three.
    1. A)-6
    2. B)-4
    3. C)-5
    4. D)-3
    Show answer

    Answer: -6

    Hint: Let the integers be n, n+1, n+2 where n is the most negative. Try factoring 120.

  9. Q9.hard

    Simplify: {(-8) × (-3)} ÷ {(-6) + (-6)} + {(-4) × 5}
    1. A)-22
    2. B)22
    3. C)-18
    4. D)18
    Show answer

    Answer: -22

    Hint: Evaluate each brace separately first, then follow the order of operations.

These are 9 of the 60 questions available for Integers. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.