BASIC MATHS

About "Basic maths"

The webpage basic maths 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

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 maths"

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"

Let us see the next concept of "basic maths"

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 

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. 

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.

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

Anything to the power zero is 1.

 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 ?

Let us see example problems on exponents of "basic maths"

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"

Let us see the next concept of "basic maths"

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 maths"

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 maths"

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 maths"

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"

Let us see the next concept of "basic maths"

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"

Let us see the next concept of "basic maths"

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" 

Let us see the next concept of "basic maths"

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"

• Algebraic identities
• Square root by long division
• Combining like terms
• Like terms and unlike terms
• Area and perimeter
• Negative exponent rules
• Logarithms
• BODMAS rule

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