Page 21 - ICSE Math 7

Example 9: If the product of two integers is 2,240 and one of the
integers is –40, find the other integer. Try This
Solution: Let the required integer be x. Write True or False.
(a) 13 × (–9) = –117
So, (x) (–40) = 2,240 (b) (–42) ÷ (–6) = –7
2,240 (c) 0 ÷ 15 = 0
⇒ x = = –56 (d) 15 × (8 – 11) = –45
(–40)

Properties of division of integers

• Closure property
3
If a and b are any two integers, then a ÷ b need not be an integer. For example, 3 ÷ 4 = which
is not an integer. Thus, integers are not closed under division. 4

• Commutative property
1
If a and b are any two integers, then a ÷ b ≠ b ÷ a. For example, 16 ÷ 4 = 4 and 4 ÷ 16 = .
Therefore, 16 ÷ 4 ≠ 4 ÷ 16. Thus, integers are not commutative under division. 4
• Associative property

If a, b and c are any three integers, then (a ÷ b) ÷ c ≠ a ÷ (b ÷ c).
For example, (32 ÷ 4) ÷ 2 = 8 ÷ 2 = 4 and 32 ÷ (4 ÷ 2) = 32 ÷ 2 = 16. Therefore, (32 ÷ 4) ÷ 2 ≠
32 ÷ (4 ÷ 2). Thus, integers are not associative under division.
• Existence of identity

Let a be any integer other than zero, then a ÷ 1 = a but 1 ÷ a ≠ a.
Thus, identity element for division of integers does not exist.
• Existence of inverse
As there is no identity element for division, thus inverse does not exist under the division of
integers.

• Property of zero
Zero divided by any non-zero integer a is equal to zero, i.e., 0 ÷ a = 0, provided a ≠ 0.
For example, 0 ÷ 7 = 0, 0 ÷ (–5) = 0

Simplification of an Expression Maths Info

When two or more operations are used in an expression, then we B (Brackets)
simplify the expression by the rule of BODMAS. O (Of)
BODMAS denotes the order of operations to be performed. According to D (Division)
M (Multiplication)
it, first the brackets are solved, then ‘of’ followed by the four operations A (Addition)
division, multiplication, addition and subtraction. S (Subtraction)
Example 10: Simplify.

(a) 16 + (126 ÷ 14) – 13 × 2 (b) 2[11 –{22 – (119 – 55 ÷ 5 + 5 of 3)}]
Solution: (a) 16 + (126 ÷ 14) – 13 × 2
= 16 + 9 – 26 (Removing small brackets and performing
multiplication)
= 25 – 26 = –1

7