An algebraic expression is an expression that can be evaluated to yield a numeric result by substituting numeric values in the variables. The value of the expression depends on the values of the variables, which are usually represented by letters.
addition and subtraction of algebraic expressions
To add or subtract algebraic expressions, we first need to understand what it means to “combine like terms.” Two terms are like terms if they have the same variables with the same exponents. For example, 5x and -3x are like terms because they both have the variable x with an exponent of 1, but 5x and 3x^2 are not like terms because one has an exponent of 1 and the other has an exponent of 2.
To add or subtract like terms, we simply combine them by adding or subtracting their coefficients. For example, if we have the expression 5x + 3x + 2x – x, we can combine the like terms to get 7x + 2x – x, which is equivalent to 8x + x.
We can use this same process to simplify complex fractions. In this case, we want to combine any like terms that appear in the numerator or denominator. For example, if we have the fraction 3/(4+2), we can simplify it by combining the like terms in the denominator to get 3/6.
multiplication and division of algebraic expressions
To multiply or divide two algebraic expressions, we first need to determine whether the operations (multiplication/division) can be performed. If the operations can be performed, we will carry out the operations and simplify the expression.
If we are multiplying two algebraic expressions, the product will be equivalent to the following:
(3x)(1422x) = 4226x^2
This expression is equivalent to the following complex fraction: 3x1422x1
exponents of algebraic expressions
In mathematics, an exponent is a number that indicates how many times a particular value is used as a factor. An exponent is usually written as a superscript to the right of the base value.
For example, the expression “54” could be read as “5 to the fourth power”, meaning 5 is used as a factor 4 times. In exponential notation, this would be written 54 = 5^4.
The expression “23” could be read as “2 to the third power”, meaning 2 is used as a factor 3 times. In exponential notation, this would be written 23 = 2^3.
Exponents are also called powers or indices.
A complex fraction is a fraction whose numerator or denominator is a fraction. 3x1422x1 is a complex fraction because its numerator is a fraction.
addition and subtraction of complex fractions
To add or subtract complex fractions, we first need to find a common denominator. In this case, the lowest common denominator is 1422. To get this number, we multiply the denominators of each fraction (3 and 1) and then multiply the numerators of each fraction (1422 and 1). This gives us an equivalent fraction of 3x1422x1.
multiplication and division of complex fractions
To multiply complex fractions, multiply the numerators and denominators separately. To divide complex fractions, flip the second fraction (the one you are dividing by) and multiply.
exponents of complex fractions
In the complex fraction 3x1422x1, the exponents of the top and bottom terms are both 2. This means that the expression is equivalent to the following fraction: 3x142x11.