Fractions

Posted in Terms Defined

Proper Fractions: The fractions, where the numerator is less than the denominator are called proper fractions.

Improper Fractions: The fractions, where the numerator is bigger than the denominator are called improper fractions.

Mixed Fractions: A mixed fraction has a combination of a whole and a part.

Equivalent Fractions: The fractions if reduced to their simplest forms are equal than these fractions are called equivalent fractions.

Simplest form of a fraction: A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1.

Like Fractions: The fractions with same denominators are called like fractions.

Unlike Fractions: The fractions with different denominators are called unlike fractions.

 

Divisibility

Posted in Terms Defined

Divisibility by 2: If a number has either 0, 2, 4, 6, or 8 in its ones place then it is divisible by 2.

Divisibility by 3: If the sum of the digits of a number is a multiple of 3, then the number is divisible by 3.

Divisibility by 4: A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.

Divisibility by 5: If a number has either 0 or 5 in its ones place then it is divisible by 5.

Divisibility by 6: If a number is divisible by 2 and 3 both then it is divisible by 6 also.

Divisibility by 8: A number with 4 digits or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8.

Algebraic Identities

Posted in Terms Defined

An identity is an equality that holds true regardless of the values chosen for its variables. They are used in simplifying or rearranging algebra expressions. By definition, the two sides of an identity are interchangeable, so we can replace one with the other at any time.

 

( x + y )2  x2 + 2 x y + y2 
( x - y )2 =  x2 - 2 x y + y2
( x + y )3 =  x+ 3 x2 y + 3 x y2 + y3
( x - y )3 =  x3 - 3 x2 y + 3 x y2 - y3
( x + y )4 =  x4 + 4 x3 y + 6 x2 y2 + 4 x y3 + y4
( x - y )4 =  x4 - 4 x3 y + 6 x2 y2 - 4 x y3 + y4
x2 - y2 = ( x + y ) ( x - y )
x- y3 = ( x - y ) ( x2 + x y + y)
x3 + y3 = ( x + y ) ( x2 - x y + y)
x4 - y4 = ( x2 - y) ( x2 + y2 )

Supplementary Angles

Posted in Terms Defined

When the sum of the measures of two angles is 180°, the angles are called supplementary angles.

For examples the following pairs are complementary:

(a) 30° and 150°

(b) 145° and 35°

(c) 100° and 80°

 When two angles are complementary, each angle is said to be the supplement of the other angle. The '100° angle' is supplement of the '80° angle'.

Complementary Angles

Posted in Terms Defined

When the sum of the measures of two angles is 90°, the angles are called complementary angles.

For examples the following pairs are complementary:

(a) 30° and 60°

(b) 45° and 45°

(c) 10° and 80°

 When two angles are complementary, each angle is said to be the complement of the other angle. The '10° angle' is complement of the '80° angle'.