The level of study in mathematics grows accordingly with the educational level. Initially, basic calculations and arithmetics are taken as the base of mathematics for learning. As a student grows in their academic level they are introduced to other sub decisions or branches of mathematics like exponential, algebra, geometry, etc.
In this article, we are going to look at algebra as a branch of mathematics, and other terms related to it. The article also includes some sample problems with solutions for better understanding.
Algebra is a branch of mathematics introduced at the elementary level. It is the study of mathematical symbols and their analysis. Algebra includes variables, coefficient of variables, and constants. The variables involved in it are the unknown quantities represented by mathematical symbols or letters. The operations in algebra are carried out for the determinations of these unknown values.
Algebraic Expressions
The expressions that consist of variable, constants, and coefficient of the variable with at least one mathematical operation is known as algebraic expression. For example, 2x+3y+1 is an algebraic expression having three terms in which +1 is constant, x and y are the variables and 2 and 3 are coefficients of variable x and y respectively.
Some terminologies
- Term: All the expressions are made up of terms. These terms can be a combination of variable, constant, and coefficient or even a single constant with an operation attached to it.
- Variables: Variables are the unknown quantities represented by alphabetical letters in the algebraic expression. For example, 2x+5 is an algebraic expression in which x is the variable.
- Coefficient: Coefficients are the fixed values attached to the variables. For example in the expression 5x+2, 5 is the coefficient attached to variable x.
- Constant: Constants are the real numbers present in the equation with one algebraic operation. They are not combined with any variable. For example: in the algebraic expression x+2xy+1, +1 is the constant.
How to translate the quotient of a number to the third power and 3?
Solution:
Let the number be ‘x’. In the expression quotient of a number to the third power and three.
=>The quotient helps to identify the operation which will be division.
=>According to the question, the quotient is x3 (as quotient of a number to the third power) which will be placed as numerator.
=>The next number given to us is 3 which will be the denominator.
Hence, the algebraic expression would be
=>x3/3
Sample Problems
Problem.1. Translate into an algebraic expression. The quotient of 12 and a number.
Solution:
Let the number be x and it will be the denominator. The quotient 12 is numerator.
The algebraic expression will be
=>12/x
Problem.2. Translate into an algebraic expression. The product of 9 and a number minus 4.
Solution:
Let the number be x. And product of 9 and a number will be written as
=>9x
And, the expression product of 9 and a number minus 4 will be written as
=>9x-4
Problem.3. Translate into an algebraic expression. The quotient of a number and 25.
Solution:
Let the number be x. The algebraic expression the quotient of a number and 25 will be written as
=>x/25