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.
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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
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
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real number concept map
Real Number
