Algebra!

The area of mathematics that generalizes the concepts and rules of arithmetic using symbols to represent numbers

What is arithmetic?

AdditionSubtractionMultiplicationDivisionExponents

What are some examples of symbols you see inside and outside of school?

In algebra, we use different symbols that we call variables

Many times, you will use letters as your symbolX, a, b, c, etc.

Sometimes you may see some Greek alphabet lettersβ = beta

How to set a problem up!

Add three to a number A number plus 3 The sum of a number and 3 3 more than a number A number increased by 3

How to set up a problem!

Subtract 12 from a number A number minus 12 The difference of a number and 12 12 less than a number A number decreased by 12 Take away 12 from a number A number less 12

Set up the problem!

2 times a number 2 multiplied by a number The product of 2 and a number

Set up the problem!

6 divided into a number A number divided by 6 The quotient of a number and 6

What would the expression be?

Five less than a number

The product of three and a number

The sum of a number and 10

A number divided by 9

Try one on your own!

Make up an algebraic expression on your own. Write it on your whiteboard.

When your finished, pass it to a neighbor and see if they can figure it out!

Two step algebraic expressions

Three times a number decreased by two

Four more than five times a number

The sum of a number and four divided by two

The difference of a number and four added to nine

Write a verbal phrase for each algebraic expression

Write each sentence as an equation

The product of four and a number is sixteen

Three less than an number is twenty

Nine more than “n” is eleven

To evaluate an algebraic expression, substitute a number for the variable!

Example: Evaluate n + 7 when n = 4

To evaluate an algebraic expression, substitute a number for the variable!

Example: Evaluate 5n + 3 when n = 6

To evaluate an algebraic expression, substitute a number for the variable!

Example: Evaluate 6n² + 2n when n = 3

Let’s try a few on our own!

1. p ÷ 2 + p when p = 4

2. 3a – 5 when a = 5

3. 6/s + 4s when s = 2

What about two variables? Example: Evaluate a + 7 - c when a = 9

b = 6

What about two variables? Example: Evaluate 2n + 7b when n = 5

b = 2

Let’s try a few on our own!

1. p ÷ 2 + 3x when p = 6 and x = 7

2. 3a – 5t when a = 6 and t = 2

3. 12/s + y² when s = 3 and y = 5

Try one on your own!

Make up an algebraic expression and assign the variable or variables values. Write it on your whiteboard.

When your finished, pass it to a neighbor and see if they can figure it out!

Definitions Term: A term can be a number, a

variable, or a product of numbers and variables.

Definitions Please list all of the terms in this

algebraic expression.

Definitions Like terms: Terms that have the same

variable raised to the same power. Examples

Definitions Unlike terms: Terms that do not have the

same variable raised to the same power. Examples

Definitions Like terms: Terms that have the

same variable raised to the same power.

Identify the like terms in the list:

You can only combine LIKE TERMS

Example: _s_ + 10s = 5

Example: 72c + 5b =

Example: 4x² + 53x =

Example: 7x + 5x =

Now let’s practice!

1. 3m + 4m =

2. 6t + 4 – 3t =

3. 17y + 3y – 2y²

4. 5 + 4r – 3 =

What about the more difficult ones?

3b² + 5b + 11b² - 4a² =

Step 3 : solve and bring down the rest of the terms

Step 2 : circle the numbers and the sign to the left of them

Step 1 : underline like terms

What about the more difficult ones?

2(b + 2a²) + 2b

Step 3 : solve and bring down the rest of the terms

Step 2 : circle the numbers and the sign to the left of them

Step 1 : distribute and underline like terms

2b + 4a² + 2b

Let’s try some on our own!

1. a + 2b + 2a + 3b + 4c

2. 18 + 2d³ + d + 3d

3. a² + 9b + 5a² + 2b + 6c

4. 3(4x + z) – 4x

Try one on your own!

Make up an algebraic expression with several variables. Write it on your whiteboard.

When your finished, pass it to a neighbor and see if they can figure it out!

Lets try a few!

2 + x = 72 plus “some number” equals 7Answer = 5How did you know this?

2 + x = 7subtract two from both sides

-2 -20 + x = 5

Additive inverse

Step 1: Draw a line down the equal sign

Step 2: Look at the number on the same side as the variable

Step 3: Look at the sign next to the number you underlined (no sign = positive)

Step 4: Do the opposite! Add or subtract that number from both sides

X + 14 = 27subtract 14 from both sides

-14 -14X + 0 = 13

Additive inverse

Step 1: Draw a line down the equal sign

Step 2: Look at the number on the same side as the variable

Step 3: Look at the sign next to the number you underlined (no sign = positive)

Step 4: Do the opposite! Add or subtract that number from both sides

Now try on your own!

1. 16 + x = 292. X + 11 = 343. 18 + X = 864. X + 12 = 195. 27 + X = 258

Problem #1

16 + x = 29

Problem #2

X + 11 = 34

Problem #3

18 + X = 86

Problem #4

X + 12 = 19

Problem #5

27 + X = 258