Algebra is a hard concept to comprehend, but it can be done easier. Are you confused by this statement? Well, the simple trick is to grasp the basic concepts of Algebra firmly, then it’d be an effortless task solving these equations. So let us understand the terms in Algebra in this article.
A term is a number or a variable in Algebra. Terms can have multiple mathematical operations like multiplied (*), added (+), subtracted (-), or divided (/) and returns a calculated value. A term can be of a constant value as well. These terms can be represented in expressions separated by plus, minus, multiply, or divide.
For example: 9a + 10 is an expression. “9a” and “10” are two terms. “9a” is a variable term, while “10” is a constant term. “9a” is variable because it has “a” multiplied to 9. The value of “9a” depends on the value of “a.” If “a” is zero, then “9a” will result in zero. You can separate these two terms by a plus (+) sign.
Let’s decode the algebraic expressions to understand the terms better!
What is Algebra, and How are Terms Used in Algebra?
Algebra is a study of mathematical symbols and how different rules are used to change those symbols’ values. “Symbols” are known as variables in the modern world. Symbols (Variables) are like a carrier of changing or a constant value.
These variables are used in combination with mathematical operations to derive relationships in the form of algebraic equations.
There are many jargons used in the world of algebra. Following is an example of fragmenting algebraic equations; this example will help you understand the use of each character in an equation.
Algebraic equation: 3x + 6y + 10 = 20
Here, The LHS of the equation is known as “expression.”
“3x” and “6y” are known as “Terms.”
3 and 6 are “coefficients.”
x and y are known as “variables.”
10 and 20 are constants
Terms are arranged in an equation with mathematical operators in between in order to form an algebraic equation. Terms include a base of algebra having one or more variables multiplied like (xy) or (x) are terms in algebra. Terms may or may not have coefficients attached as a prefix. The coefficients, by default, multiply to term.
Term: 2xy , x=1 and y=2
Value: 2 * 1 * 2 = 4
How To Identify The Number of Terms in an Algebraic Equation?
The simple way to identify a term in an algebraic equation is to look for ASMD (Addition, Subtraction, Multiplication, Division) symbols. ASMD symbols separate two terms. Each term can have one or more variables with coefficients attached. All the variables and coefficients are multiplied by default to determine a constant value out of the term. You can situate terms on the LHS or RHS of the “equal to” sign.
Let’s try identifying terms in the equations mentioned below-
5 x + 7 y + 8 z + 20 = 40
Number of terms: 5 ( 5 x, 7 y, 8 z, 20, 40 )
Number of variable terms: 3 ( 5 x, 7 y, 8 z )
Number of constant terms: 2 ( 20, 40 )
How Many Types of Terms are There in Algebra?
We can categorise the terms into different categories on the basis of their characteristics. Let us check out the categories of terms:
- Constant terms: These terms have a constant value. There is no variable involved in such a term. Manipulation of matter contained in this term is not possible. For example, 3x + 7, In this expression, “7” is a contract term.
- Variable terms: The terms having variables in it do not have a fixed value. Its value is dependent upon variables in it. You can further divide the variable terms based on the number of variables in it.
- Monomial: This type of variable term has only one variable. For example: 3x. Remember that “3x + 10 = 13” has 10 and 13 as constant terms, but they are not monomial terms. Monomial should have at least and at most one term variable involved.
- Binomial: It has two variables in a term—for example, 13xy or 10x^2 y^3. Although the second term in this example has more than one number of exponents in variables x and y, it is still binomial because only two variables are involved.
- Trinomial: It has three variables involved—for example, 10 xyz or 20x^2 y^3z^2.
- Like terms: Two terms are known as terms if their variables and exponents are the same. For example, 3 x^2 y^2 and 5 x^2 y^2 are like terms since both the variables “x” and “y” are present in both the terms with the same exponents. However, coefficients should not be identical in terms. If coefficients also become the same in like terms, the words will no longer be “like terms” while they will become the same term.
What are the Factors of Terms in algebra?
If we observe terms closely, we will notice every variable and coefficient as a factor to the term since it is a multiplication of variables and coefficients. That is why they also can divide a term with zero remainders. For example:
Algebraic Term: 3 XYZ ( assuming x, y, z can not be factored more)
Factors of the term: 3, x, y, z
Solved Examples
Let’s TERMinate all of your confusion regarding algebraic equations by solving some.
- Example 1: 5 * 8 = 4 * 10
Explanation: You can identify Expressions in an equation as an “equal” sign separates them. This equation has two expressions. Expressions on both sides of the “equal” sign should evaluate to equal value. Like here 5 * 8 = 40 and 4 * 10 =40 too. The terms used in this equation are constant.
- Example 2: 3a + 4a + 5 = 12a
Explanation: This equation has variables involved as well. The first two terms in an equation have two terms, “3a” and “4a,” and the third term is constant. The term on the RHS is monomial. This equation can have any value substituted in the place of “a” to maintain a balance. For example, if the value of “a” is taken as 1, then RHS and LHS would evaluate 12. This way, a balance is achieved.
- Example 3: What is the coefficient of term number one and two in RHS of an equation?
6a + 6b = 3a + 4b + 5
Explanation: The coefficients of terms “3a” and “4b” in the expression on RHS of an equation are “3” and “4”.
- Example 4: How many expressions and terms are present in this equation below?
6a + 6b + 10= 3a + 4b + 5 + 10
Explanation: The number of expressions present in the above equation is 2. The total number of terms present in an equation is 7. These terms have two like terms and three constant terms in it.
- Example 5: 3 a^2b = 6a
Explanation: This equation contains only one binomial term on the LHS of an equation, while a monomial term is present on the RHS of the equation. The value of RHS and LHS should be equal for this equation to be balanced. If the value of a is taken as “2” while the value of b is taken as “1,” then the expressions on RHS and LHS will be evaluated as:
LHS: 3 a^2b = 12
RHS: 6a = 12
LHS = RHS (Hence here comes the golden equation of our interest.)
Where are Algebraic Terms Used in Real Life?
You can derive multiple rules and formulas used in daily life from algebra. Like you can evaluate a^2 + b^2 as (a+b) (a-b), reducing the complications of finding a number’s square.
- Algebra is used by businesses to track profit margins and derive a relationship based on variable factors, and many fields use these expressions.
- Economists use algebra to study the stock market and evaluate a country’s economic conditions.
- Chartered accountants and cashiers use algebra in their enterprise-level investment and collection analysis.
- Many programmers use it for making mobile apps and various softwares.
These are just some examples, and you can find uses of algebra in many day-to-day operations.
Conclusion
Algebra is an illustration of representing any relationship in mathematical terms. You can mould an equation in different forms by adding or deleting the variables, coefficients, or constants by keeping the same quantitative values. That means the overall value evaluated from an expression remains the same even when you manipulate the equation. It is an exceptional way of representing a relationship. The terms are powerful as you can change the term by multiplying variables or coefficients as per the requirement. If you start playing with algebra by manipulating equations and terms, it would be effortless to derive these expressions’ relations.
If you are interested in learning more about such exciting mathematics topics, you are in the right place. Let Cuemaths be your partner in this fun learning about Algebra formulas and examples. Be ready to maintain friendly terms with Mathematics!