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In addition to the revision notes for The Meaning of Expressions. Simplifying Expressions on this page, you can also access the following Expressions learning resources for The Meaning of Expressions. Simplifying Expressions
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 6.1 | The Meaning of Expressions. Simplifying Expressions |
In these revision notes for The Meaning of Expressions. Simplifying Expressions, we cover the following key points:
By definition, algebraic expressions are those expressions in which numbers are expressed using letters or alphabets without specifying their actual values.
In scientific terminology, letters that are used to substitute numbers are known as 'variables' as their value may vary depending on the conditions presented in the exercise.
The term 'algebraic' is used to describe a mathematical expression or equation in which a finite number of symbols are combined using only the operations of addition, subtraction, multiplication, division, and exponentiation with constant rational exponents.
Algebraic expressions differ from equations in the sense that all terms are written in the same side without any equal symbol ( = ) in-between.
We must assign values to all variables of an algebraic expression in order to find the value of the whole expression (i.e. turning it into arithmetic expression).
Any number, letter, group of letters or number-letter combination separated by the symbols 'plus' or 'minus' from the rest of expression is called 'term' of the algebraic expression. The sign is counted with the term that comes after it.
If two or more terms of an algebraic expression have the same combination of letters, they are called 'like terms'. Like terms are important in an algebraic expression as we can add or subtract only like terms with each other.
All terms of algebraic expressions begin with a number called a 'coefficient'. The number that is not followed by a letter is known as a 'constant'. If there is no number written before a variable, the coefficient is taken as 1 (or -1 when the term is preceded by a negative sign). This derives from the identity element of multiplication (1 · a = a · 1 = a). On the other hand, if there is no constant in an algebraic expression, it is taken as 0. This derives from the identity element of addition (0 + a = a + 0 = a).
Simplifying algebraic expressions means completing all possible operations until there are no more operations left. In a certain sense, it means writing an algebraic expression in the simplest terms.
In order to have a better understanding of an algebraic expression, it is better to have it expressed from the highest to the lowest term. The highest term of an expression is determined by the variable with the highest power. If two terms have the same power degree, we order them according the alphabet.
It is more appropriate to write an algebraic expression containing two variables x and y in such a form that the power of the first variable x decreases when moving from left to right while the power of the second variable y increases when moving from left to right. As for the constant, it is written at the end of the algebraic expression, after finishing with all variables.
If two or more terms of an algebraic expression are multiplied or divided, we make two different kinds of operations with their components. Thus, coefficients are multiplied or divided with each other according to the operation involved in the expression. As for the variable(s), from the two properties of exponents (indices)
and
Another property of exponents applied when dealing with algebraic expressions, is
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