This concept map is partly the same as the first one design-wise. You can notice that instead of representing all the nodes with boxes, the author also used oval and cloud shapes. Aside from that, every node has a definition or example of what it represents. This tactic is a good way of helping users of the template understand what each node means.
Tags:
Similar Mind Maps
Outline
real number concept map
Real Number
Irrational number
Rational number
Terminating
X = p/q and q=0 (q is in the form of 2 and 5 Wherem n are non negative integers , then it is terminating decimal)
3/22*5 = 0.15
Non terminating
x = p/qand q*0(a is not in theform of2*5*where m, n arenon-negativeintegers, thenit isnon- terminatingdecimal)e 910 - 3.3
Euclid divisionLemma
Given positive integers aand b there exist uniqueintegers q and r satisfyinga = ba = r Oar
Euclid divisionalgorithm
If 'a' and "b'are positiveintegers such that a = bq + P,then every common divisorof 'a and "b' is a commondivisor of "b' and 'r', andvice-versa.e.g. HCF of 420 & 48420 = 48 × 8 + 3648 = 36 x1 + 1236 = 12 × 3 + 0- H.C.F, of 420 & 48 is 12
Fundamental theormof arithmetic
Every composite numbercan be expressed orfactorized as a product ofprimeseg. 48 = 2 x 2* 2 * 2.420 = 2 * 2 y 3 * 5*7
Application
e.g. Check whether 6* can end with the digit O for any naturalnumber 'n'I Sol. Any positive integer ending with the digit zero is divisibleby 5 and so its prime factorization must contain the prime 5.6 = (2 x 3) =2 x 3The prime in the factorization of G' is 2 and 35 does not occur in the prime factorization of 6* for any n.6 does not end with the digit zero for any natural number n
HCF
48 = 2 x 2 x 2 x 2 x 3420 = 2*2 x 3 x5 x7HCF 2*2*3
HCF. (48, 420) × L.C.M. (48,420)= 48> 420(This is true for 2 numbers only)
LCM
eg, 48 = 2 x 2 x 2 x 2 x 3420 = 2 x2 x3 x 5 x7LCM = 2 y 2x 2x 2 x 3 x 5 x 7LCM 1680
Some Important Results1. Let p' be a prime number and a be a positiveinteger. If 'p' divides a*, then 'p' divides a2. HCF × LCM = Prosuct of two numbers.3. LCM is always divisible by HCF
Real number concept map
95
real number concept map
Real Number
Irrational number
Rational number
Terminating
Non terminating
Euclid division
Lemma
Euclid division
algorithm
Fundamental theorm
of arithmetic
X = p/q and q=0 (q is
in the form of 2 and 5 Where
m n are non negative integers ,
then it is terminating decimal)
3/22*5 = 0.15
x = p/q
and q*0
(a is not in the
form of2*5*
where m, n are
non-negative
integers, then
it is
non- terminating
decimal)
e 9
10 - 3.3
Given positive integers a
and b there exist unique
integers q and r satisfying
a = ba = r Oar
If 'a' and "b'are positive
integers such that a = bq + P,
then every common divisor
of 'a and "b' is a common
divisor of "b' and 'r', and
vice-versa.
e.g. HCF of 420 & 48
420 = 48 × 8 + 36
48 = 36 x1 + 12
36 = 12 × 3 + 0
- H.C.F, of 420 & 48 is 12
Every composite number
can be expressed or
factorized as a product of
primes
eg. 48 = 2 x 2* 2 * 2.
420 = 2 * 2 y 3 * 5*7
Application
e.g. Check whether 6* can end with the digit O for any natural
number 'n'
I Sol. Any positive integer ending with the digit zero is divisible
by 5 and so its prime factorization must contain the prime 5.
6 = (2 x 3) =2 x 3
The prime in the factorization of G' is 2 and 3
5 does not occur in the prime factorization of 6* for any n.
6 does not end with the digit zero for any natural number n
HCF
HCF. (48, 420) × L.C.M. (48,420)
= 48
> 420
(This is true for 2 numbers only)
LCM
48 = 2 x 2 x 2 x 2 x 3
420 = 2*2 x 3 x5 x7
HCF 2*2*3
eg, 48 = 2 x 2 x 2 x 2 x 3
420 = 2 x2 x3 x 5 x7
LCM = 2 y 2x 2
x 2 x 3 x 5 x 7
LCM 1680
Some Important Results
1. Let p' be a prime number and a be a positive
integer. If 'p' divides a*, then 'p' divides a
2. HCF × LCM = Prosuct of two numbers.
3. LCM is always divisible by HCF
real number concept map
Real Number
Irrational number
Rational number
Terminating
X = p/q and q=0 (q is in the form of 2 and 5 Wherem n are non negative integers , then it is terminating decimal)
3/22*5 = 0.15
Non terminating
x = p/qand q*0(a is not in theform of2*5*where m, n arenon-negativeintegers, thenit isnon- terminatingdecimal)e 910 - 3.3
Euclid divisionLemma
Given positive integers aand b there exist uniqueintegers q and r satisfyinga = ba = r Oar
Euclid divisionalgorithm
If 'a' and "b'are positiveintegers such that a = bq + P,then every common divisorof 'a and "b' is a commondivisor of "b' and 'r', andvice-versa.e.g. HCF of 420 & 48420 = 48 × 8 + 3648 = 36 x1 + 1236 = 12 × 3 + 0- H.C.F, of 420 & 48 is 12
Fundamental theormof arithmetic
Every composite numbercan be expressed orfactorized as a product ofprimeseg. 48 = 2 x 2* 2 * 2.420 = 2 * 2 y 3 * 5*7
Application
e.g. Check whether 6* can end with the digit O for any naturalnumber 'n'I Sol. Any positive integer ending with the digit zero is divisibleby 5 and so its prime factorization must contain the prime 5.6 = (2 x 3) =2 x 3The prime in the factorization of G' is 2 and 35 does not occur in the prime factorization of 6* for any n.6 does not end with the digit zero for any natural number n
HCF
48 = 2 x 2 x 2 x 2 x 3420 = 2*2 x 3 x5 x7HCF 2*2*3
HCF. (48, 420) × L.C.M. (48,420)= 48> 420(This is true for 2 numbers only)
LCM
eg, 48 = 2 x 2 x 2 x 2 x 3420 = 2 x2 x3 x 5 x7LCM = 2 y 2x 2x 2 x 3 x 5 x 7LCM 1680
Some Important Results1. Let p' be a prime number and a be a positiveinteger. If 'p' divides a*, then 'p' divides a2. HCF × LCM = Prosuct of two numbers.3. LCM is always divisible by HCF
Mind Map
Outline
1
Page-1
1
Page-1
This work was published by EdrawMind user Oliveettom and does not
represent the position of Edraw Software.