# Algebra - Khan Academy

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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## Lessons hide description |
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## 1) The beauty of algebra | Introduction to algebra## Why the abstraction of mathematics is so fundamental |

## 2) Origins of algebra | Introduction to algebra## Where did the word "Algebra" and its underlying ideas come from? |

## 3) Abstract-ness | Introduction to algebra## The general idea behind the word 'abstract' |

## 4) Introduction to the coordinate plane | Introduction to algebra## Bridging algebra and geometry. What makes linear equations so linear. |

## 5) What are variables, expressions, and equations? | Introduction to algebra## Learn what variables, expressions, and equations really are. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/a ... |

## 6) How to solve equations of the form ax = b | Linear equations## Let's ease into this, shall we? Here's an introduction to basic algebraic equations of the form ax=b. Remember that you can check to see if you have the right answer by substituting it for the variabl ... |

## 7) Solving a more complicated equation | Linear equations## This example demonstrates how we solve an equation expressed such: ax + b = c. It's a little more complicated than previous examples, but you can do it! Practice this lesson yourself on KhanAcademy.o ... |

## 8) Introduction to solving an equation with variables on both sides## Sal solves the equation 2x + 3 = 5x - 2. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/a ... |

## 9) Algebra: Linear equations 4 | Linear equations## Solving linear equations with variable expressions in the denominators of fractions Watch the next lesson: https://www.khanacademy.org/math/algebra ... |

## 10) Algebra: Solving Inequalities## Solving linear inequalities. |

## 11) Algebra: graphing lines 1## Graphing linear equations More free lessons at: http://www.khanacademy.org/video?v=2UrcU |

## 12) Algebra: Slope and Y-intercept intuition## Getting a feel for slope and y-intercept More free lessons at: http://www.khanacademy.org/video?v=Nhn-a |

## 13) Algebra: Slope## Figuring out the slope of a line |

## 14) Algebra: Slope 2## Second part of determining the slope of a line |

## 15) Algebra: Slope 3## Part 3 of slope |

## 16) Algebra: Equation of a line## Determining the equation of a line More free lessons at: http://www.khanacademy.org/video?v=gvwKv |

## 17) Slope and Y-intercept Intuition## Using the "Graph of a line" module to understand how a line's graph changes when its slope or y-intercept is changed. More free lessons at: http://www.khanacademy.org/video?v=8sz1I |

## 18) Averages | Linear equations## Introduction to averages and algebra problems involving averages. |

## 19) Integer sums## Adding sums of consecutive integers |

## 20) Taking percentages | Linear equations## Taking a percentage of a number. |

## 21) Growing by a percentage | Linear equations## In this example we grow a whole number by a percentage of itself. Growing by percentage is a common skill often used when figuring how much is owed or earned with interest. |

## 22) Percent word problem example 1 | Ratios, rates, and percentages | 6th grade | Khan Academy## We're putting a little algebra to work to find the full price when you know the discount price in this percent word problem. Practice this lesson yourself on KhanAcademy.org right now: https://www. ... |

## 23) More percent problems | Linear equations## Slightly harder percent problems |

## 24) systems of equations## systems of equations More free lessons at: http://www.khanacademy.org/video?v=nok99 |

## 25) Introduction to ratios | Ratios, proportions, units, and rates | Pre-Algebra | Khan Academy## What a ratio is. Simple ratio problems. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-alg ... |

## 26) Ratio problem with basic algebra (new HD)## A slightly more involved ratio problem with algebra More free lessons at: http://www.khanacademy.org/video?v=ITVQr |

## 27) More advanced ratio problem--with Algebra (HD version)## More advance ratio problem with algebra. More free lessons at: http://www.khanacademy.org/video?v=ItA_h |

## 28) Alternate Solution to Ratio Problem (HD Version)## An alternate solution to the advanced ratio problem in the last video. More free lessons at: http://www.khanacademy.org/video?v=-xyTz |

## 29) Introduction to Ratios## Basic ratio problems. (from KhanAcademy.org) |

## 30) Advanced ratio problems## More advanced ratio problems More free lessons at: http://www.khanacademy.org/video?v=PASSD |

