By: Alonso Ralat, Ricardo Ramos, Victor Aguilar, and Dylan Kuan

Lesson

1.1 Words and Expressions

**Lesson 1.2 Variables and Expressions**

**That is basically what it talks about.**

Now, lets move on to lesson 1.2.

Now, lets move on to lesson 1.2.

How to evaluate a numerical expression.

Follow:

P

arenthesis

E

xponents

M

ultiplication

D

ivision

A

ddition

S

ubtraction

What is an algebraic expression?

An algebraic expression is an expression that has a number replaced with a symbol or letter called variable

What is a numerical expression?

A numerical expression is an expression that consist of at least two numbers and at least one operation. There can be no equal sign or it wouldn't be a numerical expression.

ex:

How to evaluate algebraic expressions.

You change the variable with the number that the problem indicates that the variable is and follow PEMDAS as well.

**For lesson 1.3, we shall go in the circle that you all saw in the beginning.**

Lesson 1.3

Properties

What are Properties?

Properties are statements that are true for any number in the world.

ex: Commutative Property a+b=b+a

More properties

Some other properties are:

Associative property

Distributive property

Multiplicative or Additive Identity Property

Multiplicative property of 0

A number is always represented by the same word. On the other hand, operations can be represented in many ways.

Operations and their verbal representations

( )

times the sum/difference

7

2

squared ( cubed ) raised to the power of

+

plus, addition

x

**.**

times, multiply, product

How numerical expressions are usually found :

Translating- an exercise in which a verbal phrase (or word problem) is translated into a numerical expression.

Evaluating- performing order of operations to find a numerical VALUE for a numerical EXPRESSION.

ex:

How to translate a verbal phrase into a numerical expression:

1.

Read the statement carefully and

look for number words, or operation words

2.

Write out the numbers and operations, and decide the proper order.

3.

Begin following the order of operations.

4.

Using steps that you feel are comfortable and effective, continue using order of operations until only a single value remains.

ex: The age difference between a fifteen year old and ten year old.

15, 10 subtract

15-10

5

Consider a numerical expression:

100+20

There are many ways to replace a number. For example:

a+20

2+20

The second option is incorrect because replacing a number with another number is wrong.

When we replace a number with a letter or we have a symbol that will be replaced by a number we have a variable.

An expression with at least one variable and one mathematical operation is called an algebraic expression.

These properties apply to addition and multiplication but they don't apply to division or subtraction. The way to prove it is by a counterexample, which is an example that proves that the idea is wrong.

Simplifying expressions

When you perform all possible operations. Since we will not know the exact value of the variables, we can't add or subtract them with numbers.

EX: (2+e) + 7

(2+7) + e

9+e

Any questions?

Have a nice day.

That is all, thank you for watching!

Lesson 1-1 Words and Expressions

**÷**

divided by, quotient