Introduction to algebraic expressions:
Algebraic expressions are formed from variables and constants. We simply use the combination of operations of addition, subtraction, multiplication and division on the variables and constants to form expressions. Algebraic expressions does not contain equal sign.
Some examples of algebraic expressions:
2x + 2y , 2xy , x2 - y2 , 3m + n - 5.
There are one or more terms in the algebraic expressions. For example, 3x2 + 4x + 2 is algebraic expression. It has three terms.
Let us discuss about some example problems on Algebraic expressions.
An algebraic expression is a number, a variable or a combination of the two connected by some mathematical operation like addition, subtraction, multiplication, division, exponents, and/or roots.
For eg.: 4x, 3p, 2a+b, 6z/5
Introduction about Algebraic expressions:
Expressions are a central concept in algebra. A variable can take various values. Its value is not fixed. On the other hand, a constant has a fixed value. We combine variables and constants to make algebraic expressions. For this, we use the operations of addition, subtraction, multiplication and division. We have already come across simple algebraic expressions like x + 3, y – 5, 4x + 5, 10y – 5 and so on. The above expressions were obtained by combining variables with constants. We can also obtain expressions by combining variables with themselves or with other variables.In this article we will see some definitions, facts about algebraic expressions
Terms about Algebraic Expressions
Properties about algebraic Expressions:
Like terms: When the terms are same variables then that terms are called as like terms. Otherwise it is called as unlike terms
2xy and 5xy because the factors of 2xy are 2 and x and y. and factors of 5xy are 5 and x and y both factors are same. So these are like terms.
Unlike terms: The terms 2xy and –3x , have different algebraic factors. They are unlike terms. Similarly, the terms, 2xy and 4 are unlike terms. Also, the terms –3x and -4 are unlike term.
Coefficient of the Term: The value in front of the variable is called as the coefficient of the term. The above example the coefficient of x is -3.
Facts about Algebraic Expressions
Monomial: The number of terms in an expression is one then the expression is called as monomial. For example 5x
Binomial:The number of terms in an expression is two then the expression is called as binomial. For example,
x + y, m – 5
Trinomial: The number of terms in an expression is three then the expression is called as trinomial. for example, the expressions x + y + 7, a b + a +b
Polynomial:An expression with one or more terms is called a polynomial. Thus a monomial, a binomial and a trinomial are all polynomials. For Example: 2x3+5x2+15x+22.
Finding the value of an expression:
This is nothing but substituting the values to the variables in the expression. That gives the solution to the expression. For example the area of a square is length2, where l is the length of a side of the square. If l = 8 cm., the area is 82 cm2or 64 cm2; if the side is 12 cm, the area is 122 cm2 or 144 cm2 and so on.
When an expression is written using words or phrases, it is a verbal expression. It is in a statement form. The symbols and statements used have the same meaning as they have in arithmetic.
Signs and symbols:
‘=’ means ‘is equal to’
‘≠’ means ‘is not equal to’
‘<’ means ‘is less than’
‘>’ means ‘is greater than’
‘≤’ means ‘is less than or equal to’
‘≥’ means ‘is greater than or equal to’
The following are the list of words used and their meaning:
1. Addition : sum, plus, add to, more than, increased by, total
2. Subtraction: difference of, minus, subtracted from, less than , decreased by, less
3. Multiplication: product, times, multiply, twice, of
4. Division: quotient , divide, into, ratio
Variable expressions to algebraic expressions:
In Algebra an expression is a term which consists of both symbols and numbers. There are two types in that. They are Algebraic and Verbal expressions. Algebraic expression consists of signs and symbols. The signs involve signs of several operations like addition, subtraction, multiplication and division. The symbol involves all Arabic numerals and literal numbers. Ex: 3ax, 4yz…Verbal expression is the expression which consists of verbal phrases like sum, product, less than, etc…..
Verbal Expressions into Algebraic Expressions Explanation:
Some of the important operations that are used for this verbal expression into algebraic expression are,
- Increased, Plus, more, total, add, sum +
- Difference, Minus, less, decreased, subtract, -
- Product, Times, multiply, double, twice, product *
In words they can be expressed as
Sum of a and b a + b
Difference of a and b a – b
In addition with these basic operations some other operations like less than and greater than...
- Less than <
- Greater than >
- Less than or equal <=
- Greater than or equal >=
Types of Algebraic Expressions
Monomial
A monomial is an algebraic expression formed by a single term.
Binomial
A binomial is an algebraic expression formed by two terms.
Trinomial
A trinomial is an algebraic expression formed by three terms.
Polynomial
A polynomial is an algebraic expression consists of more than one term.
In math, An algebraic expression is an expression containing symbols, variables and constants together. In math, Verbal expression is a sentence forming from an algebraic expression. Some of the verbal phrases for arithmetic operation is given below. Using these, we can frame the verbal expression for given an algebraic expression.
Let us see brief about verbal expression in math.
Verbal Expression in Math:
The verbal expression for an algebraic expression a + b may write as following,
a plus b , a added to b, a is increased by b, the sum of a and b, b is added to a, b more than a.
The verbal expression for an algebraic expression a - b may write as following,
a minus b , a is decreased by b, b subtracted from a, b less than a, a diminished by b, a reduced by b, the difference between a and b.
The verbal expression for an algebraic expression a x b may write as following,
a times b , the product of a and b, b is multiplied by a.
The verbal expression for an algebraic expression a ÷ b may write as following,
The quotient of a and b, a is divided by b.
Let us learn about how to translate algebraic expression into verbal expression.
Introduction to verbal expression in math:
In math, An algebraic expression is an expression containing symbols, variables and constants together. In math, Verbal expression is a sentence forming from an algebraic expression. Some of the verbal phrases for arithmetic operation is given below. Using these, we can frame the verbal expression for given an algebraic expression.
Let us see brief about verbal expression in math.
Verbal Expression in Math:
The verbal expression for an algebraic expression a + b may write as following,
a plus b , a added to b, a is increased by b, the sum of a and b, b is added to a, b more than a.
The verbal expression for an algebraic expression a - b may write as following,
a minus b , a is decreased by b, b subtracted from a, b less than a, a diminished by b, a reduced by b, the difference between a and b.
The verbal expression for an algebraic expression a x b may write as following,
a times b , the product of a and b, b is multiplied by a.
The verbal expression for an algebraic expression a ÷ b may write as following,
The quotient of a and b, a is divided by b.
Let us learn about how to translate algebraic expression into verbal expression.
Example Problems of Verbal Expression in Math:
Problem 1:
Translate this algebraic expression into verbal expression: 3 + b
Solution:
We can write it as,
b more than 3, 3 plus b, 3 added to b, b is increased by 3.
Problem 2:
Translate this algebraic expression into verbal expression: 3 - b
Solution:
We can write it as,
b less than 3, 3 minus b, b subtracted from 3, b is decreased by 3.
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