Examples of simplifying expressions involving rational nu...

1.1   What are variables, expressions, and equations?

1.2   How to test solutions to equations using substitution

1.3   How to solve one-step equations

1.4   Example of solving a one-step equation

1.5   How to solve equations of the form ax = b

1.6   How to solve equations of the form x/a = b

1.7   How to find mistakes in one step equations

1.8   How to plot inequalities on a number line

1.9   Example of plotting a simple inequality on a number line

1.10   How to test solutions to inequalities

1.11   Combining like terms introduction

1.12   Combining like terms, but more complicated

1.14   Factoring algebraic expressions using the distributive property

1.15   Example 1: Factor a linear binomial by taking a common factor

1.16   How to simplify an expression by combining like terms and the distributive property

1.17   Equivalent expressions with distribution and negative numbers

1.18   Why we do the same thing to both sides of equations

1.19   Solving two-step equations

1.20   Solving a more complicated equation

1.21   Example: two-step equation with numerator x

1.22   Mistakes in solving equations

1.23   Multiplying and dividing with inequalities

1.24   Multiplying and dividing with inequalities example

1.25   Solving a two-step inequality

1.26   Introduction to solving an equation with variables on both sides

1.27   Example 2: Variables on both sides

1.28   Solving equations with the distributive property

1.29   Introduction to ratios

1.30   Ratio example problems

1.31   Equivalent ratios

1.32   Ratios for recipes

1.33   Ratio word problem examples

1.34   Understanding equivalent ratios

1.35   Ratios on coordinate plane

1.36   Ratios and measurement

1.37   Ratios as fractions

1.38   Ratio word problem: boys to girls

1.39   Introduction to rates

1.40   Solving unit rates problem

1.41   Solving unit price problem

1.42   Rate problems

1.43   Determining rates with fractions

1.44   Practice computing and comparing rates

1.45   Introduction to proportional relationships

1.46   Identifying constant of proportionality graphically

1.47   Constant of proportionality from graph

1.48   Identifying the constant of proportionality from equation

1.49   Constant of proportionality from equation

1.50   Constant of proportionality from tables

1.51   Proportionality constant from table

1.52   Comparing constants of proportionality

1.53   Comparing proportionality constants

1.54   Interpret proportionality constants

1.55   Introduction to proportional relationships

1.56   Movie ticket proportionality

1.57   Banana proportionality

1.58   Proportional relationships example

1.59   Identifying proportional relationships from graphs

1.60   How to visually identify proportional relationships using graphs

1.61   Interpreting graphs of proportional relationships

1.62   Solving a proportion with an unknown variable (example)

1.63   Setting up proportions to solve word problems

1.64   Proportion word problem (example 1)

1.65   Proportion word problem (example 2)

1.66   Equations of proportional relationships

1.67   Writing an equation for a proportional relationship (example)

1.68   Writing proportional equations

1.69   Comparing rates

1.70   Representing and comparing rates

1.71   Graphing proportional relationships example

1.72   Graphing proportional relationships example 2

1.73   Graphing proportional relationships example 3

1.74   Using factors and multiples to figure out days of the week

1.75   Math patterns example 1

1.76   Math patterns example 2

1.77   Number patterns: Seeing relationships

1.78   Number patterns: interpreting relationships

1.79   Number patterns: interpreting and graphing relationships

1.80   Number patterns: visualizing sequence relationships

1.81   What is a function?

1.82   Evaluating functions given their formula

1.83   Function notation in context example

1.84   Evaluating functions given their graph

1.85   Difference between equations and functions

1.86   Solving for F in terms of C

1.87   How to create a function from an equation (example)

1.88   Interpreting linear tables word problems example 1

1.89   Modeling with linear equations example 1

1.90   Linear function example: spending money

1.91   Constructing linear functions example 1

1.92   Constructing linear functions example 2

1.93   Recognizing linear functions

1.94   Linear and nonlinear functions (example 1)

1.95   Linear and nonlinear functions (example 2)

1.96   Linear and nonlinear functions (example 3)

1.97   Interpreting a graph exercise example

1.98   Introduction to square roots

1.99   Introduction to cube roots

1.100   Square root of decimal (example)

1.101   Introduction to rational and irrational numbers

1.102   Recognizing rational and irrational numbers (examples)

1.103   How to classify numbers

1.104   Exponents with negative bases

1.105   Raising a number to the 0 and 1st power

1.106   Multiplying and dividing even and odd numbers of negatives

1.107   Patterns in raising 1 and -1 to different powers

1.108   Exponent properties involving products

1.109   Products and exponents raised to an exponent properties

1.110   Exponent properties involving quotients (examples)

1.111   Negative exponents

1.112   Negative exponent intuition

1.113   Multiplying & dividing powers (integer exponents)

1.114   Powers of products & quotients (integer exponents)

1.115   Introduction to square roots

1.116   Introduction to cube roots

1.117   Cube root of a negative number (example)

1.118   Square root of decimal (example)

1.119   Dimensions of a cube from its volume

1.120   Combining like terms introduction

1.121   Combining like terms, but more complicated

1.122   Examples of simplifying expressions involving rational numbers

1.123   Factoring algebraic expressions using the distributive property

1.124   Example 1: Factor a linear binomial by taking a common factor

1.125   How to simplify an expression by combining like terms and the distributive property

1.126   Equivalent expressions with distribution and negative numbers

1.127   Interpreting a graph exercise example