शि

Schooling · Class 7 · Mathematics · Operations with Integers · Chapter on a page

CBSE Class 7 · Mathematics · NCERT Ganita Prakash-II

Operations with Integers: chapter on a page

A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).

About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.

This note's current text has no applied fact-check on record.

Mind map

Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.

Mind map of Operations with Integers: Key ideas, Formulas and facts, Watch out forKey ideasIntegersOn a number line, numbers to the…Adding a positive integer means…Subtracting an integer is the same…Multiplying two integers with the…Multiplying two integers with…Dividing integers follows the same…Formulas and facts(+) + (+) = (+)(−) + (−) = (−)(+) + (−) or (−) + (+)a − b = a + (−b)(+) × (+) = (+)(−) × (−) = (+)(+) × (−) = (−)Watch out forThinking −5 + (−3) = −2 because you…Forgetting to flip the sign when…Saying (−4) × (−2) = −8Believing 0 ÷ 5 and 5 ÷ 0 are the sameMixing up rules for addition and…Operations withIntegers
The mind map as a list
  • Key ideas
    • Integers
    • On a number line, numbers to the…
    • Adding a positive integer means…
    • Subtracting an integer is the same…
    • Multiplying two integers with the…
    • Multiplying two integers with…
    • Dividing integers follows the same…
  • Formulas and facts
    • (+) + (+) = (+)
    • (−) + (−) = (−)
    • (+) + (−) or (−) + (+)
    • a − b = a + (−b)
    • (+) × (+) = (+)
    • (−) × (−) = (+)
    • (+) × (−) = (−)
  • Watch out for
    • Thinking −5 + (−3) = −2 because you…
    • Forgetting to flip the sign when…
    • Saying (−4) × (−2) = −8
    • Believing 0 ÷ 5 and 5 ÷ 0 are the same
    • Mixing up rules for addition and…

What this chapter is about

In earlier classes, you learned about positive whole numbers and zero. Now you will work with integers, which include positive numbers, negative numbers and zero. Think of a thermometer showing 5°C above zero or 3°C below zero. The temperature below zero is written as −3. These negative numbers are part of the integer family.

Key ideas

  • Integers are the set of numbers: …, −3, −2, −1, 0, 1, 2, 3, … They go on forever in both directions.
  • On a number line, numbers to the right of 0 are positive and numbers to the left are negative.
  • Adding a positive integer means moving right on the number line; adding a negative integer means moving left.
  • Subtracting an integer is the same as adding its opposite: a − b = a + (−b).
  • Multiplying two integers with the same sign (both positive or both negative) gives a positive product.
  • Multiplying two integers with different signs (one positive, one negative) gives a negative product.
  • Dividing integers follows the same sign rules as multiplication.
  • Multiplying or dividing any integer by zero has special rules: a × 0 = 0, and division by zero is not allowed.

Formulas and facts to remember

  • Rule: (+) + (+) = (+) · Meaning: Sum of two positives is positive.
  • Rule: (−) + (−) = (−) · Meaning: Sum of two negatives is negative; add the numbers and keep the minus sign.
  • Rule: (+) + (−) or (−) + (+) · Meaning: Find the difference and keep the sign of the larger absolute value.
  • Rule: a − b = a + (−b) · Meaning: To subtract, add the opposite.
  • Rule: (+) × (+) = (+) · Meaning: Positive times positive is positive.
  • Rule: (−) × (−) = (+) · Meaning: Negative times negative is positive.
  • Rule: (+) × (−) = (−) · Meaning: Positive times negative is negative.
  • Rule: (−) × (+) = (−) · Meaning: Negative times positive is negative.
  • Rule: Same sign rules apply to division. · Meaning: Divide the numbers, then apply the sign rule.
  • Rule: a × 0 = 0 · Meaning: Any integer times zero is zero.
  • Rule: Division by zero is undefined. · Meaning: You cannot divide any number by zero.

Common mistakes

  • Thinking −5 + (−3) = −2 because you subtract → add the numbers and keep the minus sign, so the answer is −8.
  • Forgetting to flip the sign when subtracting a negative → a minus of a minus becomes a plus.
  • Saying (−4) × (−2) = −8 → two negatives multiply to give a positive, so the answer is +8.
  • Believing 0 ÷ 5 and 5 ÷ 0 are the same → 0 ÷ 5 = 0, but 5 ÷ 0 is not allowed.
  • Mixing up rules for addition and multiplication → remember, addition uses the number line idea; multiplication uses the same-sign-positive, different-sign-negative rule.

Quick revision

  • Integers include all positive and negative whole numbers along with zero.
  • To subtract any integer, add its opposite.
  • Same signs multiply or divide to give a positive result.
  • Different signs multiply or divide to give a negative result.
  • Anything multiplied by zero is zero; division by zero is never allowed.