Ch. 06. Integers
लेखक
ॐ जितेन्द्र सिंह तोमर
M.A., B.Ed., DNYS, MASSCOM.
10/4/10/2/2022
6.1 Integers
The collection of the Negative and positive numbers along with zero form integers.
–∞ ....... –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, ....... ∞
Positive (+) Sign Shows –> Above, west, south, loss, left of zero, more, Increase
Negative (–) Sign Shows –> Below, east, north, profit, right of zero, less, decrease
–∞ <..., <–2, <–1, <0, <1, <2,...... <∞
RHS Middle LHS
Addition & Subtraction
* Numbers of Same signs added and the number of the difference signs is subtracted and written with the sign of greatest number.
If you add two positive numbers like (+3) + (+2) = +5 [= 3 + 2]. You also add when you have two negative numbers, but the answer will take a minus (–) sign like (–2) + (–1) =
– (2+1) = –3.
So, when you have one positive and one negative integer, you must subtract, but answer will take the sign of the bigger integer (Ignoring the signs of the numbers decide which is bigger).
Additive Inverse
The same number with opposite sign is known as additive inverse of the number.
Number + additive inverse of the number = 0
The additive inverse of m is –m
The additive inverse of –m is +m
The additive inverse of 6 is –6
Subtraction of two negative integers
To subtract two negative integer from another is enough to add the additive inverse of the integer that is being subtracted, to the other integer.
(Integer-1) –(Integer-2)
= (Integer-1) + (additive inverse of Integer-2)
Q. Subtract (– 4) from (– 10)
Sol.
(– 10) – (– 4)
= (– 10) + (additive inverse of – 4)
= –10 + 4
= – 6
Chapter - 6
Integers
* The collection of numbers ..., -3, -2, -1, 0,1, 2, 3, ... is called integers.
* The numbers -1, -2, -3, ... are called negative integers.
* The numbers 1, 2, 3, ... are called positive integers.
* Additive inverse of a positive integer is a negative integer. e.g. additive inverse of 5 is (–5).
* Additive inverse of a negative integer is a positive integer. e.g. additive inverse of (–8) is 8.
* When two positive integers are added, sum is also a positive integer.
e.g. (+6) + (+9)=(+15)
* When two negative integers are added, sum is also a negative integer.
e.g. (–11)+(–7)=(–18)
* When a positive integer and a negative integer are added, actually they will be subtracted like whole numbers and the difference will take the sign of the integer which is greater in magnitude.
e.g.
(a) 8+ (–5)=3
(b) (–9)+(+2) = –7
* The subtraction of an integer is the same as the addition of its additive inverse.
e.g. subtract 4 from 9:
9–4= 9+(–4)=5
* The sum of an integer and its additive inverse is always zero.
* Zero is neither a positive integer nor a negative integer.
RATIONAL NUMBERS
INTEGERS --3-2-1
WHOLE NO.
NATURAL NUMBERS
1, 2, 3, 4,
Representations through integers:
(a)
Going up
(b)
Going down
Going right
Negative integer Positive integer
(d)
(e)
(h)
Going left
Above sea level
Negative integer
Positive integer
Below sea level
Negative integer
Positive integer
Temperature above 0°C
Temperature below 0°C
Negative integer
Positive integer
(1)
Deposit in bank
Withdrawal from the bank
Negative integer
Going East/North
Going West/South
Positive integer
Positive integer
Negative integer
(k)
(1)
NORTH
WEST
EAST
SOUTH
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