Numbers

Question 1

Non-negativity (modulus)

Answer 1

Modulus of any function is always non-negative (positive without a zero)

Question 2

AM-GM inequality

Answer 2

AM>=GM

Question 3

Condition for terminating decimal in fractions

Answer 3

Terminating means the decimals are fixed and have an end (they terminate). Must have 2 or 5 or both in its denominator!!

Question 4

Non terminating fractions

Answer 4

/3 or /7 or /9 or /11 (primes except 2)

Question 5

Product of Factors

Answer 5

Every number has a unique pof.
pof = (Number) ^ (NOF/2)

Question 6

Relation of LCM and numbers

Answer 6

If number is increased k times, LCM also increases k times.

Question 7

Relation of HCF and numbers

Answer 7

If number is decreased k times, HCF also decreases k times. (divide)

Question 8

LCM of Fractions

Answer 8

LCM of numerator / HCF of denominator

Question 9

HCF of Fractions

Answer 9

HCF of numerator / LCM of denominator

Question 10

LCM and HCF of (0,A)

Answer 10

LCM = doesnt exist and HCF = A

Question 11

LCM(A,B) ___ Larger(A,B)

Answer 11

LCM(A,B) >= Larger(A,B)
lcm is greater than the greater no.
When is LCM = Larger number? - When one number is a multiple of the other!

Question 12

HCF(A,B) ___ Smaller(A,B)

Answer 12

HCF(A,B) <= Smaller(A,B)
hcf is always smaller than the smaller no.

Question 13

a^n + b^n

Answer 13

(a^n + b^n) is divisble by (a+b) if n is ODD