Introduction to Algebra

1. What is Algebra?

2. The Language of Math
 Algebra is a mathematical language that uses symbols
and letters.
26 + x = 84
 Symbols represent the operation and numbers.
+ - ∙ ÷ ≥ ≤ ± = ≠ 1 2 3
 Letters represent unknown quantities.
a + b
p/q
x

3. The Language of Math
 When symbols and numbers are combined into a mathematical
phrase, the phrase is an numerical expression.
14 + 32 = 46
 When letters (known as variables) are combined with symbols
the mathematical phrase is an algebraic expression.
x + 32 = 46
 In algebra, variables/letters are used for unknown quantities.
 In arithmetic, an empty box or other shape was used to represent
unknown quantities.
4 + 3 =

4. Understanding
 A mathematical quantity is anything that can be
measured or counted.
 Algebra uses symbols to represent quantities that are
unknown or may vary.
 You can represent mathematical phrases and real-world
relationships using symbols and operations.

5. Let’s Practice (Write only the expression)
3. The quotient of 207 and a number n?
Quotient means?
Divide.
The unknown variable is represented by the letter?
n.
The algebraic expression is?
207 ÷ n
4. The difference of a number x and ½?
Difference means?
Subtract.
The unknown variable is represented by the letter?
x.
The algebraic expression is?
x – ½.
1. The total number of fish if you had
eight and brought nine more?
How many fish do you have?
8.
How many more fish did you buy?
9.
Together you have?
8 + 9
2. The total length of songs on a CD if
each of nine songs is three minutes
long?
How many songs are on the CD?
9.
Each song is how long?
3 minutes.
The total length of the CD is?
9 x 3

6. Check Your Understanding
 Translate the following: Do Not Solve…Write the phrases into a
numerical or algebraic expression.
1. The total amount of money if you have nine dollars and 12 dollars?
2. The cost of six electronic hand-held games if each cost eight dollars?
3. The sum of a number m and 8?
4. y minus 12?
5. The difference of 15 and 10?
6. A number t divided by 82?
7. The number of students I each group if fifteen students are divided into
five equal group?