Mathematics for GIS Professionals

Addition and Subtraction of Algebraic terms

Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. e.g. $x + x + x$ can be written as $3x $ , $m \times m \times m \times m = m^4 $.

It’s also seen as a gatekeeper subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it’s impossible to move forward.

It’s used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we’ll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

The word “algebra” comes from Arabic (just like “algorithm” and “al jazeera” and “Aladdin”)? And what is so great about algebra anyway? Why all the letters?

Letters in algebra represent unknown quantities acting as place holders. The equation $$x -5 =10$$ is a mathematical statement saying that an unknown number is equal to 10 after 5 is subtracted from it, what is that number?

$x + x + x$ can be written as $3x$ If the context of the question is cars then the expression is saying that 1car + 1car + 1car = 3cars in this case x=car

Addition and Subtraction of Algebraic expressions

Term – is an expression involving letters and/or numbers (called factors), multiplied together.

Example 1

The algebraic expression $5x$ is an example of one single term. It has factors $5$ and $x$.

The $5$ is called the coefficient of the term and the $x$ is a variable.

Example 2

$5x + 3y$ has two terms.

First term: $5x$, has factors $5$ and $x$

Second term: $$3y$$, has factors $3$ and $y$

The $5$ and $3$ are called the coefficients of the terms.

Example 3

The expression $3x^2 – 7ab+2e\sqrt{\pi}$ has three terms.

First term: $3x^2$ has factors $3$ and $x^2$

Second term: $-7ab$ has factors $-7$, a and b

Third Term: $2e\sqrt{\pi}$ has factors $2$, $e$ and $ \sqrt{\pi}$

The $3$, $-7$ and $2$ are called coefficients of the terms.

Like Terms

 “Like terms” are terms that contain the same variables raised to the same power.

Example 4

$3x^2 $ and $7x^2$ are like terms.

Example 5

$-8x^2 $ and $ 5y^2$ are not like terms, because the variable is not the same.

Adding and Subtracting Terms

Important: We can only add or subtract like terms.

Why? Think of it like this. On a table we have 4 pencils and 2 books. We cannot add the 4 pencils to the 2 books – they are not the same kind of object.

We go get another 3 pencils and 6 books. Altogether we now have 7 pencils and 8 books. We can’t combine these quantities, since they are different types of objects.

Next, our sister comes in and grabs 5 pencils. We are left with 2 pencils and we still have the 8 books.

Similarly with algebra, we can only add (or subtract) similar objects, or those with the same letter raised to the same power.

Example 6

Simplify $13x + 7y – 2x + 6a$

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