NCERT Solutions for Class 7th Maths Chapter 2 In-text Questions — Multiplication of Integers
Book page 32–33 Updated on2026-09-19
Q1.
Using this understanding, let us construct a sequence of multiplications and observe the patterns. What do you notice in this pattern? Can you describe it?
The sequence of multiplications printed on page 32, with a positive multiplicand; the multiplier drops by 1 at each step.
Answer
The pattern is: every unit decrease in the multiplier drops the product by the multiplicand.
Statement
Product
Change
4 × 3
12
3 × 3
9
–3
2 × 3
6
–3
1 × 3
3
–3
0 × 3
0
–3
Multiplier goes 4, 3, 2, 1, 0 — down by 1 each time Product goes 12, 9, 6, 3, 0 — down by 3 each time and 3 is the multiplicand
Why it happens: the multiplier counts how many 3s are in the bag. Lowering it by 1 means one fewer 3, so the total falls by exactly 3. The multiplicand is the size of one step, which is why the product steps down by the multiplicand and by nothing else.
Q2.
Will this pattern continue when the multiplier goes below zero and becomes a negative number?
The sequence of multiplications printed on page 32, with a positive multiplicand; the multiplier drops by 1 at each step.
Why it happens: nothing special happens at zero. The rule “one fewer 3” keeps making sense — going one step below zero means the bag owes one 3, which is –3. This pattern gives the same answers the tokens gave, and that agreement is what tells us the sign rules are not arbitrary but forced.
Tip: a pattern that has to continue is a strong reason for a definition. If (–1) × 3 were anything but –3, the neat staircase of –3s would break for no reason.
Q3.
What is the pattern when the multiplicand is a negative integer?
The sequence of multiplications printed on page 32, with a negative multiplicand; the multiplier drops by 1 at each step.
Answer
The staircase turns the other way: every unit decrease in the multiplier now raises the product by the multiplicand’s magnitude.
Statement
Product
Change
4 × (–3)
–12
3 × (–3)
–9
+3
2 × (–3)
–6
+3
1 × (–3)
–3
+3
0 × (–3)
0
+3
As the multiplier falls by 1, the product increases by 3 This is the inverse of the earlier pattern
Why it happens: the step size is still the multiplicand, but the multiplicand is now –3. Removing one lot of –3 means removing a debt of 3, which lifts the total by 3. So the same sentence — “the product decreases by the multiplicand” — is still true; it is just that decreasing by –3 means going up by 3.
Q4.
Will this pattern continue when the multiplier goes below zero and becomes a negative integer?
The sequence of multiplications printed on page 32, with a negative multiplicand; the multiplier drops by 1 at each step.
Answer
Yes — and this is where the last sign rule appears.
Each line is 3 more than the one above it, so the products march up through the positive numbers.
Why it happens: the staircase has climbed by 3 at every single step so far, and there is no reason for it to stop at zero. Continuing it forces (–1) × (–3) to be +3. The tokens said the same thing when reds were pulled out of zero pairs. Two different models agreeing is strong evidence that negative × negative = positive is the only sensible choice.
Did you know? Whatever is true for multiplication when the integers are positive stays true when they are negative. That is the whole point of these patterns.