Lesson 6: Algebraic Expressions (I)January 3, 2011
1. What is algebra?
Learning algebra is a little like learning another language. In fact, algebra is a simple language, used to create mathematical models of real-world situations and to handle problems that we can’t solve using just arithmetic. Rather than using words, algebra uses symbols to make statements about things. In algebra, we often use letters to represent numbers.
Algebra is a formal symbolic language, composed of strings of symbols. The symbol set of algebra includes numbers, variables, operators, and delimiters. In combination they define all possible sentences which may be created in the language.
Because of this it is important to learn to translate words into algebra. This task is essential to solve word problems through equations.
Practise this skill on:
It is also useful to practice writing variable expressions to represent diagrams
2. Evaluating expressions
Evaluating an algebraic expression consists on substituting numbers we are given for variables in expressions and working out the outcome.
One advise: recall order of operations.
Practise on this web.
At the bottom of this page you can also find puzzles on the main vocabulary of this lesson.
A monomial is an algebraic expression formed by the product of a number and one or more letters.
The factor expressed in Arabic numerals is sometimes called numerical coefficient or simply coefficient. The numerical coefficient is customarily written as the first factor of the term.
The letters are called literal numbers or literal part.
Degree of a monomial is the sum of all the exponents of the letters in the literal part.
Practise identifying terms and coefficients
Like monomials. Monomials are called similar or like ones, if they are identical or differed only by coefficients. Therefore, if two or some monomials have identical letters, they are also similar (like) ones. In other case they are called unlike monomials.
4. Operations with monomials
Operations with monomials follow the same rules as operations with numbers. You must respect the order of operations or hierarchy.
4.1 Addition and subtraction of monomials
Like monomials are added or subtracted by adding or subtracting the numerical coefficients and placing the result in front of the literal factor,
Dissimilar or unlike monomials cannot be added or subtracted when numerical values have not been assigned to the literal factors.
Practise this skill on
4.2. Multiplying and dividing monomials
When multiplying monomials, we multiply their numeric coefficients and multiply their literal numbers separately.
When dividing monomials, we multiply their numeric coefficients and multiply their literal numbers separately if we can.
Practise operations with monomials on this web. Every time you click on the different operation you want to practice you will get a different example.
Practise collecting like terms and eliminating brackets on this web. These exercises are more complicated
Finally, try to understand this videos on operations with monomials