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# Variables And Expressions

Variables are the symbols starting with English alphabets used to represent any value which changes from time to time. When these two or more variables are joined together with the help of the symbols are called expressions. For instance V is a symbol to represent any speed, t is the symbol to represent the time. In order to form the formula for acceleration we write:
A = v / t. Here the value of v is divided by t and a = v / t is an expression.

Any expression formed by joining the variable and the mathematical symbols with another variable or a constant value is called a variable expression. These mathematical operators may be addition, subtraction, multiplication and division. Variables and Expressions are co related terms. Expressions cannot be formed without the variables and the mathematical symbols. Variable and expressions join together to form the equations, which have a major role to play in solving the real life problems related to certain expressions.

Let us take an example: to form the variable expression, we need to first understand which symbols are used to represent which words. We must remember the following tips:
+ Sign is used to replace the words Add, Sum, Plus, In All, Increased By, join.
-  Sign is used to represent the words like difference, less, reduced by, subtracted, and decreased by,
X  Sign is used to replace the words like product, multiply , times and,
Sign is used to represent the word divide, quotient
Now let us try to form some expressions:
a)      Add a to 5 to get b
We write the above expression as:
=> a + 5 = b
b)      7 is reduced from m to get n,
We write the above expression as:
=> m – 7 = n
c)        The product of x and y is 35,
We write the above expression as:
=> x * y = 35
d)      If t is divided by 3 we get 8,
We write the above expression as:
=>  t / 3 = 8,
Thus we observe here that x, y, t, m, n, and b are the variables and x-y, t/3 is the expressions. More over they are equated with the equal to sign, so the equations are formed with the support of variables, constants and the mathematical symbols.
The expressions can be evaluated by putting the values of different variables and the values can be attained.
Let us understand it more clearly with an example: Solve x + 2y, when x = 3 and y = 5.
Here putting the values of x and y in the equation x + 2y, we get:
= 3 + 2 * 5,
= 3 + 10,
= 13.
Again let us try another expression:
Evaluate x – y/2, if x = 7 and y = 2
Putting the value of x and y in the given expression we get,
=  7 – 2/ 2,
= 7 – 1 (as 2/2 is 1),
= 6.

## Order of Operations

Algebra is basically the Combination of variables and the operations written in form of the expressions. Let us learn about order of operations in Algebra. The Order of Operations is a standard that defines the order in which one should simplify different operations such as addition, subtraction, multiplication and division. When we write any algebraic expression, we...Read More

## Distributive Properties

Word distribution in Algebra means breaking. We also call the distributive property as distribution law. By distributive property definition, we Mean “to separate“ or “to break into parts”.
In algebra when we say we are applying distributive properties, we mean we are expanding the given expression or we are distributing the terms of the given expression.

## Associative Property

Associative property is a basic property of the binary operations which is used in mathematics. This property says that if we perform addition or multiplication operation on any Set of Numbers then both the operations will be same without considering the grouping of the numbers i.e. it does not matter how numbers are grouped. This property basically includes more th...Read More

## Open Sentences

Sometimes it is difficult to determine the truth value of a given sentence even when the sentence shows the complete meaning, the sentence may be true for a number of population and false for the same.
Open sentence in Math usually refers to the equation or equality and described as open in the sense. The open sentence math is a general expression that contains one or mo...Read More

## Identity and Equality Properties

There are different properties of Algebra which makes the understanding of concepts of algebra easier to understand. By applying these properties we can find the solution of different Algebraic Equations easily. Identity And Equality Properties of algebra can be understood by the following ways. Once we are able to recognize the property of identity and ...Read More

## Commutative Property

Commutative property in mathematics is a property of binary operations. These binary operations are mainly multiplication and addition. A binary operation will be commutative if we change the order of operands then it will not change or affect the end result of the operation. In this we do not change the order of operation which is done for Associative Property of a...Read More