Distributive property of multiplication over addition
a x (b + c) = (a x b) + (a x c)

Improper
numerator is greater than or equal to its denominator
e.g. 8/3, 19/7..

equivalent fractions
multiply its numerator & denominator by the same nonzero number

Product of two or more fractions = product of numerators / product of denominators
e.g. (3/4) x (5/6) = (3 x 5)/ (4 x 6) = 15/ 24= 5/8

The product of two proper fractions is smaller than each of the two fractions

The product of two improper fractions is greater than each of the two fractions

The product of an improper & a proper fraction is greater than the proper fraction & less than the improper fraction.

Reciprocal of a number is also known as its multiplicative inverse

Suffixing zeros to the extreme right of the decimal part of a decimal number doesn't change its value

If whole number part is equal
compare the tenth digits
If tenth digits are same than compare 100th place...so on

two decimals or whole number
Multiply the decimals as if they are whole numbers. then mark the decimal point in the product leaving as many as places to the right of decimals as is the sum of such places in the given decimals.
e.g. 0.6 X 0.4 = 0.24

Two Decimal or whole number
convert the decimals to fractions first & then cancel the common factors

The ratio of two quantities with the same unit is the fraction that one quantity is of the other

ratio remains unchanged if both its terms are multiplied by the same nonzero number

Two ratio can also be compared by making their denominators same

three numbers x,y, z are said to be in continued proportion, if x : y : : y : z
Here y is called mean proportional between x and z

y2 = xz

Cost Price that is abbreviated as CP
Total Cost Price = Purchase price + Overhead charges

Profit = SP - CP ( SP > CP)
Loss = CP - SP (CP > SP)

Profit or loss % is always calculated on the cost price of an article

Profit % = (Profit/ CP) x 100
Loss % = (Loss/CP) x 100

Two Useful Formulae

SP/CP = (100 + profit %) / 100 , when there is profit

SP/CP = (100 - loss %) / 100 , when there is loss

Lender : Financial body or individual from whom the money is borrowed for a specified period of time.

Borrower : individual who borrows the money

Interest (I) : additional money paid by the borrower

Amount (A) : total amount paid by the borrower

Rate (r) : interest on the borrowed money is paid according to a certain percentage of the principal.

When the principal remains the same for the entire loan period, the interest charged is called simple interest

A combination of constants & variables connected by any of the symbols +, - , X or / is called an algebraic expression

Perimeter Formulae (P) : sum of lengths of its sides

Geometrically X2 = X x X represents the area of a square of side x units.

In 9ab2, number 9 is the coefficient of ab2, a is coefficient of 9b2 and b2 is the coefficient of 9a

In the algebraic expression 12x2 + 15y2 -16, the constant term is -16

Like Terms : terms having the same algebraic factors.
e.g. : 2x2, 3x2, -18x2

Unlike Terms : Terms having different algebraic factors are unlike terms
e.g. 4p, 5q

Monomial : expression containing only one term
Binomial : expression containing two unlike terms
Trinomial : which contains three unlike terms
Quadrinomial : which contains four unlike terms
Multinomial : two or more terms is called a polynomial : in two or more variables with every variable in it having only positive integral powers

Horizontal Method : all expressions are written in a horizontal line & different like terms are arranged into their individual groups & then added

Column Method : expression to be added is written in a separate row such that their like terms are arranged one below the other in a column

Complementary : Two angles are said to be complementary if the sum of their measures is 90

In right angled triangle, two acute angles will be complementary as sum of all the angles of triangle is 180

Supplementary : Two angles are supplementary if their sum is 180

Two angles are said to be adjacent if they have
a. a common vertex
b. a common arm and
c. the other two arms on opposite sides if the common arm.

Linear pair is the pair of adjacent angles whose non-common arms are opposite rays
the sumof angles forming a linear pair is 180

If two lines intersect, then the vertically opposite angles are equal

Line segments or rays are said to be intersecting if they have a common point

The distance between two parallel lines is the same everywhere

Each pair of corresponding angles are equal in measures.
The "F" - shape shows corresponding angles

Each pair of alternate interior angles are equal in measure
The "Z" - shape shows alternate interior angles

Area & Perimeter of a Rectangle
For a rectangle with length L units & breadth B units

1. Perimeter of rectangle = 2 x (L + B) Units
2. Area of rectangle A = L x B sq Units
3. Length of rectangle = Area / Breadth = A / B units
4. Breadth of rectangle = Area / Length = A / L Units

Area & Perimeter of a Square
for a square whose each side is of measure 's' units

1. Perimeter of square = 4 x side = 4s units
2. Area of square = side X side = S2 sq. units
3. Area o square = (diagonal)2 / 2

Area of 4 walls of a room= 2 x (L x H) + 2 x (B X H)

Area of parallelogram = Base X corresponding height
Base = Area of parallelogram / corresponding height
Height = Area of the parallelogram / corresponding base

Area of a rectangular path = Area of outer rectangle - Area of inner rectangle