Multiplying Fractions

In the previous post we have discussed about Dividing Fractions and In today's session we are going to discuss about Multiplying Fractions. Number system can be considered as a important part of mathematical body because without using a number system we can’t solve any mathematical problem. In the category of number system, fraction is a special one which is able to solving various kinds of problems. Fraction is a way of representing any two whole in the form of ratio. Here the word ratio refers to put two numbers in that manner like one number is divided by another number. Suppose there are two numbers like a and b. Now it can be represented in the form of a/b.

In the simple sense we can say that fraction is a mathematical concept to divide an object into equal parts. Suppose there is a number 6 / 5 where upper value of fraction called as numerator and below value known as denominator. Here we are going to discuss about Multiplying Fractions where the given name specifies that calculating product value between more then one fractional numbers.

To perform the successful multiplying fractions we need to follow some steps that are given below:

STEP A): First of all multiply the numerators of both given values. 

STEP B): After that do the same task for denominators values.

STEP C): In the last step we there is any need then simplify the obtained fraction as possible.

The above are the most basic steps that helps the user to clarify their doubts about the concept of Multiplying Fractions very easily. The above task can be performed by simplify the fraction first after that performing the calculation of product between both value of fraction. The process of simplifying the fraction can be done by obtaining the concept of multiplication between numerator of one fraction with denominator of another fraction. that minimize the given fraction before calculating product of fractions. (know more about Multiplying Fractions, here)

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Dividing Fractions

In the previous post we have discussed about How to Solve Multi Step Equation and In today's session we are going to discuss about Dividing Fractions. Hi friends, we will study many types of number in mathematics. Here we will discuss about the fraction. The number written in form of numerator by denominator or (in x / y form) is known as fraction. For example: 5/15, 8/10, 79/200 and so on all are fraction numbers. The upper part present in a fraction is said to be numerator and the lower part present in a fraction is said to be denominator. Now we will see how to dividing fraction numbers. To Dividing Fractions we need to follow some steps.

Step 1: First we have to take two fraction values. Suppose we have 7 / 10 and 11 / 17, then divide the fraction. First of all write both fraction values in the division form. So we can write it as:

= (7 / 10) / (11 / 17).

Step 2: To divide the fraction number first write the multiplication form. So if we write the fraction values in multiplication then numerator value become denominator and denominator value become numerator. The above fraction values we can write as:

= (7 / 10) / (11 / 17),

= (7 / 10) * (17 / 11).

Step 3: Then cancel the term which can be easily cancel out. Other wise multiply the numerator value to the numerator and the denominator value to the denominator. The above values are not in the position to cancel out so multiply. So we can write it as:

= 7 * 17 / 10 * 11. on multiplying we get:

= 119 * 110. This is the required solution.

For example: Divide (5 / 9) / 15 / 20. (know more about Dividing Fractions, here)

solution: Here we need to follow the above steps to divide the number.

= (5 / 9) / (15 / 20). write the number in multiplication form. So it can be written as:

= 5 / 9 * 20 / 15. if we solve this fraction value we get 20 / 27 as an answer.

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How to Solve Multi Step Equation

In the previous post we have discussed about Rational Function and In today's session we are going to discuss about How to Solve Multi Step Equation. In multi – step equations, we solve the equation in one – step and two steps. When we solve the multi – step equation then we change the position of like variable in one side and unlike variable in other side of equation. Now we will see how to solve multi step equations.
To solve multi step equations we have to follow some of the steps:
Step1: To solve multistep First we have a multistep equation.
Step2: Then combine all the like term in one side or divide that number on both sides of the equation.
Step3: And take the constant number in other side of the equation.
Step4: Then we make one term equation in both the equations.
Step5: If we calculate the equation then we change the sign of the variable. If the number is positive then we change it into negative and the number is negative then we change it into positive.
Step6: At last we get the answer.
Now we will see some of the example by using all the above steps:
Step1: firstly we have a multistep equation:
      -7 (6q -8) = 6q + 24, then we solve the bracket and make the equation in proper form.
      ⇒-42q + 56 = 6q + 24, Now follow the same processor i.e. (know more about Multi Step Equation, here)
Step 2:- This equation has its own variable on both side of equal sign. So put the like variable on the same side. Let’s move the value 6q from the right side to left side and by subtraction 6q on both side of the equation.
         -42q + 56 = 6q + 24;
         -6q              -6q
        -48q +56 = 24,
Step: 3- On solving the equation we use new procedure of one and two step equations. On subtract 56 on both side of the equation:

       -48q + 56 = 24
                 -56   -56
             -48q = -32
Now divide the equation by -48 on both sides.
          -48q     =   -38
           -48            -48
  q = 38/48;
  q = 0.79;
 We get the value of q = 0.79. This is how we can solve the multistep equation.
Now we will see What are Isotopes? It can be defined as the atoms of same element have different number of neutrons. Before preparing for exam please prefer the online tutorial of icse board papers.

Rational Function

In the previous post we have discussed about 

Define Complex Number 

and In today's session we are going to discuss about Rational Function. Rational function in the math can be defined as that function that can be expressed in the form of the ratio of the 2 functions which are polynomial. It is not necessary that the coefficients of the polynomials should be rational numbers or the values which are  accepted by the function should be rational numbers. (know more about Rational Function, here)

When we have only single variable say x then any function is said to be the rational function only when that can be expressed in the way which is given below as follows. 

g ( x ) = p ( x ) / q ( x ),

In the above expression the functions p and q are the polynomial functions with variable as x. Also q should not be the 0 polynomial.

Now let us talk about the domain of the rational function. The domain of the function g ( x ) includes all those values of the x for which the function q ( x ) in the denominator does not come equal to 0. It is considered here that the fraction has been expressed in the terms of the lowest degree.  

It can also be said that every single polynomial type of the function is known as the rational function with the condition that q ( x ) = 1. And any function that can’t be expressed in the way described above cannot be called as the function which is rational but we do not use the term irrational for those functions, we use it only for the numbers.

Now let us take some one example of the rational function. For example y = ( x2 – 6x – 7 ) / ( x2 – 5 ) is a rational function which has degree two.

In order to get more help on topics: Rational Function, How Do You Find the Area of a Rectangle and Karnataka Board Syllabus, you can visit our next article.

Define Complex Number

The complex number can be defined as such a number that we can frame in the form of the p + qi in which p and q are the numbers which lie on the real line while i is known as the imaginary unit. It should be known that i * i = i2 = -1. In the form written above for the complex number p is known as the real part of the complex no. whereas q is known as the imaginary part of this number.(want to Learn more about Complex Number, click here)

It can be said that the complex numbers are the ones which help in extending the thought of the number line which is one dimensional to the plane which is complex by utilizing the x axis for the part which is real and by utilizing the y axis for the part which is imaginary.

We can identify any complex number of the form p + qi by any point represented by ( p, q ). It should be known that such a complex no. the real part of which is equal to 0 is known as purely imaginary while such a complex no. the imaginary part of which is equal to zero is simply known as any real number. Thus we can say that the complex numbers include just the simple real numbers but extend them for solving such problems which in general can’t be solved by just the real numbers.  

Now let us take an example of the complex no. say 2 + 3i. Thus in this example 2 is known as the real part of the complex no. whereas 3 is known as the imaginary part of the complex no.. To get area of a rectangle we need to understand formula for area of a rectangle. You can get icse syllabus for class 8 on various online educational portal and In the next session we will discuss about Rational Function.