QUANTITIES MATHEMATICAL EXPRESSION

Introduction

Quantities in the form of mathematical expression

Mathematical expressions are the combination's of mathematical symbols or numbers or both. Every expression contains important elements called variables. Expression generally does not contain equality sign, if it has an equality sign then it represented as an equation.

Example:

    x²-2x+5 it is an expression

    y=x²-2x+5 is an equation.

Defined and undefined forms

Defined and undefined forms these are very important things to be noted in expressions. They are generally used to give an expression meaningful value. The meaning of any expression depends up on the elements which are present in the expression i.e. symbols, variables, integers etc.

Example for undefined forms:

0/1, ∞, -∞, 0/∞, (1)×∞, 0⁰ etc

Properties

1) An expression should have a variables, symbols, and numbers.

2) An expression should not have equality symbol.

Expressions can be obtained by different mathematical operations such as:

1) Additions

2) Subtractions

3) Multiplication

4) Division

5) Factoring etc

Simplifying expression

Algebraic expressions contain alphabetic symbols and numbers. When an algebraic expression is simplified, an equivalent expression is found simpler than the original. This usually means that the simplified expression is smaller than the original expression.

Example:

Simplify x + y+2x-3y=0

Given expression, x + y+2x-3y=0

Add and subtract the like terms:

       X+2x+y-3y=0

       3x-y=0

Mathematical expressions contain letters called Variable, which play an important role in writing an expression or equation.

Example:

The expression is X/Y i.e.

Where,X and Y are variables of given expression.

Variables

Variables are generally used to assign some value; it is a symbol which represents a number. In general n, s, x are used as variables. We generally use these variables in formulas, and while determining unknown values. There other type of variables called free and bond variables; Free variables are generally used variables and where as bond variables are correlated with each other.

Free variables: n, x, s etc.

Bond variables: (x+2)² = x²+4x+4 (or)

                     (x²-4) = (x+2) (x-2)

Here in the above cases the variable x is related to both the sides.

Properties:

1) Any equation can be added, subtracted, or divided to get the variable value.

2) Variables play an important role in algebra and functions.

Evaluating an expression with variables

A mathematical expression contain variable as part of the expression .The variable with expression can be simplified by substituting the variables in expression. It can be evaluated based on number on variables.

Single variable: X+1=0

Two variables: X+Y=0

Solved problems

1)Jane has bought 5 apples and 6 oranges for 30 Find the cost of apples if each orange is 2 ?


Solution:Given that, 5(A) +6(O) =$30
Each apple = $2
So we get 5(2) + 6(O) = $30
10 + 6(0) = 30
6(O) = 30-10
6(O) = 20
O = 20/6=3.3
Therefore each orange is $3.3.
In the above problem the question was changed into mathematical format using equations.
2) Find out the roots for the given quadratic expression x²-5x+6.


Solution:Given that, Quadratic expression is x2^-5x+6
Make it into equation x²-5x+6=0
                           x²-3x-2x+6=0
                          x(x-3)-2(x-3)=0
                          (x-3) (x-2)=0
                   The roots are x= 3,2.
3)Solve x - 12 + 20 = 37?


Solution:Given, x-12+20=37
We need to find x values so “x” term should be independent, Hence we will bring constants to other side.
x=37+12-20
x=49-20
x=29.