Maths 1 Mark Question

400000 - 98798 = 301202
Verification:
301202 + 98798 = 400000

15 + 5) (15 - 5)
= 20 × 10
= 200
= 225 - 25

1243 × 8975 = 8975 × 1243

200000 - 97531 = 102469
Verification:
102469 + 97531 = 200000

False.
Solution:
(2 + 4 = 6; 6 is an even number)

54321 + (489 + 699) = 489 + (54321 + 699)

15409 + 112 = 15521
And,
112 + 15409 = 15521

The sum of two odd numbers is an even number.
Solution:
The numbers 3, 7 , 11, 35 etc. are odd numbers. Now observe the following:
3 + 7 = 10, 3 + 11 = 14, 3 + 35 = 38, 7 + 11 = 18, 7 + 35 = 42 etc.
Here, the last digits of 10, 14, 38, 18, 42 ... ends with 0, 4, 8 and 2.
We know that, the number whose last digits is 0, 2, 4, 6 or 8 is an even number.
Thus, 10, 14, 38, 18, 42 etc. are all even numbers. Hence,
The sum of two odd numbers is an even number.

2359 + 641 = 3000
And,
641 + 2359 = 3000

625 × 20 × 8 × 50
= (625 × 8) × (20 × 50)
= 5000 × 1000
= 5000000

57839 - 2983 = 54856
Verification:
54856 + 2983 = 57839

4567 × 1 = 4567

True .
Solution:
[The whole number set is {0, 1, 2, 3, 4 …), whereas the natural number set is {1, 2, 3, 4 …)]

A number when divided by 12 gives 7 as quotient and 9 as remainder. The number is 93.
Solution:
By division algorithm, we have
dividend = divisor × quotient + remainder
Here, divisor = 12, quotient = 7 and remainder = 9.
Therefore
dividend = divisor × quotient + remainder
= 12 × 7 + 9
= 84 + 9
= 93
Hence, the required number is 93.

495 × 625 × 16
= (625 × 16) × 495
= 10000 × 495
= 4950000

Ture.
Solution:
(2 + 4 = 6; 6 is an even number)

888 + 777 + 555
= 111 (8 + 7 + 5)
= 111 × 20

True.
Solution:
(2 + 3 = 5; 5 is an odd number)

5628 + 39784 = 45412
And,
39784 + 5628 = 45412

785 × 0 = 0

2 × 1497 × 50
= (2 × 50) × 1497
= 100 × 1497
= 149700

Yes, there exists only one triangular number that is both a triangular number and a square number, and that number is 1.

75 × 425
= (70 + 5) × 425
= (70 + 5) (340 + 85)

When a whole number a is divided by a non-zero whole number b, then there exists whole numbers q and r,
Such that a = bq + r, where r = 0 or r < b
Solution:
Let a be dividend and b is the divisor. If q is the quotient and r is the remainder, then by division algorithm
a = bq + r, where r = 0 or r < b
Hence, r = 0 or r < b.

12 × 45 = 12 × 50 - 12 × 5

89 × (100 - 2)
= 89 × 98
= 98 × 89
= 98 × (100 - 11)

953 + 407 + 647
Therefore, 53 + 47 = 100
Therefore,(953 + 647) + 407 = 1600 + 407 = 2007

90758 + 0 = 90758

(500 + 7) (300 - 1)
= 507 × 299
= 299 × 507

923584 + 178 = 923762
And,
178 + 923584 = 923762

78 × 89 = 78 × 100 - 78 × 16 + 78 × 5

49 × 66 + 49 × 34 = 49 × (66 + 34)

False.
Solution:
[The whole number set is {0, 1, 2, 3, 4 …), whereas the natural number set is {1, 2, 3, 4 …)]

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
= 10 × 112
= 55

True.

False
Solution:
(3 + 5 = 8; 8 is an even number)

3030301 - 868686 = 2161615
Verification:
2161615 + 868686 = 3030301

66 × 85 = 66 × 90 - 66 × 4 - 66

If the product of two whole numbers is zero, then it means that either one of them is zero or both of them are zero.

2008 + 1952 = 1952 + 2008

27 × 18 = 27 × 9 + 27 × 4 + 27 × 5

4 × 358 × 25
= (4 × 25) × 358
= 100 × 358
= 35800

The product of an odd number and an even number is an even number.
Solution:
The numbers 3, 7 , 11 etc. are odd numbers and the numbers 8, 10, 12 etc. are even numbers.
Now observe the following:3 × 8 = 24, 3 × 12 = 36, 7 × 2 = 14, 7 × 8 = 56, 11 × 12 = 132, 11 × 10 = 110 etc.
Here, the last digits of 24, 36, 14, 56, 132, 110 ... ends with 0, 2, 4 or 6.
We know that, the number whose last digits is 0, 2, 4, 6 or 8 is an even number.
Thus, 24, 14, 36, 14, 56, 132, 110 etc. are all even numbers. Hence,
The product of an odd number and an even number is an even number.

False.

359 + 476 = 476 + 359

False.
Solution:
(3 + 2 = 5; 5 is not an even number)

10 × 100 × 10 = 10000

9 × (10000 + 974) = 98766

True .
Solution:
[That number is zero.]

92507 - 10879 = 81628
Verification:
81628 + 10879 = 92507

Ture.
Solution:
(3 + 5 = 8; 8 is an even number)

False.

5050501 - 969696 = 4080805
Verification:
4080805 + 969696 = 5050501

If a whole number a is divided by a non-zero whole number b such that the quotient is q, then the remainder is a - bq.
Solution:
Let a be dividend and b is the divisor. If q is the quotient and r is the remainder, then by division algorithm
a = bq + r, where r = 0 or r < b.
Now,
a = bq + r
⇒ r
= a - bq
Hence, r = a - bq.

475 × 129 = 129 × 475