A1:
The product of GCF (greatest common factor) and LCM ( least
common factor) of two numbers if equal to the product of two numbers.
LCM×GCF=a×b (let the numbers are a and b)
A2:
Every integer greater than 1 that is not a prime can be
written as a product of primes. e.g, 12 can be written as 2×2×3
A3:
Every integer has a finite set of factors (or divisors) and
an infinite set of multiples.
A4:
Some important points about integers:
1. If two integers are both
even or both odd, their sum and difference are even.
2. If one integer is even and
the other is odd, their sum and
difference are odd.
3. The product of two
integers is even unless both of them are odd.
A5:
Important inequalities for numbers between 0 to 1:
1. If 0<x<1, and a is
positive, then xa<a
2. If 0<x<a, and m and
n are integers with m>n>1, then xm<xn<x.
3. If 0<x<1, then squrare root of x>x
4. If 0<x<1, then 1/x>x.
In fact,1/x>1
A6:
If fraction have the same nominator then , if the
denominators are positive, then the fraction with smaller denominator is
greater.
A7:
In solving percent problems, first convert sentences into
equation, for this replace
1. “what” by “x”
2. “of” by sign of multiply
i.e, “×”
3. “is” by sign of equality
i.e, “=”
4. “Percent” means “per cent”
means 1/100
. So replace percent by 1/100
.
A8:
Use following formula while solving percentage questions:
1. Original × percentage=
apart
This formula can also be
written as: actual × percent = changed.
A9:
For any positive number a : a % of 100 is a.
A10:
For any positive numbers a and b: a% of b = b% of a
A11:
If a set of objects is divided into two groups in the ratio
of a:b, then the first group contains a/(a+b)
of the objects and the second group contains b/(a+b) of the objects.
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