Adding Integers

In the previous section we have discussed about how to multiply fractions and In today's session we are going to discuss about Adding Integers, When we talk about integers, we say that integers are the series of all positive and negative integers, with zero as the middle number.  The series of integers is endless and extends from minus infinite to positive infinite. We will look at Adding Integers, and how the result of addition of two integers can be attained.  Let us first look at the rules of adding two integer numbers:
a)      If we have two integers a and b such that both the integers are positive integers then we will simply add the digits and get the sum of the two numbers along with the positive sign. Now we see the following example for such sum of integers: +4 + ( + 5 ) = +9
b)      If we have two integers a and b such that  one of the integers is a  positive integers and the second number is a negative number, then we will simply find the difference of the two digits  and get the sum of the two numbers along with the sign of the number which has a greater absolute value. If the negative number has greater magnitude, then we say that sign will be negative and if the positive number has a greater magnitude then we have the result as a positive number.  Now we see the following example for such sum of integers: +4 + ( -7 ) = -3 and  -4 + ( + 7 ) = + 3
c)      If we have two integers a and b such that both the integers are negative integers then we will simply add the  magnitude of the two digits and get the sum of the two numbers along with the negative sign. Now we see the following example  for  such sum of integers : -4 + ( - 5 ) = -9

We will learn about Integration by Parts in class 11 CBSE syllabus of mathematics.

how to multiply fractions

Fractions are the numbers which can be expressed in the form of a/ b, where a and b are the whole numbers and b <> 0. We can perform all the mathematical and the logical operations on the fraction numbers. The mathematical operations involve addition, subtraction, multiplication and division of the two or more fraction numbers. On another hand we say that the logical operation means the comparison of two or more fraction numbers. Logical operations can help us to arrange the series of the fraction numbers in the ascending or descending order.  To learn about How to Multiply Fractions, we say that we will multiply the numerator with the numerator and the denominator is multiplied with the denominator. The new fraction which we get after the multiplication of the numerator with the numerator and the denominator with the denominator, we get the product of the two fraction numbers. We will convert the product of the two fraction numbers in its standard form, so for this we will divide both the numerator and the denominator with the H.C.F of the two numbers.
Once we get the fraction in its lowest form, we will check if we have got the resultant fraction in the proper fraction or improper fraction.  In case the resultant fraction is in the standard form and in the form of the proper fraction, we say that this is the final result. In case the result is in the form of the improper fraction, we say that we will be expressed in the form of mixed fraction.
To learn about the topic of Standard Deviation in statistics, which is covered in the Syllabus for Class 11th Cbse, we will visit the site of any of the math online tutorimg and get the guidance regarding the different method of solving the value and In the next session we will discuss about Adding Integers.

math tutor

We visit the Math Tutor, to learn about the Algebraic Expression, where we can learn how to perform on the algebraic expressions, which can be addition, subtraction, multiplication and division.  Thus let us see how to work with the addition of the algebraic expression. If the two algebraic terms are like terms, then we say that the coefficient of the two terms can be added, else we cannot add them (for detail study click here) . Let us look at the following examples: 3x + 4y + 2x – y
 Here we have two types of terms, one with the variables x and the with the variable y. So we say that the terms with the variable x will be added together and the coefficients of the terms with variable y will be added separately. Thus we get :
3x + 2x + 4y – y
= 5x + 3y Ans
 In the same way we will perform the subtraction in the algebraic expressions. So for subtraction too, we will first bring together the like terms and then get the result for the given algebraic expression.
 Now we will learn the operation of multiplication, which can be performed on the algebraic expressions. For this let us look at a monomial multiplied to a monomial.
Eg : 3x>2 *  4 x>4
 Here we will multiply the coefficients of both the monomial and the powers of the variables are added up when the two terms are multiplied. So we observe here that the constant values 3 and 4 are multiplied to get 3 * 4 = 12.  Similarly we add the powers of x to get x>6
= 12 * x>6 is the product of two expressions.

To learn about the Logic Tamilnadu Board Sample Paper, we need to look at the different types of the papers available online and understand their patterns.

column multiplication

Column multiplication can be done for solving the multiplication problems (read more on multiplication) which are  for the larger numbers. In order to learn column multiplication, we put the first number to  be multiplied in  one row and the number with which we need to multiply in another row. Now we will start picking one row after another from the ones place and each number of the row  of the multiplicand is multiplied with the multiplier. In case the product is greater than 9, then we will carry over the digit of the tens place and thus we get the result.
Let learn it with the help of an example :
If we have the problem : 3402 * 4, then we say that the multiplicand is 3402 and the multiplier is 4. The two numbers are placed under the  place values and so it looks as follows :
   Thousands           hundreds         tens         ones
        3                          4                   0              2

                                                      X                4

  12                                16             0              8
 Here each digit starting from the ones place is  multiplied by the  number 4, so we get 4 * 2 = 8 ,  4 * 0 = 0 ,  4 * 4 = 16 , 4 * 3 = 12
 Now in hundreds and in thousands place, we observe that the result is 16 and 12, which is in two digits, so we will carry over the digit “1 “ from 16 to the thousands place and thus the result will appear as follows :
   Thousands           hundreds         tens         ones
        3                          4                   0              2

                                                      X                4                                                                                                                                      

    13                         6                     0            8
In this way we will get the product of the two numbers by column method.
 To learn about  Area of a Circle Formula we have the online books and content available. AP secondary school education board  also has a good content for mathematics learning. In upcoming posts we will discuss about math tutor and How to perform Unit Conversions.

Mathematical Reasoning

In math online tutoring, Mathematical reasoning is technique of problem solving without knowing about what will be done for solving the problem, if you know about the methods of solving the problems then it will not be defined as mathematical reasoning.
Mathematical reasoning has problems that does not occur in daily life and they are not solved by using any procedure or method but these types of problems are solved by making some strategies that is not defined anywhere and also these are not based on the single rule or perception but have variety of strategies for problem solving.
These problems do not follow any procedure or rule and if you are stuck anywhere at any time because of some problem then you have to do something to solve the problem without following any rules and regulations occur at that time.
Examples (from central board of secondary education) of problems related to reasoning are:
Like write the numbers that are made from 11 tens, 8 ones and 2 hundreds?
Like If Jon has 23 chocolates and he put equal number of chocolates in two bags and after putting seven chocolates are left then how many chocolates he put into each bag?
These are some problems that are needed little bit attention by the solver to solve and because of this; problems are known as mathematical reasoning problems.
We can take an example for multiplying the number 36 * 17, it will be solved as by multiplying them but for solving this problem in minimum time add 4 to 36 that is equal to 40 and add 3 in 17 to make it 20 and multiply them that is much easier than the multiplication of 36 * 17. So answer for multiplication of 40 * 20 = 800 then subtract 7 (4+3) from 800 that is equal to 793, is the answer.


In upcoming posts we will discuss about column multiplication and Elapsed time problems in Grade IV. Visit our website for information on how to do trigonometry