Algebraic Expressions Worksheet

Algebraic Expressions Worksheet Explained

Have you ever heard of algebra? I’m sure you must have heard about it somewhere. It is a basic concept of maths. Algebra comes from an Arabic word which means a reunion of broken parts. The study of the mathematics of symbols and the guidelines for changing these symbols is known as algebra. Algebra is divided into parts :

  1. Elementary Algebra

  2. Abstract Algebra/ Modern Algebra

Elementary algebra is important for the study of math, science, engineering and is also applied in medicine and economics.

Abstract Algebra is for advanced mathematics and is studied by professional mathematicians.

It helps us by providing a way to write formulas that easier to comprehend as compared to expressing everything in words.

Before we proceed to know more about Algebraic Expressions first let’s know about a few other important terms.


What Is a Term?

A term can be anything. It can be a number, a variable, or a combination of both a number and a variable joined by the sign of multiplication or division.

For example: x, 8, 4y, t/2 etc.


What Is An Expression?

An expression is a term or a combination of terms that are brought together by operations like addition or subtraction.

For example:

6x, 3w – 8, 7b + 5t – 6 etc.

What is the coefficient?

A coefficient is a number that is attached to a variable. 

For example:

6x, here 6 is a coefficient.


Algebraic Expressions:

An algebraic expression is a combination of things. This combination consists of integers, variables, constants and algebraic operations like addition, subtraction, multiplication, division and has an exponent that is a rational number.

An example of an algebraic expression is: 

3x2 − 2xy + c

In the given equation 3 and 2 are coefficients. The power on x is an exponent. The 3x2 and 2xy are the terms. C is a constant. The signs ‘-’,’+’ are operators. The x, y are variables. Algebra has its own terminology.


Types of Algebraic Expressions:

There are 3 main types of Algebraic Expressions:

  • Monomial Expression

  • Binomial Expression

  • Polynomial Expression


Monomial Expression

An algebraic expression with one term only is called a monomial.

For Example 3x4, 3xy, etc.


Binomial Expression

An algebraic expression with two terms that are dissimilar.

For Example 5xy + 8, xyz + x3, etc.


Polynomial Expression

An algebraic expression which has more than one term with a non-negative integral exponent of a variable is known as a polynomial expression.

For Example ab + bc + ca,  etc.


Other Types of Expression:

Other than monomial, binomial and polynomial types of expressions, an algebraic expression is also classified into two additional types of expressions which are:

  • Numeric Expression

  • Variable Expression


Numeric Expression:

An expression consisting of numbers and operations, with the absence of a variable, is called numeric expression. For example 10+5, 15÷2, etc.


Variable Expression:

An expression containing variables, numbers and operation to define an expression is called a variable expression.  For example 4x+y, 5ab + 33, etc.


Rules of Algebra:

Algebra follows some rules while solving mathematical problems. These rules are:

  1. Commutative property of addition

  2. Associative property of addition

  3. Additive identity property

  4. Additive inverse property

  5. Commutative property of multiplication

  6. Associative property of multiplication

  7. Multiplicative identity property

  8. Multiplicative inverse property

  9. Distributive property


Commutative Property Of Addition And Multiplication

If a function is swapped and we still get the same result then this property is known as Commutative property. It would not give a different result even if the terms are shuffled in the equations.

For example : a+b =b+a

a x b= b x a

Note:  1. This is not applicable for subtraction

2. This is not applicable for division.


Associative Property Of Addition And Multiplication

When you group numbers together to perform some operation it is known as Associative. No matter in what order you group the terms the result will be the same.

For example : (a+b)+c =(b+c)+a

(axb)xc=(cxb)xa

Note:  1. This is not applicable for subtraction

2. This is not applicable for division.


Distributive Property

When you split the multiplication of a number by another term this property is known as the distributive property.


Additive Identity Property

The property of a number that it is equal to itself is known as its identity. When you perform an operation on two numbers so that it becomes equal to the variable of the sum. When you add any number and 0 it is equal to itself. This is the additive identity.

Note:  1. This is applicable for subtraction


Multiplicative Identity Property

When any number is multiplied to 1 we get the number itself. This property is the multiplicative identity property.

Note: 1. This is applicable for division. To understand better you can go through algebraic expressions for grade 6 worksheets and answer.


Fun Facts:

  1. Every variable part of an expression has a coefficient. The coefficient is either the number attached to it or 1.

  2. We can perform any mathematical operation on an algebraic expression without changing its value simply by doing it on both the sides of the equation. 

FAQ (Frequently Asked Questions)

1. How Do You Formulate Algebraic Expressions?

An algebraic expression is a combination of things. This combination consists of integers, variables, constants and algebraic operations like addition, subtraction, multiplication, division and has an exponent that is a rational number. Let’s take an example to understand it in a better manner.

For example, Simmi’s age is thrice more than Kina’s. The sum of the ages of Simmi and Kina is 40. If we have to express this in algebraic form rather than in words, we’ll write it in the following way:

3x + x = 40 ⇒ 4x = 40; where x is the age of Kina. you can find more sums like this on the internet under the name algebraic expressions worksheets. 

2. Are All Algebraic Expressions Polynomials?

The answer is no. All algebraic expressions are not polynomials but the converse of it is true. That is all polynomials come under algebraic expressions. An algebraic expression which has more than one term with a non-negative integral exponent of a variable is known as a polynomial expression.

Algebraic expressions include irrational numbers but polynomials include only variables and coefficients with mathematical operations(+, -, ×) 

An algebraic expression may or may not be continuous functions whereas all polynomials are a continuous function.

There are 3 main types of Algebraic Expressions:

  • Monomial Expression

  • Binomial Expression

  • Polynomial Expression

Since the algebraic expression can also be monomial and binomial therefore,  all algebraic expressions are not polynomial.