Algebriac Expressions and More

What is an Algebraic Expression?

An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms. 

Key Words in Algebraic Expressions

Addition: sum, more, more than, plus, increased by, gain

Subtraction: difference, less, less than, minus, decreased by, loss

Multiplication: product, multiplied by, times, double, triple

Division: quotient, divided by, per, ratio, half, third, fourth, into, equal groups

Exponents: times itself, squared, cubed

Variables, Coefficients, Constants & Terms

• In the expression pictured,

  x is a variable, whose value is unknown to us which can take any value.

• 5 is known as the coefficient of x, as it is a constant value used with the variable term and is well defined.

• 3 is the constant value term which has a definite value

• The whole expression has two terms. Terms are separated by addition and subtraction signs.

Multiple Choice

How many terms are in the following expression?

3x + y + 42

• 2 terms

• 3 terms

• 4 terms

Multiple Choice

How many terms are in the algebraic expression?

2y + x + 4 + y²

• 4

• 3

• 5

• 2

Multiple Choice

How many terms are in the following expression?

5 - 72x + 43y - 109 + 5z

• 3 terms

• 4 terms

• 5 terms

• 6 terms

Multiple Choice

Identify the constant in the expression.

2y + x + 8 + 7p

• 7

• 2

• 1

• 8

Multiple Choice

Identify the coefficient in the expression.

6y + 7

• 6y

• 7

• 6

• 1

How to Write an Algebraic Expression

Generally, you'll do this by replacing the words with operators that mean the same thing.

Multiple Choice

Identify the Variable in the expression 5y+7?

• x

• 5y

• y

• 7

Multiple Select

Choose the algebraic expression that matches the verbal phrase. Choose all that apply.

Multiple Select

Choose the algebraic expression that matches the verbal phrase. Choose all that apply.

Multiple Select

Choose the algebraic expression that matches the verbal phrase. Choose all that apply.

Multiple Choice

Choose the algebraic expression that matches the verbal phrase.

Multiple Choice

Choose the algebraic expression that matches the verbal phrase.

Combine Like Terms

Terms: the "words" in a math sentence

Like Terms: terms that have the same variable raised to the same power.

Multiple Choice

Combine like terms.

$$3x^2+3y+4-2y+x$$  

• $$4x^2+1y+4$$  

• $$3x^2+1y+4+x$$  

• $$3x^2+3y+4-2y+x$$  

• 13xy

Multiple Choice

Combine like terms.

3x + 2x + 7

• 12x

• 5x + 7

• 14x

• 3x + 2x + 7

Order of Operations

Mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation.

Multiple Choice

Which operation is performed FIRST?
(13 - 1) + 4

• addition
• subtraction
• multiplication

Fill in the Blank

10(x+4)

Multiple Choice

Which operation would you do first?

( 12 + 10) ÷ 10 · 14 - 6

• Division

• Multiplication

• Addition

• Subtraction

Multiple Choice

Which operation should be done first? $$3\ \times\ 4\ +\ 8\ -\ 2$$  

• addition

• subtraction

• multiplication

• division

How to Evaluate an Algebraic Expression

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

Multiple Choice

$$Evaluate\ 5a-9\ when\ a=3.$$  

• 44

• 6

• 116

Multiple Choice

$$Evaluate\ 3x+2y\ when\ x=7\ and\ y=2.$$  

• 25

• 59

• 46

Multiple Choice

Evaluate when a = 15:

2(a - 5) + 2

• 22

• 27

• 14

• 7

Multiple Choice

2x + 3 + x²; for x = 4

• 17

• 27

• 19

• 25

Poll

How do you feel about simplifying algebraic expressions?

• I feel pretty good!

• I think I understand most of it.

• I have some questions.

• I'm really struggling.

Multiple Choice

Which net will form this solid?

Multiple Choice

Which figure will this net make?

• Cone
• Triangular Prism
• Square Pyramid 
• Cube

Multiple Choice

Which figure will this net make?

• Rectangular Prism 
• Triangular Prism
• Triangular Pyramid 
• Cube

Multiple Choice

• triangular pyramid

• triangular prism

• rectangular prism

• cube

Multiple Choice

How many Faces does this Prism have?

• 4

• 6

• 18

• 12

Multiple Choice

A pyramid is made up of ...

• Triangle Faces and One Base

• Triangle Faces and Two Bases

• Rectangle Faces and One Base

• Rectangle Faces and Two Bases

Multiple Choice

A Prism is made up of:

• Rectangle Faces and One Base

• Rectangle Faces and Two Bases

• Triangle Faces and One Base

• Triangle Faces and Two Bases

Multiple Choice

A cube is made up of ...

• rectangles
• squares
• circles
• triangles

Multiple Choice

How many edges does this prism have?

• 3

• 6

• 9

• 12

Multiple Choice

How many Faces does this pyramid have?

• 3

• 4

• 5

• 6

Thank You, Gracias, Danke, Merci, Spasibo

for learning with me today!