NCERT Solutions for Class 7th Maths Chapter 2 In-text Questions — Multiplication of Integers
Book page 29–30 Updated on2026-09-19
Q1.
Suppose we put some positive tokens into an empty bag as shown in the figure. How many positives are in the bag now?
The figure on page 29 — green (positive) tokens being put into the empty bag, shown group by group.
Answer
There are 8 positives in the bag.
The picture shows 2 positive tokens being dropped in, and that is done 4 times.
2 positives, 4 times = 4 × 2 = 8
Here 4 is the multiplier (how many times), 2 is the multiplicand (what is being put in each time), and 8 is the product.
Why it happens: multiplication is repeated addition of the same amount. Each round adds the same 2 greens, so after 4 rounds the bag has gained 2 + 2 + 2 + 2 = 8. Naming the two numbers multiplier and multiplicand matters here, because soon they will play very different roles.
Q2.
We have seen this kind of multiplication of positive integers before. Can we use tokens to give meaning to multiplications like 4 × (– 2)?
Answer
Yes. Just change the colour of the tokens you drop in.
Start with an empty bag. 4 × (–2) means placing 2 negatives into the bag, 4 times. Negatives are red tokens.
2 reds, 4 times = 8 reds 4 × (–2) = –8
Two green tokens four times gives 8; two red tokens four times gives –8.
Why it happens: the multiplier 4 only says “do it four times”. It does not care what is being put in. So if each round puts in –2 instead of +2, the bag falls by 2 each round instead of rising by 2. Four rounds of falling by 2 lands on –8.
Q3.
Similarly find the values of 4 × (– 6) and 9 × (– 7)? How can we interpret (– 4) × 2?
Answer
4 × (–6) = –24 and 9 × (–7) = –63.
4 × (–6): put 6 reds in, 4 times → 24 reds = –24 9 × (–7): put 7 reds in, 9 times → 63 reds = –63
Now (–4) × 2. Here the multiplier is negative, and that changes the instruction.
When the multiplier is positive, you place tokens into the bag.
When the multiplier is negative, you remove tokens from the bag.
So (–4) × 2 means: remove 2 positives (2 green tokens) from the bag, 4 times.
(–4) × 2 = remove 2 greens, 4 times = –8
Why it happens: the multiplier is the instruction and the multiplicand is the material. A positive multiplier repeats “put in”; a negative multiplier repeats “take out”. Taking 8 greens out of an empty bag leaves it 8 short, and being 8 short is exactly what –8 means.
Q4.
Why are we trying to remove green tokens and not red tokens?
Answer
Because the multiplicand decides which colour is handled, and here the multiplicand is +2.
In (–4) × 2, read the two numbers separately.
Number
Role
What it tells us
–4
Multiplier
Remove (because it is negative), and do it 4 times
2
Multiplicand
Remove 2 positives — greens, because 2 is positive
Why it happens: if we removed reds instead, we would be modelling (–4) × (–2), a completely different product. The sign of the multiplicand names the colour, the sign of the multiplier names the action. Keeping the two jobs apart is what makes all four sign cases come out right.
Check it yourself: read 4 × (–2) the same way. Multiplier +4 says “place, 4 times”; multiplicand –2 says “2 reds”. Place 2 reds four times → –8.
Q5.
What happens when both the integers in the multiplication are negative? How do we model (–4) × (–2) with tokens?
Answer
The product is positive: (–4) × (–2) = 8.
Read the instruction as before. The multiplier –4 says remove, 4 times. The multiplicand –2 says 2 negatives — red tokens.
But the bag is empty, so first stock it with zero pairs, exactly as in subtraction.
Round 1: put in 2 zero pairs (2 greens + 2 reds), then take out the 2 reds → 2 greens stay Do this 4 times Left in the bag: 8 greens (–4) × (–2) = +8
So the four basic results the tokens have now established are:
Why it happens: a zero pair costs nothing, so you may create as many as you need. Each time you pull a red out of a pair, the green half is left behind. Removing something negative therefore leaves something positive — which is why two negatives multiply to a positive.
Tip: in everyday words, taking away a debt makes you richer. Removing 8 units of debt is the same as gaining 8 units of fortune.