Algebra Terms and Expressions

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Learning Algebra involves a whole new language and vocabulary.

When learning a foreign language we have to learn its component parts like Nouns, Verbs, Adjectives, Pronouns, etc.

We then have to learn how to assemble these individual items into phrases and sentences.

If we are going to learn guitar, we have to learn the strings, the fret notes and scales, and assemble these into chords, then into chord progressions and songs.

If we are learning Basketball, we have to learn to dribble, learn the shots, learn defensive actions, and then assemble this into game play.

For Algebra the component parts are Terms, Coefficients, Pronumerals, Index Powers, and Constants.

We then assemble these parts into mathematical phrases called “Expressions”, or even full Algebra sentences called “Equations”.

In this lesson we will learn the language of Algebra, which is called “Algebra Notation”.

When you learn how to play guitar or a sport, and get good at it, your friends can relate to what you are doing and enjoy watching you perform.

When you learn Algebra, it’s not quite the same thing. But if you are great at Algebra, you can become a computer programming wiz, create a “killer” app or game and that could make you an instant millionaire !

If you want to find out more about how Algebra is used in the real World, and why it is so important, then check out our lesson about this at the link below:

Real World Algebra Formulas

Be prepared, it will be an uphill climb coming to grips with Algebra.
Algebra Terms

Items made up of letters and numbers, which can also have little “power” index numbers on them, are called “Terms”.

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Items like 4x, -5y, 6ab, 8efh, 1/3k are all Algebra Terms.

Pronumeral letters are also called “Variables”.

Indexes and Indices are also called “Exponents”.

If the term is just a normal number, decimal, or fraction, without any letters on it, it is called a “Constant”.

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Constants can be normal positive numbers if there is an addition sign coming before the term.

If there is a subtraction sign coming before a constant (or any type of Algebra term), then the term is negative.

Try to remember it like this:

The sign in front of a term is part of the term, like the driveway into a house is part of the home.

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Binomials and Trinomials

If we join up some Algebra terms using addition and subtraction signs, we create “polynomials’.

The simplest joining involves linking up two terms and is called a “Binomial”.

If we join three terms together we have a “Trinomial”.

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Expressions Versus Equations

An Equation is a complete Algebra sentence that contains an Equals sign.

Eg. 3n + 1 = 13 . We could solve this equation and figure out that n = 4 is the answer.

An “Expression” does not have an equals sign.

Eg. If we just write “3n + 1” on its own, then it is an expression.

Without an equals sign we cannot work out the exact number value of “n”.

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Algebra Division Uses Fractions

In Algebra expressions we do not write divided by signs.

Instead we use fractions. Eg.

y divided by 4 is written as y/4.

The / bar in a fraction means the same as divided by.

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Algebra Multiplying

In Algebra we always leave the multiply signs out, and bunch the letters and numbers up next to each other.

In each Term, the sign (- or +) comes fist, the number comes next, and then the letters in Alphabetical Order.

We leave the positive sign off the front of normal numbers, just like we do in Integers.

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Algebra and the Correct Order

Just like in all languages, there is a correct order to put our items in when we do Algebra.

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Algebra Terms Order

The order rules for individual Terms are as follows.

The MULTIPLY items in the term are put into this order :

Sign – If there is a negative sign, it goes first.
(Like the driveway into the house comes first).

Number Coefficient – Number, Fraction, and Decimal, Coefficient comes next.

Letter Pronumerals – These come last and should be put in Alphabetic Order.

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Fractions are done the same as normal number Coefficients.


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Algebra Expression Order

There is also a set way we arrange the individual Terms when we group them together to make an Expression.

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However, there is an exception to the Expressions rule. This exception is that we do not usually start an expression with a negative sign term.


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So here is the full rule for writing down expressions in the correct order.

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Examples

The following examples are typical Algebra questions where we need to identify Coefficients, Constants, Pronumerals, Binomials, and Trinomials.

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Image Source: Copyright 2012 Passy’s World of Mathematics

Image Source: Copyright 2012 Passy’s World of Mathematics

Image Source: Copyright 2012 Passy’s World of Mathematics

Related Items

Algebra Expressions
Introduction to Powers Indices and Exponents
Algebra Substitution Using Positive Numbers.
Algebra Substitution Using Negative Numbers.
Real World Algebra Formulas
Survivor Algebra – Class Activity

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