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NCERT Solutions for Class 5th Maths Chapter 4 Even and Odd Numbers — Even and Odd Numbers

Book page 54 Updated on2026-09-19

Q1.
Circle the numbers that are even. (a) 297 (b) 498 (c) 724 (d) 100 (e) 199 (f) 789 (g) 49 (h) 6,893 (i) 846 (j) 111 (k) 222 (l) 1,023
Answer

The even numbers are (b) 498, (c) 724, (d) 100, (i) 846 and (k) 222. Circle those five.

How to tell in one look: only the last digit matters. If the number ends in 0, 2, 4, 6 or 8 it is even. If it ends in 1, 3, 5, 7 or 9 it is odd.

NumberLast digitEven or odd
(a) 2977odd
(b) 4988even
(c) 7244even
(d) 1000even
(e) 1999odd
(f) 7899odd
(g) 499odd
(h) 6,8933odd
(i) 8466even
(j) 1111odd
(k) 2222even
(l) 1,0233odd
Why only the last digit matters: Tens, hundreds and thousands can always be shared into two equal groups — 10 is 5 and 5, 100 is 50 and 50. So they never leave anything over. Only the ones digit can leave one behind, and that is what decides even or odd.
Q2.
Observe the given arrangement.
Paired arrangement for 18Paired arrangement for 23
The two paired arrangements printed with the question.
Add 2 to 18. What changes or does not change in the arrangement? Add 2 to 23. What changes or does not change in the arrangement?
Answer

In both cases the arrangement gets one more full pair. Whether anything is left over does not change.

18 — nine complete pairs, nothing left over 20 — one more pair joins; still nothing left over The two green counters are the pair that 2 adds on.
Adding 2 to an even number simply adds one more complete pair, so it stays even.

Add 2 to 18

  1. 18 is arranged as 9 complete pairs, with nothing left alone. That is why 18 is even.
  2. The 2 new counters make one more pair on the end.
  3. 20 is now 10 complete pairs. Nothing is left over.
  4. What changes: the number of pairs, from 9 to 10. What does not change: there is still no counter standing alone — 20 is even, just as 18 was.

Add 2 to 23

  1. 23 is arranged as 11 complete pairs and 1 counter left over. That is why 23 is odd.
  2. The 2 new counters make one more pair.
  3. 25 is now 12 complete pairs and still 1 counter left over.
  4. What changes: the number of pairs, from 11 to 12. What does not change: the single lonely counter is still there — 25 is odd, just as 23 was.
The big idea: Adding 2 always adds exactly one whole pair. It can never rescue a lonely counter and it can never create one. So an even number stays even and an odd number stays odd.
Q3.
What do you notice about the sums in each of the following cases? Do you think it will be true for all pairs of such numbers? Explain your observations. You may use the paired arrangement to explain your thinking.
Paired arrangement for 18Paired arrangement for 23
The two paired arrangements printed with the question.
(a) 12 and 6 are a pair of even numbers. Choose 5 such pairs of even numbers. Add the numbers in each of the pairs. (b) 13 and 9 are a pair of odd numbers. Choose 5 such pairs of odd numbers. Add the numbers in each of the pairs. (c) 7 and 12 are a pair of odd and even numbers. Choose 5 such pairs of odd and even numbers. Add the numbers in each of the pairs.
Answer

(a) even + even is always even. (b) odd + odd is always even. (c) odd + even is always odd. Yes, these are true for every such pair, without exception.

(a) Five pairs of even numbers

PairSumEven or odd
12 and 618even
8 and 412even
20 and 1030even
14 and 1630even
2 and 1820even

Each even number is made only of complete pairs. Put two such sets together and you still have only complete pairs — so the total is even.

(b) Five pairs of odd numbers

PairSumEven or odd
13 and 922even
7 and 512even
11 and 314even
15 and 2136even
1 and 910even

Each odd number leaves one counter alone. Put two odd numbers together and the two lonely counters find each other and make a pair. Nothing is left over, so the sum is even.

5 (odd) + 3 (odd): the two lonely counters join up 5 + 3 = 8 4 full pairs The two pink counters are the ones left over. Togetherthey make a pair.
Two odd numbers each leave one counter alone; the two lonely counters pair up, so the sum is even.

(c) Five pairs of one odd and one even number

PairSumEven or odd
7 and 1219odd
3 and 811odd
9 and 615odd
15 and 419odd
11 and 2031odd

The even number brings only complete pairs. The odd number brings complete pairs and one lonely counter. There is no second lonely counter for it to join, so it is still alone at the end — the sum is odd.

Check it yourself: Try any pair you like — 100 and 46 give 146 (even), 101 and 47 give 148 (even), 101 and 46 give 147 (odd). The rule never breaks.
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