Page 25 - ICSE Math 7

Properties
• Closure: a × b is again an integer.

• Commutative: a × b = b × a
• Associative: (a × b) × c = a × (b × c)
• Distributive: a × (b + c) = (a × b) + (a × c)
• Existence of multiplicative identity: Since a × 1 = a = 1 × a for every integer a, ∴ 1 is the
multiplicative identity.
¾ Division: If a and b ≠ 0 are any integers, then a is divisible by b, i.e., a ÷ b, if there exists a
unique integer c such that a = bc.
• For any integer a, 0 ÷ a = 0 and a ÷ 0 is not defined.
• The properties, i.e., closure, commutative and associative are not true for integers.
¾ Order of operations: When division, multiplication, addition and subtraction appear in an
expression without brackets, multiplication and division are done first in order of their appearance
from left to right followed by addition and subtraction in order of their appearance from left to
right. Any calculation in parenthesis is done first or one can follow the order given in BODMAS.
¾ Division by zero is not possible.
–
¾ Expression involving brackets are simplified in order ‘ ’, ( ) { } and [ ].

MENTAL MATHS

1. Write True or False.

(a) 99,999 is the largest positive integer.
(b) Integers are closed under all the four fundamental operations.
(c) Modulus of an integer is always greater than the integer.
(d) For any two integers a and b, if a > b, then –a < –b.

(e) 1 is the multiplicative identity and 0 is the additive identity of integers.
(f) Every integer is either positive or negative.
2. Fill in the boxes with ‘>’, ‘<’, or ‘=’.

(a) |–25| |25| (b) –|–9| |9|
(c) –15 14 (d) 0 –210

(e) |–4| – |–5| |4 – 5| (f) (–11) × 11 (–11) × (–11)
(g) (–4) × (–3) (–5) × 0 (h) 7 × (–9) (–6) × (–5)

3. Complete the tables given below.
(a) Multiplicand (b) Dividend

÷
× (–6) (–7) (–8) (–13) (–52) 104 (–156)
6
Multiplier (–7) Divisor (–4)

8 2

11