Grade 9 Principles of Mathematics, Introduction Lesson 1: Algebra: Terminology and review
Course text:
Mathematics helps us to describe and understand our world. For example, architects and engineers use algebra to describe the forces that act on buildings so that they can understand how to make the structures they design safe, and able to stand the test of time.
In this lesson, you will review numeric calculations and be introduced to algebraic terminology such as "term," "factor," "coefficient," and "like terms." These words will all be explained to help you feel more comfortable with the language of algebra.
Term
A number, variable or a number and variable(s) multiplied together.
In an expression or equation, terms are separated by +, - and = signs.
Think about this:
3, 5
x, -2
y² and 6
x²y are all terms.
Factor
A number, variable or expression that can be multiplied by another number, variable or expression to make a certain product.
Think about this:
What are the factors of 20?
Solution:
1 × 20 = 20
2 × 10 = 20
4 × 5 = 20
Therefore, the factors of 20 are 1, 2, 4, 5, 10 and 20.
In this example, 20 is the certain product, and the factors are all numbers that can be multiplied by another number to make 20.
Coefficient
The numerical value of a term that consists of one or more variables.
In other words, it is a number that is being multiplied by one or more variables.
Think about this:
For the expression -3
x² +
xy - 2 :
The coefficient of -3
x² is -3
The coefficient of
xy is 1
Note: The coefficient is 1 if there is no number or letter beside the variable.
Like Terms
Terms that are alike, or the same.
In other words, like terms have the same variable with the same exponent, while the coefficients can be different.
Think about this:
This equation has all like terms:
x3 + 3
x3 – 7
x3
This equation contains unlike terms
X2 + 7
x +
ab +
x3
Algebra is a powerful tool for describing relationships. For example, if a store sells CDs for [FONT=MathJax_Math]
x[/FONT] dollars and Blu-ray Discs for [FONT=MathJax_Main]3[/FONT][FONT=MathJax_Math]
x[/FONT] dollars, this indicates, without revealing the actual price, that Blu-ray Discs cost three times the price of CDs.
Consider the following rectangle. Its length is double its width, and it has a perimeter of 80 m. If we want to make this same statement using algebra, we can say that [FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]
a[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]
a[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]80[/FONT], where [FONT=MathJax_Math]
a[/FONT] is the width of the rectangle.
You will learn how to use algebra in similar situations. This lesson will show you how to visualize variables in geometric form. The ideas explained here are the foundation for many of the topics in the course.
After completing this lesson, you will be able to
- add, subtract, multiply, and divide integers and fractions
- identify the types and parts of algebraic expressions
- apply the rules for the order of operations to evaluate expressions or solve equations
a. State a term with a coefficient of 12 and a variable of ten.
b. State a term with a coefficient of –8 and factors.