What kind of numbers are rational numbers?
Are all integers called rational numbers also?
Rational numbers are basically any number, positive or negative, that can be written as a fraction. Repeating decimals are rational numbers.
Which of these are rational numbers?
3 -1.7777 ∞ 2/3 2.8 pi 1.567 repeating
Answer: All are rational numbers except infinite and pi.
Order these rational numbers from least to greatest:
-1.2 -0.1 -3/8 -1.01 -2/11 -1/6
How did you find out the correct order?
There are 2 strategies that mathematically prove the order of these numbers.
1) Change the numbers so that you can compare them using common denominators.
2) Change the numbers into decimals by dividing the fractions (top goes in the house).
Answer: -1.2 -1.01 -3/8 -2/11 -1/6 -0.1
What are the steps of the order of operations?
Why do we have an order of operations in math?
Multiply AND divide go together, whichever comes first in the problem from left to right.
Add AND subtract go together, whichever comes first in the problem from left to right.
What is the meaning of absolute value, and why is it always positive?
How does absolute value differ from an opposite?
Notes: Guided Notes WS.
Find the absolute value:
|-3| ----------> 3
|1,000| ---------> 1,000
|-2.5| ------------> 2.5
|1/2| ----------> 1/2
Find the opposite:
-3 -----------> 3
1,000 ----------> -1,000
-2.5 -----------> 2.5
1/2 ------------> -1/2
When is it appropriate to combine like terms?
Create an example showing the parts of an expression.
Terms have to be the same before you can combine them through addition or subtraction.
A constant is a term that looks like a regular number.
A variable is an algebraic term that has an unknown value.
A coefficient shows how many variables there are.
Variables can only be combined with other variables of the same letter and exponent.
1. 3x^2 + 11x + 3
2. 9x + 5y + 12
3. 36 - 11z^2
-Demonstrate an expression that uses the distributive property to reach the same solution that you would using the order of operations.
-Give an example of a real life situation that could be used to represent the distributive property.
-Show how to solve the following expression using the distributive property: 14(x - 4)
-How do I know when the distributive property can be applied?
The factor on the outside of the parentheses is used to multiply the terms inside the parentheses.
The factor may be on either side of the parentheses, left or right.
To use the distributive property, the terms inside the parentheses must be adding or subtracting.
Practice: Done through warm-up as well as further practice on Friday.