NCERT Solutions for Class 5th Maths Chapter 9 True or false, completing statements, and always / sometimes / never true — Mathematical Statements

Book page 135 Updated on2026-09-19

Q1.

1. Find out whether the following statements are True (T) or False (F). A true sentence is one where both sides of the '=' sign have the same value. (a) 8 × 9 = 70 + 2 (b) 20 – 6 = 7 × 3 (c) 48 ÷ 3 = 4 × 4 (d) 89 – 9 = 90 + 0 (e) 25 + 10 = 45 – 10

Answer

Work out each side on its own, then compare.

Part	Statement	Left side	Right side	True or False
(a)	8 × 9 = 70 + 2	72	72	True
(b)	20 − 6 = 7 × 3	14	21	False
(c)	48 ÷ 3 = 4 × 4	16	16	True
(d)	89 − 9 = 90 + 0	80	90	False
(e)	25 + 10 = 45 − 10	35	35	True

What the '=' sign really means: It does not mean "here comes the answer". It means "the two sides are worth exactly the same". So 8 × 9 = 70 + 2 is a perfectly good sentence — both sides are worth 72.

How to fix the false ones:
(b) 20 − 6 = 7 × 2, or 20 + 1 = 7 × 3.
(d) 89 − 9 = 90 − 10, or 89 + 1 = 90 + 0.

Q2.

2. Complete the following statements such that they are true. (a) 7 × 6 = ____ + 17 (b) 87 + 6 = ____ × 31 (c) 63 + ____ = 74 – 4 (d) ____ ÷ 9 = 16 ÷ 2

Answer

(a) 25 (b) 3 (c) 7 (d) 72

The method is the same each time: work out the side you can, then make the other side match.

(a) 7 × 6 = ____ + 17

Left side: 7 × 6 = 42
So the blank + 17 must be 42
Blank = 42 − 17 = 25
Check: 25 + 17 = 42 ✓

(b) 87 + 6 = ____ × 31

Left side: 87 + 6 = 93
So the blank × 31 must be 93
Blank = 93 ÷ 31 = 3
Check: 3 × 31 = 93 ✓

(c) 63 + ____ = 74 − 4

Right side: 74 − 4 = 70
So 63 + the blank must be 70
Blank = 70 − 63 = 7
Check: 63 + 7 = 70 ✓

(d) ____ ÷ 9 = 16 ÷ 2

Right side: 16 ÷ 2 = 8
So the blank ÷ 9 must be 8
Blank = 9 × 8 = 72
Check: 72 ÷ 9 = 8 ✓

Tip: Always finish the side that has no blank in it first. That gives you a target number, and then you only have one small step left.

Q3.

3. (a) "When two odd numbers are added, the sum is even." Find 5 examples for the above statement. Can you find an example to show that the statement can be false?

Answer

The statement is ALWAYS TRUE. Five examples are given below, and no counter-example exists.

Odd number	Odd number	Sum	Odd or even?
3	5	8	even
7	9	16	even
11	13	24	even
1	7	8	even
25	31	56	even

Can you find an example to show the statement is false? No — and here is why.

An odd number is pairs plus one spare. Two spares make a pair, so nothing is left over.

Why it is always true: Every odd number is a pile of pairs with one lonely counter left over. Put two odd numbers together and the two lonely counters find each other and make a pair. Nothing is left alone, so the sum is even.

Answer to the second part: There is no example that makes it false. Try as many as you like — 99 + 1 = 100, 501 + 499 = 1000 — the sum is even every single time.

Q4.

3. (b) "Multiplying a number by 2 can give an odd number." Give some example for this statement. Can you find any?

Answer

The statement is NEVER TRUE. There is no such example.

Number	× 2	Result	Odd or even?
3	3 × 2	6	even
7	7 × 2	14	even
10	10 × 2	20	even
25	25 × 2	50	even
99	99 × 2	198	even

Why no example can ever be found: Multiplying by 2 means making two equal groups of the same size. Whatever the number, the answer splits perfectly into two equal halves — and a number that splits into two equal whole halves is exactly what "even" means.

Another way to see it: Look at the Ones digit. Doubling 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 gives 0, 2, 4, 6, 8, 0, 2, 4, 6, 8. Every one of those endings is even, so the whole answer is even.

Q5.

3. (c) "Halving a number always leads to an even number." Give 3 examples for the statement. Can you find 3 examples when this is not true?

Answer

The statement is SOMETIMES TRUE. Sometimes half a number is even, sometimes it is odd.

Three examples where it IS true:

Number	Half of it	Odd or even?
8	4	even ✓
16	8	even ✓
20	10	even ✓

Three examples where it is NOT true:

Number	Half of it	Odd or even?
6	3	odd ✗
10	5	odd ✗
14	7	odd ✗

What makes the difference: If the number can be halved twice (like 8 → 4 → 2, or 20 → 10 → 5), then the first half is even. If it can be halved only once (like 6 → 3), the half comes out odd.

One example is enough to break a rule. The word "always" in the statement makes it a big claim. Half of 6 is 3, and 3 is odd — that single example is enough to show the claim is not always true.

Q6.

4. Tick in the appropriate cell for the following statements (Always True / Sometimes True / Never True): Adding 10 to a number gives a multiple of ten. Changing the order of the numbers in subtraction makes no difference. In multiplication, doubling one number and halving the other keeps the product the same. Multiplication by an odd number gives an even number. Multiplying a number by 5 leads to numbers which have '0' in the Ones place.

Answer

Statement	Always True	Sometimes True
Adding 10 to a number gives a multiple of ten.		✓
Changing the order of the numbers in subtraction makes no difference.		✓
In multiplication, doubling one number and halving the other keeps the product the same.	✓
Multiplication by an odd number gives an even number.		✓
Multiplying a number by 5 leads to numbers which have '0' in the Ones place.		✓

1. Adding 10 to a number gives a multiple of ten — sometimes true.

20 + 10 = 30, and 30 is a multiple of ten ✓
3 + 10 = 13, and 13 is not a multiple of ten ✗

It works only when you start from a multiple of ten.

2. Changing the order in subtraction makes no difference — sometimes true.

9 − 4 = 5 but 4 − 9 is not 5 ✗
7 − 7 = 0 and 7 − 7 = 0 ✓

The only time the order does not matter is when the two numbers are the same. For every other pair the order changes everything. (Addition is different — 4 + 9 and 9 + 4 are always equal.)

3. Doubling one number and halving the other keeps the product the same — always true.

6 × 8 = 48
Double the 6, halve the 8: 12 × 4 = 48 ✓
Double again, halve again: 24 × 2 = 48 ✓
Once more: 48 × 1 = 48 ✓

Why it always works: Picture 6 rows of 8 counters. Cut every row in half and stack the halves — you now have 12 rows of 4. Not a single counter was added or taken away, so the total cannot change.

4. Multiplication by an odd number gives an even number — sometimes true.

3 × 4 = 12, which is even ✓
3 × 5 = 15, which is odd ✗

It depends on the other number. Odd × even is always even; odd × odd is always odd.

5. Multiplying by 5 gives a 0 in the Ones place — sometimes true.

5 × 4 = 20, ends in 0 ✓
5 × 6 = 30, ends in 0 ✓
5 × 3 = 15, ends in 5 ✗
5 × 7 = 35, ends in 5 ✗

Multiplying by 5 always ends in 0 or 5. You get the 0 only when the other number is even.

How to decide any of these yourself: Hunt for one example that works and one that fails. Two examples that work and none that fails, over many tries, points to "always true" — but then look for the reason, as we did for statement 3.

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