2. Operations with Integers

6 topics58 min

Chapter 2 of NCERT Mathematics for Class 7: Operations with Integers. Three sections — Integers revisited, Multiplying and dividing integers and The laws integer arithmetic obeys. Six videos, 58 min in all.

Worked answers to the 25 exercise questions in this chapter →

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Part 1

Integers revisited

9 minNegative numbers on the number line, and adding and subtracting themA signed number is a piece of compression, and a puck sliding on a straight track is the argument for paying its price.9 min · 12 partsहिंदी

Part 2

Multiplying and dividing integers

10 minWhy a negative times a negative must be positiveYou cannot count your way to (−4) × (−2). There is no such thing as adding something minus four times.10 min · 12 partsहिंदी10 minThe sign rule for division, and why it follows from multiplicationDivision of integers gets no picture of its own — no bag, no tokens, no staircase. That absence is the whole point.10 min · 12 partsहिंदी9 minMagic grids of integersSixteen integers and three rules: circle a number, strike out its row and column, repeat. The total is the same whatever you circle.9 min · 12 partsहिंदी

Part 3

The laws integer arithmetic obeys

10 minCommutative, associative, and distributive over the integersYou already know these three laws, and that is exactly the problem. Knowing a rule and knowing where it is allowed to go are different.10 min · 12 partsहिंदी10 minEvaluating expressions that mix integers and bracketsOne habit is worth more than any technique here: when a situation turns into arithmetic, write the whole plan down before computing anything.10 min · 12 partsहिंदी

What you will be able to do

  • Recover two integers from their sum and their difference by systematic trial, and say why the search always closes
  • Interpret 4 × 2 and 4 × (−2) as placing tokens into an empty bag, and state what the multiplier and the multiplicand each control
  • Restate any integer division as a multiplication with an unknown factor
  • Play the grid game correctly: circle, strike out the whole row and column, repeat until nothing is left
  • State the commutative, associative and distributive properties for integers in letters, and read each statement aloud correctly
  • Turn a described situation into a single expression before evaluating it

What this chapter assumes you already know

  • Class 6: negative numbers exist, are read off a number line to the left of zero, and are added and subtracted using green and red tokens
  • Class 6: a green and a red token together are worth nothing — the zero pair
  • Whole-number addition and subtraction, and the idea that they undo each other
  • Reading a position on a number line, and the convention that right is the direction of increase
  • Multiplication of whole numbers read as repeated addition, and the times tables
  • Class 6: adding and subtracting integers
  • Reading a descending pattern and predicting its next term
  • Division of whole numbers as the inverse of multiplication — knowing 6 × 7 = 42 gives 42 ÷ 7

It builds directly on Writing a situation as an expression before computing it, Factorise and regroup instead of multiplying head-on and Comparing two expressions by reasoning, not by evaluating.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "A difference cannot be negative."
  • "The minus sign means the number is small."
  • "Four direction cases means four rules to remember."
  • "Adding zero pairs is cheating — you are changing the number."
  • "7 − 18 cannot be done."
  • "−(−18) is some new operation."
  • "The carrom coin's position is a distance, so it cannot be negative."
  • "Multiplying always makes things bigger."