Consider two whole numbers a and b such that a is greater than b.
(i) Is a - b a whole number? Is this result always true?
(ii) Is b - a a whole number? Is this result always true?
Answer
(i) Since a is greater than b, the difference a - b is a positive number.
So, a - b is a whole number, and yes, this result is always true (whenever a is greater than b).
(ii) Since a is greater than b, the difference b - a is a negative number, and negative numbers are not whole numbers.
So, b - a is not a whole number, and yes, this result is always true (whenever a is greater than b, b - a is always negative).
Write the identity number, if possible for subtraction of whole numbers.
Answer
For any whole number x, we have x - 0 = x, but 0 - x ≠ x.
An identity element must give the same number when applied from both sides, but for subtraction 0 works only from the right side and not from the left.
Hence, the identity number for subtraction of whole numbers is not possible (it does not exist).
Fill in the blanks:
(i) 12 × (9 - 6) = ............... = ...............
(ii) 12 × 9 - 12 × 6 = ............... = ...............
(iii) Is 12 × (9 - 6) = 12 × 9 - 12 × 6? ...............
(iv) Is this type of result always true? ...............
Answer
(i) 12 × (9 - 6) = 12 × 3 = 36.
(ii) 12 × 9 - 12 × 6 = 108 - 72 = 36.
(iii) Both results are equal to 36, so yes, 12 × (9 - 6) = 12 × 9 - 12 × 6.
(iv) Yes. By the Distributive Law of Multiplication over Subtraction, this type of result is always true.
Fill in the blanks:
(i) (16 - 8) × 24 = ............... = ...............
(ii) 16 × 24 - 8 × 24 = ............... - ............... = ...............
(iii) Is (16 - 8) × 24 = 16 × 24 - 8 × 24? ...............
(iv) Is this type of result always true? ...............
Answer
(i) (16 - 8) × 24 = 8 × 24 = 192.
(ii) 16 × 24 - 8 × 24 = 384 - 192 = 192.
(iii) Both results are equal to 192, so yes, (16 - 8) × 24 = 16 × 24 - 8 × 24.
(iv) Yes. By the Distributive Law of Multiplication over Subtraction, this type of result is always true.
Find the difference between the largest number of four digits and the smallest number of six digits.
Answer
The largest number of four digits = 9999.
The smallest number of six digits = 100000.
Difference = 100000 - 9999 = 90001.
Hence, the required difference is 90001.
Find the difference between the smallest number of eight digits and the largest number of five digits.
Answer
The smallest number of eight digits = 10000000.
The largest number of five digits = 99999.
Difference = 10000000 - 99999 = 9900001.
Hence, the required difference is 9900001.