1. Algebraic Expressions

2. Unit 7 – Simplifying Algebraic Expressions

3. Vocabulary
Expressions - A mathematical representation containing numbers, variables, and operation symbols; an expression does not include an equality or inequality symbol.
Example: (5+2)− 27 ÷3 (arithmetic/numerical expression)
2a +3b (algebraic/symbolic expression)
Constant – A quantity that does not change its value in a given expression or equation
Example: 3s + 4,
3 and 4 are constants
Coefficient – A constant that multiplies a variable
Example: 3x + 4y = 14,
3 is the coefficient of x and 4 is the coefficient of y

4. Simplifying Algebraic Expressions Geometry Example
Solve.
A square has a length of g yards. Find the perimeter of the square in terms of g. g + g + g + g 4g yards

5. Simplifying Algebraic Expressions Geometry Example
Solve.
An equilateral triangle has sides measuring d inches long. Find the perimeter of the equilateral triangle in terms of d. d + d + d 3d inches

6. Simplifying Algebraic Expressions Geometry Example
Solve.
A rectangle has a width of 2 feet and a length of m feet. Find the perimeter of the rectangle in terms of m. m m + 2 2m + 4 feet

7. Simplifying Algebraic Expression Geometry Practice
Solve.
A piece of wire is bent in the shape of a regular octagon. Each side of the octagon is h centimeters long. What is the total length of the wire in terms of h? h + h + h + h + h + h + h + h 8h cm

8. Simplifying Algebraic Expressions Addition Examples
Simplify each expression
2c + 3c
c + c + c + c + c 5c
3g + 4g
g + g + g + g + g + g + g 7g

9. Simplifying Algebraic Expressions Addition Practice
Simplify each expression
8p + 3p
11p
6m + 10m
16m
42d + d
43d
16y + 4y
20y

10. Simplifying Algebraic Expressions Subtraction Examples
Simplify each expression
5t - 2t 3t
7x - 4x 3x

11. Simplifying Algebraic Expressions Subtraction Practice
Simplify each expression
18p - 2p
16p
44m - 15m
29m
6d - 6d
15y – y
14y

12. Simplifying Algebraic Expressions Mixed Practice
State whether each pair of expressions is equivalent
7p + 3p and 3p + 6p
10p and 9p no
9t + 3t and 6t + 6t
12t and 12t
yes
5d - d and 6n
4d and 6n no
7i – 2i and 9i - 4i
5i and 5i
yes