Simplify Numerical Expressions

Simplifying Numerical Expressions Part II

by Mr.Alvarez

Before we begin:

​We must have a full understanding of our lesson from yesterday.

• ​Expressions

• ​Grouping symbols

• ​Using parentheses to represent multiplication

Poll

How can we define an expression? 

• A mathematical phrase with an equal sign or comparison symbol.

• A grouping symbol.

• A mathematical phrase without an equal sign or comparison symbol.

• When you express your feelings to someone you love. 

Multiple Select

Select all the grouping symbols we may see within an expression.

• [ Brackets ]

• “Quotations”

• (Parentheses)

Fill in the Blanks

Simplify: 7(3)

Fill in the Blanks

5+(4x20)

​Yesterday:

​We simplified expressions with one level of grouping, such as:

4+(12x3)

​

​

​Today:

​We will simplify expressions with up to two levels of grouping.

​Examples:

​​3x(7+2)-(8+4)+2

​

​

​(10÷2)x(3+17)-75

​But before we get into that, we must take a side quest!

​Let's talk about the Order of Operations

Poll

Do you know the Order Of Operations?

• Never heard of it.

• Absolutely, I do!

• I've heard of it, but I don't know what it is.

​Order Of Operations-

​the order of operations are simply rules that say which calculation comes first in an expression. Especially when having multiple operations in the same expression.

​

​Example:

​

(10÷2)x(3+17)-75

Multiple Choice

What is the very first thing we need to do in this expression? 5+(3x2)-1

• Subtract 1

• Add the 5

• Multiply the (3x2)

Poll

Yesterday we said if you have any groupings with parentheses, you MUST do that...

• When Mr. A says to

• First!

• Last!

• Before bed -.-

​You already know the first step in the order of operations!

• The very first step​ is to do everything in parentheses.

• Your'e smarter than you think!

​Order Of Operations

1. Do everything in the parentheses.

2. ​Multiplication/Division from left to right (whichever comes first)

3. ​Addition/Subtraction from left to right (whichever comes first)

​P( )

​MD->

​AS->

​Side mission complete!

​Let's get back to the lesson.

​Let's look at an example:

P( )

​MD->

​AS->

​20÷(20-15)x3

​

Another one:

P( )

​MD->

​AS->

​4x(7+3)-5+10

​

Now with two groupings:

P( )

​MD->

​AS->

​(7x4)-20+(16÷2) 

​Now it's your turn...

Fill in the Blanks

(10- 5)+4÷2

Fill in the Blanks

(3x4)+(2+6)x3

Fill in the Blanks

(20+16)÷(18- 6)

Poll

How would you rate your understanding of simplifying expressions? 

• 1- I need help, I don't understand some things.

• 2- I understand most of it, I just need more practice.

• 3- I understand it 120%, I'm ready to move on. 

​Objective complete! Part III will include:

• ​Expressions with grouping symbols within grouping symbols​

​3x[7+2-(8-4)]+2

​

​3x(7+2-(8-4))+2