The basic rules or properties of algebra for variables, algebraic expressions, or real numbers a, b and c are as given below,. Example 2: The age of a person is double the age of his son. Ten years ago, it was four times the age of his son. Use the concept of algebra and find the present age of the son.
Let us consider the present age of the son as 'x' years. Give that the age of the person is double the age of his son, let us take the age of the person as '2x' years.
Now considering the situation 10 years ago, the age of the person is x - 10 years and the age of the son is 2x - 10 years. The various types of algebra are elementary algebra, abstract algebra, linear algebra, boolean algebra, and universal algebra.
These are named based on the problem we are able to solve through the use of algebra. In algebra, which is a broad division of mathematics, abstract algebra, or modern algebra is the study of algebraic structures including groups, rings, fields, modules, vector spaces, lattices, and algebras. The highest level of algebra involves complex math topics of calculus, trigonometry, three-dimensional geometry, to name a few.
Here algebra is used to represent complex problems and obtain the solutions for those problems. The basics of algebra include numbers , variables, constants, expressions, equations, linear equations, quadratic equations. Further, it involves the basic arithmetic operations of addition, subtraction, multiplication, and division within the algebraic expressions. The four basic rules of algebra are the commutative rule of addition, commutative rule of multiplication, associative rule of addition, associative rule of multiplication.
The fundamental theorem of algebra states that an algebraic expression of n degree has n roots. The easiest way to learn algebra is to know the three basics of problem representation and solving.
First, the problem statement should be represented in the form of a solvable equation. Secondly, the manipulation of the values by moving the numbers across the equals to sign should be performed with ease. Third, the arithmetic operations like addition, subtraction, multiplication, and division should be performed proficiently. Algebra helps to find the values of unknown quantities in our daily life. The unknown quantities are represented as variables x, y in the form of an equation.
Further, the equations involving arithmetic operations are solved to find the values of those variables. Quantities like speed, time, distance, currencies can be represented as variables in algebra.
Solving the algebraic expressions involves three simple steps. First, identify and group the variables of the same kind. Second, transform the variable on one side and the constants on another side. Thirdly bring all the variables of a similar kind to one side.
And at last, perform the needed arithmetic operations. The four basic operations in algebra are addition, subtraction, multiplication, and division. Learn Practice Download. Algebra Algebra helps in the representation of problems or situations as mathematical expressions. Solution: Let us consider the present age of the son as 'x' years. You can find "x" or solve the equation for "x" by isolating the "x" on one side of the algebraic equation.
To solve for "x", you need to understand the basic rules of algebraic operations. Isolate "x" on one side of the algebraic equation by subtracting the sum that appears on the same side of the equation as the "x. Isolate "x" on one side of the algebraic equation by adding the negative number that appears on the same side of the equation as the "x. Isolate "x" on one side of the algebraic equation by dividing the number that appears on the same side of the equation as part of "x.
Isolate "x" on one side of the algebraic equation by multiplying the number that appears on the same side of the equation as part of an "x" fractional component.
There are a few other ways to show multiplication in algebra. As you saw when we multiplied coefficients, you can simply write variables next to each other to multiply them. If you wanted to multiply x and y , you could simply write xy. There are a few ways to show division in algebra. You're probably most familiar with division problems that look like this:. You will see division written this way in algebra. However, you'll also see it written like this especially in our lessons :.
If you're dividing groups of numbers, you can also show division with a horizontal line. For example, look at this problem:. You're probably used to seeing parentheses used in writing, most often with part of a sentence that isn't essential although they can also be used for other things.
In algebra, parentheses are used a bit differently. Parentheses are used to group parts of an algebraic expression. When you see part of an algebra problem enclosed in parentheses, you'll need to solve that part before tackling the rest of the problem.
In this problem, you would start by solving everything in the parentheses first; then you'd solve everything else. Curious about why you solve the part in parentheses first? Check out our lesson on the order of operations. What happens when two sets of parentheses are next to each other, without any operators in between?
If you remembered that two variables next to each other are multiplied , you might guess that you would multiply two sets of parentheses side by side too.
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