Class 7 Maths Chapter 1 Exercise 1.4 Pdf Notes NCERT Solutions
Class 7 Maths Chapter 1 Integers Exercise 1.4 pdf notes:-
Exercise 1.4 Class 7 maths Chapter 1 Pdf Notes:-
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Ncert Solution for Class 6 Maths Chapter 1 Integers Exercise 1.4 Tips:-
Introduction:-
DIVISION OF INTEGERS
We know that division is the inverse operation of multiplication. Let us see an example
for whole numbers.
Since 3 × 5 = 15
So 15 ÷ 5 = 3 and 15 ÷ 3 = 5
Similarly, 4 × 3 = 12 gives 12 ÷ 4 = 3 and 12 ÷ 3 = 4
We can say for each multiplication statement of whole numbers there are two
division statements.
Can you write multiplication statement and its corresponding divison statements
for integers?
From the above we observe that :
(–12) ÷ 2 = (– 6)
(–20) ÷ (5) = (– 4)
(–32) ÷ 4 = – 8
(– 45) ÷ 5 = – 9
We observe that when we divide a negative integer by a positive integer, we divide
them as whole numbers and then put a minus sign (–) before the quotient. We, thus,
get a negative integer.
We also observe that:
72 ÷ (–8) = –9 and 50 ÷ (–10) = –5
72 ÷ (–9) = – 8 50 ÷ (–5) = –10
So we can say that when we divide a positive integer by a negative
integer, we first divide them as whole numbers and then put a minus
sign (–) before the quotient. That is, we get a negative integer.
In general, for any two positive integers a and b
a ÷ (– b) = (– a) ÷ b where b ≠ 0
Lastly, we observe that
(–12) ÷ (– 6) = 2; (–20) ÷ (– 4) = 5; (–32) ÷ (– 8) = 4; (– 45) ÷ (–9) = 5
So, we can say that when we divide a negative integer by a negative integer, we first
divide them as whole numbers and then put a positive sign (+). That is, we get a positive
integer.
In general, for any two positive integers a and b
(– a) ÷ (– b) = a ÷ b where b ≠ 0
PROPERTIES OF DIVISION OF INTEGERS
We observe that integers are not closed under division.
Justify it by taking five more examples of your own.
We know that division is not commutative for whole numbers. Let us check it for
integers also.
You can see from the table that (– 8) ÷ (– 4) ≠ (– 4) ÷ (– 8).
Is (– 9) ÷ 3 the same as 3 ÷ (– 9)?
Is (– 30) ÷ (– 6) the same as (– 6) ÷ (– 30)?
Can we say that division is commutative for integers? No.
You can verify it by taking five more pairs of integers.
Like whole numbers, any integer divided by zero is meaningless and zero divided by
an integer other than zero is equal to zero i.e., for any integer a, a ÷ 0 is not defined
but 0 ÷ a = 0 for a ≠ 0.
When we divide a whole number by 1 it gives the same whole number. Let us check
whether it is true for negative integers also.
Observe the following :
(– 8) ÷ 1 = (– 8) (–11) ÷ 1 = –11 (–13) ÷ 1 = –13
(–25) ÷ 1 = _ (–37) ÷ 1 = (– 48) ÷ 1 = ___
This shows that negative integer divided by 1 gives the same negative integer.
So, any integer divided by 1 gives the same integer.
In general, for any integer a,
a ÷ 1 = a
What happens when we divide any integer by (–1)? Complete the following table
(– 8) ÷ (–1) = 8 11 ÷ (–1) = –11 13 ÷ (–1) = _ (–25) ÷ (–1) = (–37) ÷ (–1) = – 48 ÷ (–1) = _
What do you observe?
We can say that if any integer is divided by (–1) it does not give the same integer.
Can we say [(–16) ÷ 4] ÷ (–2) is the same as
(–16) ÷ [4 ÷ (–2)]?
We know that [(–16) ÷ 4] ÷ (–2) = (– 4) ÷ (–2) = 2
and (–16) ÷ [4 ÷ (–2)] = (–16) ÷ (–2) = 8
So [(–16) ÷ 4] ÷ (–2) ≠ (–16) ÷ [4 ÷ (–2)]
Can you say that division is associative for integers? No.
Verify it by taking five more examples of your own.
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