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.
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"
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 math rules"
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.
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
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"
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 math rules"
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"
Here, we explain two methods to add two fraction with different denominators.
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"
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
Let us see example problems on radicals of "basic math rules"
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 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 math rules"
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 math rules"
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 math rules"
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"
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
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
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
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
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 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