# VARIABLES AND EXPRESSIONS

"Variables and Expressions" is the basic topic required for the students who would like to study Algebra in math.

## What is Variable?

The Symbol which has no value is called as variable. The value of the variable may change from one problem to another problem.The alphabets are being used to represent variables.

## What is expression?

Expression is an algebraic or mathematical statement involves numbers,one or more variables and the operation symbols like +,-, x ,÷.

## Examples of Variable:

To understand this topic better let us consider the following examples.

 Example 1  x - 3 = 5   x = 5 + 3   x = 8In this problem the value of the variable x is 8. Example 2:  x + 1 = -3  x = -3 -1  x = -4In this problem the value of the variable x is -4.

In both the problem we are finding the value of the same variable "x". But we got  different values. From this we come to know that the value of variable gets changed from one problem to another problem.

## Examples of expression:

(i) 5x + 3

(ii) a - 9

(iii) 2y + 7

these are the examples of expressions.

## Difference between equation and expressions:

An equation contains expressions that are separated by an equals sign.

2x - 4 is the example of expression.

2x - 4 = 5 is the example of equation.

The difference between them is just "equal sign".

## How to write algebraic expressions from word problems?

Here you can find some basic ideas to write algebraic expressions from word problems. "Translating word problems into equations" is a much needed thing to the students who study math in all levels.

For some students, solving word problems in math is never being easy and always it is a challenging one. Once students understand the technique of solving word problems,it will become easy.

Let us take a example,

Cost of one chocolate is \$2. From this we need to find the cost of 5 chocolates.

To find the cost of 5 chocolates we need to add 2 + 2 + 2 + 2 + 2 = 10. Instead of adding 2 five times simply we can multiply 5 and 2.So we will get 10.

Like that now we have to find the cost of "n" chocolates if the cost of one chocolate is \$3. The answer is "3n".

 Terms are being used in word problems Corresponding signs to be used more,sum difference,differtimes (or) ofistwicethrice + (addition)- (Subtraction)x (Multiplication)= (equal to)Multiply by 2Multiply by 3

## Examples of variables and expressions

Problem 1:

A taxi fare after each km when the fare is \$15 for the first km and \$8 for each km that he traveled. Find the total cost that he has to pay for the whole journey.

Solution:

Let "x" be the number of kilometer that he traveled additionally.

Total cost that he has to pay is 15 + 8x Let us see the next example of "variables and expressions".

Problem 2:

John has 10 more marbles than Peter. Then find the total number of marbles.

Solution:

Number of marbles that Peter has = x

John is having 10 more marbles than Peter

The mathematical sign for the term more is "+" . 10 more means we have to write 10 + x.

Number of marbles that John has = 10 + x

Total number of marbles = x + (10 + x)

Let us see the next example of "variables and expressions".

Problem 3:

Write the algebraic expression for the product of two consecutive even integers.

Solution:

Let "x" be the even number

then "x+2" be the consecutive even number

the product of two consecutive even integer is  x(x+2)

Let us see the next example of "variables and expressions".

Problem 4:

The length of the rectangle is twice its breadth. Write the algebraic expression to find its area.

Solution:

Let "x" be breadth of the rectangle

= 2x

Area of the rectangle = (Length + breadth)

= x x 2x

Let us see the next example of "variables and expressions".

Problem 5:

Solution:

Let "x" be number of mango cookies

Let us see the next example of "variables and expressions".

Problem 6:

Write the algebraic expression to show the sum of three consecutive numbers.

Solution:

Let "x" be number a number

Then "x + 1" and "x + 2" are the next two consecutive numbers

Sum of the numbers "x + (x + 1) + (x + 2)"

Problem 7:

"2 increased by a" write the algebraic expression for the above statement.

Solution:

"increased" means "positive" sign

"2 + a" is the algebraic expression for the above statement.

## Related topics of "variables and expressions"

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WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

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