Algebraic Expressions

In this section we will talk about the basic algebra1 like operations related to the algebraic expressions. We will learn here about the process for evaluating algebraic expression in the algebraic mathematics. All the algebra in this article will be around the level of grade VI of CBSE math Syllabus.

In the mathematics, pupils learn about some standard fractions, decimals, exponential, and some other algebraic math. We form the algebraic expressions with the help of these algebraic components. In algebra we generally learn about the linear equations, linear function, graphs, positive linear function, factors, greatest common factor (GCF) etc.  In the field of evaluation of algebraic expressions and equations we learn about balancing equation and also about the solution of them.For practicing you can refer number sets algebra 1 worksheets,
In algebra, if we add some thing with some other quantity then they also form an expression. Any of the expressions is the first step to solve an algebraic expression. The algebraic expressions are the way to show any problem in the word form which contains some variables in it and tells the story of the problem in the expression form. It’s not always necessary that an algebraic expression contains an operation in it. An algebraic expression may contains some of the variables, some operations (+, -, x, / ) applied on those variables or some times only variables within it. As per the naming is concerned, the variables are the components of the expressions, the elements whose products form a single term of the algebraic expression, are called as factors and the numerical factors present with the variables are called as the coefficient of the expressions.
A simple example: the algebraic expression 5x + 6y – 8z = xyz. While evaluating algebraic expression, we have four different terms in the expression. 5 is coefficient of the x and in the R.H.S. term x, y, z individually are the factors of that term.If you want more information on algebra, click here.
The elements whose product forms a term of an algebraic expression are called the factors of that term.  The numerical factor of a term containing a variable is called the coefficient of the term.
The evaluation of algebraic expressions includes the formation of simple algebraic expressions with the help of some data. For example, while evaluating algebraic expressions we write an algebraic equation. Let n be any number then we can write expressions of several type according to the condition given. For example:
1.      Number “n” is increased by 45 can be written as n + 45;
2.      Number is decreased by 36 as n - 36;
3.      Number is get multiplied by 6 as 6 * n;
In some other form If n = 4 then (- 4) n + n² = ?
If x = 3, y = 4 and z = 2 then expression 2 x + 3 y + z² =?.
Similarly we can make a number of algebraic expressions. The expressions are categorized according to the number of terms contained in them into monomials, binomials, and trinomials.

In above content we have discussed about algebraic expressions and if anyone want to know about Proportions then they can refer to Internet and text books for understanding it more precisely. You can also refer Grade 7 blog for further reading on inequalities

Evaluating formulas

Hello children, in this section we are going to learn some of the concepts of algebra 2 help. We will discuss how to evaluate formulas for algebra. Chiefly variables are used for evaluating formulas.
The term variable means something that can vary or change. In other words, we can say that value of variable is not fix i.e. it keeps changing. Now we discuss the steps to evaluate formulas for algebra:
Step 1: For evaluating formulas first of all we measure what kind of variables are used in that geometric figure like rectangular is combination of length and width, then we assume variable for length and width like l = length and w = width.
Step 2: After measurement of variables, we evaluate what kind of operation is to be performed between variables like in area of rectangle, multiplication operation perform between length and width. So, area of rectangle = l * w .
Now we take some example to understand process of evaluating formulas –
Perimeter of square:
Step 1: We all know that all side of square are equal than there is only one variable exist length and we assume that l = length.
Step 2 : Now, we all know that perimeter of polygon is equal to sum of all side’s length . So perimeter of square is = l + l + l + l = 4 l.
So, formula to evaluate perimeter of square is 4l.
Area of triangle:
Step 1: We all know that there are two variable lengths and height exist in triangle. So, we assume that length = l and height = h.
Step 2 : Now we all know that area of triangle is half of multiplication of length and height . So, area of triangle = 1 * l * h.
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Perimeter of rectangle:
Step 1: We all know that there are two variable lengths and width exist in rectangle. So, we assume that l = length and w =width.
Step 2: Now, we all know that perimeter of polygon is equal to sum of all side’s length. So perimeter of rectangle is = l + b + l + b = 2 l + 2b
So, formula to evaluate perimeter of rectangle is 2l + 2b.
Area of circle :
Step 1: We all know that circle has only one variable which is radius. So we assume R = radius .
Step 2: Now we all know that area of circle is equal to mulplication of pi and square of r. So, area of circle = Π * r².
Similarly we can evaluate formula for each and every figure of geometry like perimeter of hexagon = 6 * l, area of cube = 6 * l * l etc.

In upcoming posts we will discuss about Algebraic Expressions. Visit our website for information on ICSE class 12 syllabus

  

math blog on grade VI

Mainly when we study about relationship of operators on numbers then this study is called the algebra. In grade V of icse board we learn how to use operations like addition, subtraction, multiplication, associative property of addition and multiplication worksheets and division on numbers, but in grade VI, we have to learn some new topics from algebra 2, but here we discuss topics about Equations which shows linear relationships.
So, first of all we discuss what is linear? Linear means one side is equal to other side like: x = 9
This means this equation is represent value of x is equal to 9.
Now we discuss what is relationship? Basically when one quantity is related to other quantity or we can say that one quantity is depend on other quantity then this dependency is known as a relation.(want to Learn more about algebra, click here),
Linear relationship is a way to represent relationship between two or more quantities in linear form. As we know velocity depends on acceleration and time and these three quantity are related with each other, then we define relationship in mathematical equation way –
v = at + c
And this equation as a representation between these linear relative quantities is called an Equations for linear relationships. We can call Equations for linear relationships as linear equations in short. So, we further proceed to understand linear equation:
 1)  Linear equation with two variables and one constant:
We take an example to understand about linear equation of two variables and one constant like we have two variables x, y, constant c and m is slope then linear equation between x and y is -
 y = mx + c
This is standard linear equation and this equation is also known as a line equation. So , when we draw graph between two variables x and y, then it  shows straight line and each point of straight line shows result of linear equation like we take an example -

Here slope m = 2 and constant c = 1
2) linear equation with three constants and two variables : We take an example to understand linear equation of three constants  and two variables like we have A , B and C three constants and two variables x and y , then linear equation is -
                  Ax + By = C  
Now, we will discuss about graphical representation of these type of linear equation : it shows straight line graph and each point of  straight line shows result of linear equation . So, graphical representation of above equation Ax + By = C is -

To determine the y intercept of the line,
Put x= 0, solve for y = C/B =b;
To determine the x intercept of the line,
Put y = 0, solve for x = C/A = a;
This graph shows us how we get x intercept and y intercept from linear equations like Ax + By = C.
This is all about the algebra and if anyone want to know about Algebraic Expressions then they can refer to Internet and text books for understanding it more precisely. Read more maths topics of different grades such as Arithmetic sequences in the upcoming blogs.