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 = 8

In this problem the value of the variable x is 8.

Example 2:

  x + 1 = -3

  x = -3 -1

  x = -4

In 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,differ

times (or) of

is

twice

thrice

+ (addition)

- (Subtraction)

x (Multiplication)

= (equal to)

Multiply by 2

Multiply 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

Length = twice its breadth

             = 2x

Area of the rectangle = (Length + breadth)

                                       = x x 2x

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

Problem 5:

George made 54 chocolate cookies and some mango cookies.How many cookies did he make?

Solution:

Let "x" be number of mango cookies 

Total number of cookies that he made is "54 + x"

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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ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

Quantitative aptitude

Multiplication tricks

APTITUDE TESTS ONLINE

Aptitude test online

ACT MATH ONLINE TEST

Test - I

Test - II

TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices

ORDER OF OPERATIONS

BODMAS Rule

PEMDAS Rule

WORKSHEETS

Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

SOHCAHTOA

Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem

MENSURATION

Mensuration formulas

Area and perimeter

Volume

GEOMETRY

Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem

ANALYTICAL GEOMETRY

Analytical geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance

Midpoint

Area of triangle

Area of quadrilateral

Parabola

CALCULATORS

Matrix Calculators

Analytical geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator

MATH FOR KIDS

Missing addend 

Double facts 

Doubles word problems

LIFE MATHEMATICS

Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work

SYMMETRY

Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry

CONVERSIONS

Converting metric units

Converting customary units

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic 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