Showing posts with label Number line. Show all posts
Showing posts with label Number line. Show all posts

Support Course with Tracy Redden

Tracy Redden's support course.

1. A review of graphing lines, finding slope, and finding equations of lines from 2 points and a perpendicular line.


2. Review how to multiply and Factor all types of Polynomials.  I cover Common Factoring, Factor by grouping, Trinomial factoring, and difference and sum of cubes!



3. I show you how to solve all types of linear equations from  basic linear equations to more complicated ones with fractions and variables on both sides.  There are also the ones that end up with no solutions and all reals as a solution.



4. The first step into learning how to solve a quadratic is by factoring.  Here I show you how and explain why.



5. In addition we will look at the domains and restrictions of Rational Expressions.



6. How to Add and Subtract Rational Expressions.  I show you how to find common denominators so you can simplify.



7. How to simplify Complex Fractions.  I show you two different methods.



8. Solving quadratic equations.


... more to come soon.

Visual Real Numbers and Their Operations

Chapter 1 video compendium:



   1.4 Fractions





Real Numbers and the Number Line

Natural Numbers – The set of counting numbers { 1, 2, 3, 4, 5, …}.
Whole Numbers – Natural numbers combined with zero  { 0, 1, 2, 3, 4, 5, …}.
Integers – Positive and negative whole numbers including zero {…,−5, −4, −3,−2, −1, 0, 1, 2, 3, 4, 5…}.
Rational Numbers – Any number of the form a/b where a and b are integers where b is not equal to zero.
Irrational Numbers – Numbers that cannot be written as a ratio of two integers.

When comparing real numbers, the larger number will always lie to the right of smaller numbers on a number line.  It is clear that 15 is greater than 5, but it might not be so clear to see that −5 is greater than −15.
Number line showing numbers in order from left to right.
Use inequalities to express order relationships between numbers.
<   "less than"
>   "greater than"
≤   "less than or equal to"
≥   "greater than or equal to"

It is easy to confuse the inequalities with larger negative values.  For example,
−120 < −10     “Negative 120 is less than negative 10.
Since −120 lies further left on the number line, that number is less than −10.  Similarly, zero is greater than any negative number because it lies further right on the number line.
0 > −59     "Zero is greater than negative 59."

Write the appropriate symbol, either < or >.
List three integers satisfying the given statement. (Answers may vary.)
Absolute Value – The distance between 0 and the real number a on the number line, denoted |a|. Because the absolute value is defined to be a distance, it will always be positive. It is worth noting that |0| = 0.
Point of confusion: You may encounter negative absolute values like this −|3|. Notice that the negative is in front of the absolute value. Work the absolute value first, then consider the opposite of the result. For example,
−|3| = −3
−|−7| = −7

Believe it or not, the above are correct! Look out for this type of question on an exam.

Video Examples on YouTube: