Fill in the blanks :
(i) 156 x 48 - 156 x 38 = ...............
(ii) 76 x 53 + 76 x 47 = ...............
(iii) 138 x 67 + 62 x 67 = ...............
(iv) 4 x 269 x 25 = ...............
(v) There are ............... whole numbers up to 40.
(vi) ............... is the whole number which has no predecessor.
Answer
(i) 156 x 48 - 156 x 38 = 156 x (48 - 38) = 156 x 10 = 1,560.
(ii) 76 x 53 + 76 x 47 = 76 x (53 + 47) = 76 x 100 = 7,600.
(iii) 138 x 67 + 62 x 67 = 67 x (138 + 62) = 67 x 200 = 13,400.
(iv) 4 x 269 x 25 = 269 x (4 x 25) = 269 x 100 = 26,900.
(v) There are 41 whole numbers up to 40.
(vi) 0 is the whole number which has no predecessor.
Write T for true and F for false statement :
The least natural number is 0.
Answer
False
Reason
The set of natural numbers is defined as the set of positive integers: {1, 2, 3, 4, ...}. The least natural number is 1.
Write T for true and F for false statement :
Subtraction is associative on natural numbers.
Answer
False
Reason
For an operation to be associative, the following property must hold for any three numbers a, b, and c:
(a − b) − c = a − (b − c)
Let us take an example with natural numbers (e.g., 5, 3, and 1):
L.H.S. = (5 − 3) − 1 = 2 − 1 = 1
R.H.S. = 5 − (3 − 1) = 5 − 2 = 3
Since, 1 ≠ 3, the associative property does not hold for subtraction.
Write T for true and F for false statement :
In whole numbers, the multiplicative identity is 1.
Answer
True
Reason
The multiplicative identity is a number that, when multiplied by any other number, leaves the other number unchanged.
In the set of whole numbers, this number is 1, because for any whole number 'n': n × 1 = n and 1 × n = n.
Write T for true and F for false statement :
For whole numbers a, b, c, we always have (a + b).c = a.c + b.c.
Answer
True
Reason
For whole numbers a, b, c, we always have (a + b).c = a.c + b.c.
This is known as the Distributive Property of Multiplication over Addition.
Write T for true and F for false statement :
78 x 395 + 78 x 605 = 78000
Answer
True
Reason
Given, 78 x 395 + 78 x 605 = 78000
Taking L.H.S. = 78 x 395 + 78 x 605
= 78 x (395 + 605)
= 78 x 1,000
= 78,000
Taking R.H.S. = 78,000
So, L.H.S. = R.H.S.