BASIC MATH RULES

About "Basic math rules"

The webpage, basic math rules is going to provide you some preliminary concepts in maths. Some students will have the feeling that the subject math is very though for me. Actually it is not like that. If some one will guide them from the basic level, they will feel better. 

We have designed this page especially for those kind of students.

How to add two numbers with different signs?

Rules of adding integers with different signs

 Sign of first and second number

What do we have to do?

 + +

- -

Add both numbers and put "big number" sign for the answer.

 + -

(or)

 - +


Subtract small number from large number and put "large number" sign for the answer.

Easy way of understanding this concept:

This flowchart will explain you how to handle two numbers with different symbol.

The above rule is applicable for simplifying any two or more integers,fractions and decimals.

Note: Always we have to put big number symbol for answer.

Let us see example problems on adding integers of "basic math rules"

Example problems on adding integers

Problem 1 :

Simplify  -5 + 3

Solution :

What we have to check?

Consider the symbol of two numbers. The symbol of first number is negative and the symbol of second number is positive.

Do we have to add or subtract?

Since the symbols of both numbers are different we have to subtract small number from large number.Here small number is 3 and large number is 5. By subtraction we will get 2.

What symbol we have to put for answer?

We have to put symbol of big number. Here the big number is 5 and we have negative symbol for this.

-5 + 3 = -2 is the answer.

We have explained this concept in the below flowchart.

Problem 2 :

Simplify  -15 + 13 - 27 - 43 + 77

Solution :

First we have to write the numbers which are having same symbol.Here the numbers 15,27 and 43 are having same symbol

          = - 15 - 27 - 43 + 13 + 77

For more examples please visit the page "adding integers with different signs"

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Exponents

What is exponent?

The exponent of a number says how many times to use the number in a multiplication.

for example 5³ = 5 x 5 x 5

In words 5³ could be called as 5 to the power 3 or 5 cube.

Basic Exponent Rules 

Rule 1 :

When we have to simplify two or more the terms which are multiplying with same base,then we have to put the same base and add the powers. 

Rule 2 :

Whenever we have two terms which are diving with the same base,we have to put only one base and we have to subtract the powers.

Rule 3 :

Whenever we have power to the power,we have to multiply both powers. 

Rule 4 :

Anything to the power zero is 1.

Rule 5 :

 If we have same power for 2 or more terms which are multiplying or dividing,we have to apply the powers for every terms.

Note:

This rule is not applicable when two are more terms which are adding and subtracting.

For example (x + y) ^m = (x^m + y^m) is not correct

How to move an exponents or powers to the other side ?

If the power goes from one side of equal sign to the other side,it will flip.

that is x = 4²

Let us see example problems on exponents of "basic math rules"

Example problems on exponents

Problem 1 :

Find the value of (8/27)^(-1/3) (32/243)^(-1/5)

Solution :

For more examples please visit the page "Exponent rules"

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How to convert fraction into decimal?

To convert the given fraction into decimal, first we have to check whether the denominator of the mixed fraction is convertible to 10 or 100 using multiplication.  

If it is convertible to 10 or 100 using multiplication, we can convert the given mixed number into decimal as explained below. 

For more examples please visit the page "Fraction into decimal"

Adding fractions with different denominators

Here, we explain two methods to add two fraction with different denominators.

  • Cross multiplication method
  • L.C.M method

If the denominators of the fractions are co-prime or relatively prime, we have to apply this method.

For example, let us consider the two fractions 1/8,  1/3.

In the above two fractions, denominators are 8 and 3.

For 8 and 3, there is no common divisor other than 1. So 8 and 3 are co-prime.

Here we have to apply cross-multiplication method to add the two fractions 1/8 and 1/3 as given below. 

L.C.M method

If the denominators of the fractions are not co-prime (there is a common divisor other than 1), we have to apply this method.

Let us see the next concept of "basic math rules"

Radicals

A symbol used to indicate square of any number is called radical. The number which is under the root is called radicand.

    √3 is called square root of 3.  

How to simplify a radical number?

To simplify a number which is in radical sign we need to follow the below steps

  • Split the number as much as possible
  • If two same numbers are multiplying in the square root sign,we need to take only one number from the radical sign.
  • In case we have any number in front of radical sign already,we have multiply the number taken out by the number in front of radical sign already.
  • If we have cube root ∛ or fourth root ∜ like that we have to take one term from 3 same terms or four same terms respectively. 

Let us see example problems on radicals of "basic math rules"

Example problems on radical

Problem 1:

Simplify the following radical expression 

√27 + √75 + √108 - √48

Solution:

= √27 + √75 + √108 - √48

First we have to split the given numbers inside the radical as much as possible. 

 =  √(3 x 3 x 3) + √(3 x 5 x 5) +

                        √(3 x 3 x 2 x 2 x 2) - √(2 x 2 x 2 x 2 x 2)

=  3 √3 + 5 √3 + 2 x 3 √2 - 2 x 2 √2

=  3 √3 + 5 √3 + 6 √2 - 4 √2

= (3 + 5) √3 + (6-4) √2

= 8 √3 + 2 √2  

For more examples please visit the page "Simplifying radical expression"

Let us see the next concept of "basic math rules"

Simplifying fractions

Simplifying fractions means reducing the numerator and denominator as much as possible same numbers.

We have to divide the numerator and denominator by the same number at a time.

Step 1:

Write the numerator and denominator in single line and draw the L shape.

Step 2:

Divide them by common factors as much as possible. If two numbers are not divisible by any common number then we have to leave it as it is.

Step 3:

The pair of numbers which is at the last step is the simplified form of the given original fraction.

Problem 1:

Simplify 42/60 in simplest form

Solution:

Step 1:

Write the two numbers on one line

Step 2:

Draw the L shape

Step 3 :

Divide out common prime numbers starting from the smallest

For more examples please visit the page "Simplifying fractions"

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Converting percent into fraction

Step 1 :

Write the given percentage as fraction by taking 100 as denominator. 

Step 2 :

If it is needed, the fraction can be simplified further. That's it. 

In the process of converting percentage into fraction, we may have the following situations.

% (<100) ----> Proper fraction

% (>100) ----> Improper fraction / Mixed fraction

(multiple of 100) ----> Integer

Example  :

Convert the percentage given below into a proper fraction

24%

Solution :

24%  =  24/100  =  6/25

Hence the proper fraction equal to the given percentage is 6/25

For more examples please visit the page "Converting percent into fraction"

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Place value and face value

Place value :

Place value of a digit in a number is the digit multiplied by thousand or hundred or whatever place it is situated.

For example,

In 25486, the place value of 5 is = 5x1000 = 5000.

Here, to get the place value of 5, we multiply 5 by 1000. Because 5 is at thousands place. 

Face value :

Face value of a digit in a number is the digit itself.

More clearly, face value of a digit always remains same irrespective of the position where it is located.    

For example,

In 25486, the face value of 5 is = 5. 

To know more about place value and face value please visit the page "Place value and Face value

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Solving equations

A one-step equation is as straightforward as it sounds. We just have to perform one step in order to solve the equation. 

We have to isolate the variable which comes in the equation. 

Example 1 :

Solve :  5 + x  =  3

Solution : 

Here 5 is added to the variable "x". To get rid of 5, we have to take "negative 5" on both sides and solve the equation as explained below.  

For more example please visit the page "Solving one step equation"

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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