# Posts Tagged: "algebraic expressions"

## Distributive Property

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One of the properties of real numbers is distributive property, also known as distributivity of multiplication over addition. It is used to solve variable expression which is in the form of $a(b+c)$ and the like.

The property says, for any $a,b,c \in \mathbb{R}, a(b+c)=ab+ac$.

## Simplifying Variable Expressions

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Simplifying variable expression is basically combining like terms or using the distributive property. Thus, signs of grouping such as parentheses ( ), brackets [ ], and braces { } may present in simplifying algebraic expressions. The word parentheses, which will refer to any of these symbols, are used to enclose terms whose sum is to act as a single number.

Using the distributive property, i.e. $a(b+c)=ab+ac$ for all real numbers a, b, and c, a factor multiplying a sum within parentheses should be used to multiply each term of the sum.

## Variables and Verbal Expressions

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Some real-life situations involving numbers can directly be solved using the four fundamental operations: addition, subtraction, multiplication and division. For instance, if 1 apple cost 5 pesos, how much do 15 apples cost? To solve this problem simply multiply 15 by 5. However, there are other practical applications which can best be solved by looking for a general pattern, relationship or formula before arriving at the answers.

An example would be, study the sequence: 2, 4, 8, 16, 32 and so on, what is the sum of the first 12 numbers in this sequence? This problem entails a formula to shorten the procedure. It is on this context, that the core of Algebra lies on representing quantities, patterns or relationships by symbols other than numbers. These symbols, which can be any letter in the English alphabet, are called variables that can take on more than one value. These symbols can further be grouped using the four fundamental operations, which in turn give meaning to equations or inequalities. These groups of symbols are called mathematical expressions which are used to represent verbal expressions or phrases.

## Evaluating Variable Expressions

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A variable is a letter which is used to represent a number or a set of numbers. It is usually denoted by a letter of the English alphabet. Greek letters too can denote a variable. Examples of variables are x, y, r, s, t, and n.

Greek letters such as $\alpha$, and $\beta$ can be used also to denote a variable.