NCERT Solutions for Class 4th Maths Chapter 10 Practice sums and the number-square puzzle — In-text Questions

Book page 163 Updated on2026-09-19

Q1.

Add a) 2783 + 378 b) 8948 + 97 c) 7006 + 367 d) 8009 + 485 e) 6062 + 3809 f) 3792 + 2688 g) 4999 + 3888 h) 5005 + 4895 i) 5768 + 4053 j) 3480 + 479

Answer

	Sum	Carries	Answer
a)	2783 + 378	ones and tens	3161
b)	8948 + 97	ones, tens and hundreds	9045
c)	7006 + 367	ones	7373
d)	8009 + 485	ones and tens	8494
e)	6062 + 3809	none	9871
f)	3792 + 2688	tens and hundreds	6480
g)	4999 + 3888	ones, tens and hundreds	8887
h)	5005 + 4895	ones, tens and hundreds	9900
i)	5768 + 4053	ones, tens and hundreds	9821
j)	3480 + 479	tens and hundreds	3959

One of them in full:

g) 4999 + 3888
Ones: 9 + 8 = 17 → write 7, carry 1
Tens: 9 + 8 + 1 = 18 → write 8, carry 1
Hundreds: 9 + 8 + 1 = 18 → write 8, carry 1
Thousands: 4 + 3 + 1 = 8
= 8887

Tip: For (g) you can also think 5000 + 3888 = 8888, then take 1 away, giving 8887.

Q2.

Subtract a) 4456 – 2768 b) 5300 – 467 c) 8067 – 4546 d) 5302 – 1034 e) 8004 – 3107 f) 3400 – 897 g) 9382 – 4857 h) 7561 – 2933 i) 6478 – 5986 j) 3444 – 2555

Answer

	Sum	Borrowing	Answer
a)	4456 − 2768	ones, tens, hundreds	1688
b)	5300 − 467	across two zeros	4833
c)	8067 − 4546	none	3521
d)	5302 − 1034	across the zero in tens	4268
e)	8004 − 3107	across two zeros	4897
f)	3400 − 897	across two zeros	2503
g)	9382 − 4857	ones and tens	4525
h)	7561 − 2933	ones and hundreds	4628
i)	6478 − 5986	tens and hundreds	492
j)	3444 − 2555	ones, tens, hundreds	889

One of them in full:

f) 3400 − 897
Ones: 0 − 7 cannot be done. Tens is 0 too.
4 hundreds → 3 hundreds and 10 tens
10 tens → 9 tens and 10 ones
Ones: 10 − 7 = 3 Tens: 9 − 9 = 0
Hundreds: 3 − 8 cannot be done → borrow 1 thousand, 13 − 8 = 5
Thousands: 2
= 2503

Check it yourself: 2503 + 897 = 3400.

Q3.

Fill the squares with the numbers 1–9. The difference between any two neighbouring squares (connected by a line) must be odd. Can you find other ways to fill the squares?

Nine empty squares. A line joins every pair of neighbours.

Answer

Nine empty squares. A line joins every pair of neighbours.

An odd difference needs one odd number and one even number.

odd − even = odd (for example 7 − 4 = 3)
odd − odd = even (7 − 3 = 4)
even − even = even (8 − 4 = 4)

So odd and even must sit like the black and white squares on a chess board. There are 5 odd numbers (1, 3, 5, 7, 9) and 4 even numbers (2, 4, 6, 8). The 5 odd numbers go on the four corners and the centre.

One correct filling. Every joined pair is one odd and one even number.

Check a few: 1 and 2 → 1 5 and 6 → 1
1 and 4 → 3 3 and 6 → 3 5 and 8 → 3
All the differences are odd. ✔

Yes, there are other ways. Keep the odd numbers on the corners and the centre, and just move them about.

Another correct filling. The odd numbers still sit on the corners and the centre.

Why it happens: The five odd numbers just fit the five chess-board squares of one colour, and the four even numbers fit the other four.

Q4.

Can you do the same thing such that the difference between any two neighbouring squares is even?

Nine empty squares. A line joins every pair of neighbours.

Answer

Nine empty squares. A line joins every pair of neighbours.

No, it cannot be done.

An even difference needs both numbers to be the same kind:
odd and odd (9 − 5 = 4) or even and even (8 − 2 = 6)

Every square is joined to another square, and those to others again, until all nine are linked. So if the first square is odd, its neighbour must be odd, and then the next, and so on — all nine numbers would have to be odd.

But 1 to 9 has only 5 odd numbers: 1, 3, 5, 7, 9
And only 4 even numbers: 2, 4, 6, 8
We can never get nine of one kind.

Why it happens: The whole grid is joined up in one piece. Once the first square is fixed, every other square is forced to be the same kind.

Try This: With numbers 1 to 9 it is impossible. But with 2, 4, 6, 8, 10, 12, 14, 16, 18 every difference would be even, because all of them are even.

Was this helpful?