## 31) Age word problems 1 | Linear equations## Age word problems |

## 32) Age word problems 2 | Linear equations## Second set of age word problems |

## 33) Age word problems 3 | Linear equations## Part 3 of the presentation on age word problems |

## 34) Level 1 multiplying expressions## (Ax+By)(Ax+By) More free lessons at: http://www.khanacademy.org/video?v=Sc0e6 |

## 35) Solving a quadratic by factoring | Quadratic equations## Factoring quadratics |

## 36) Introduction to i and imaginary numbers | Imaginary and complex numbers | Precalculus | Khan Academy## Introduction to i and imaginary numbers Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ... |

## 37) Calculating i raised to arbitrary exponents | Precalculus | Khan Academy## Calculating i raised to arbitrarily high exponents Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ... |

## 38) i as the principal root of -1 (a little technical) | Precalculus | Khan Academy## i as the principal square root of -1 |

## 39) Complex Numbers (part 1)## Introduction to complex numbers. Adding, subtracting and multiplying complex numbers. |

## 40) Complex Numbers (part 2)## Dividing complex numbers. Complex conjugates. |

## 41) Introduction to the quadratic equation | Quadratic equations## Introduction to using the quadratic equation to solve 2nd degree polynomial equations |

## 42) Quadratic equation part 2 | Quadratic equations## 2 more examples of solving equations using the quadratic equation |

## 43) Completing the square## Solving a quadratic by completing the square. |

## 44) Quadratic formula (proof) | Quadratic equations## Deriving the quadratic formula by completing the square. |

## 45) Quadratic inequalities | Polynomial and rational functions | Algebra II | Khan Academy## Solving quadratic inequalities using factoring |

## 46) Quadratic inequalities (visual explanation) | Algebra II | Khan Academy## How to solve a quadratic inequality. Visual intuition of what a quadratic inequality means. |

## 47) Introduction to functions## An introduction to functions. More free lessons at: http://www.khanacademy.org/video?v=VhokQ |

## 48) Functions Part 2## More examples of solving function problems More free lessons at: http://www.khanacademy.org/video?v=XEblO |

## 49) Functions (Part III)## Even more examples of function exercises. Introduction of a graph as definition of a function. More free lessons at: http://www.khanacademy.org/video?v=5fcRS |

## 50) Functions (part 4)## An example of a functions problem submitted by a youtube viewer More free lessons at: http://www.khanacademy.org/video?v=rbt51 |

## 51) Domain of a function | Functions and their graphs | Algebra II | Khan Academy## Figuring out the domain of a function Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 52) Proof: log a + log b = log ab | Logarithms | Algebra II | Khan Academy## Proof of the logarithm property: log a + log b = log ab |

## 53) Proof: a log b = log(b^a), log a - log b = log(a/b) | Logarithms | Algebra II | Khan Academy## Proofs of the logarithm properties: A(log B) = log (B^A) and log A - log B = log (A/B) |

## 54) Proof: log_a (B) = (log_x (B))/(log_x (A))## Proof of the logarithm property log_a (B) = (log_x (B))/(log_x (A)) |

## 55) Algebraic Long Division## Dividing one polynomial into another |

## 56) Introduction to conic sections | Conic sections | Algebra II | Khan Academy## What are conic sections and why are they called "conic sections"? Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 57) Conic Sections: Intro to Circles## Introduction to the Circle |

## 58) Conic sections: Intro to ellipse | Conic sections | Algebra II | Khan Academy## Introduction to the ellipse. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 59) Conic sections: Intro to hyperbolas | Conic sections | Algebra II | Khan Academy## Introduction to the hyperbola |

## 60) Conic sections: Hyperbolas 2 | Conic sections | Algebra II | Khan Academy## Continuation of the intro to hyperbolas |

## 61) Conic sections: Hyperbolas 3 | Conic sections | Algebra II | Khan Academy## Part 3 of the intro to hyperbolas Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 62) Identifying an ellipse from equation | Conic sections | Algebra II | Khan Academy## Part 1 of identifying and graphic conic sections |

## 63) Identifying a hyperbola from an equation | Conic sections | Algebra II | Khan Academy## Part 2 of identifying and graphing conic sections |

## 64) Identifying circles and parabolas from equations | Conic sections | Algebra II | Khan Academy## Let's identify (and graph) a couple of more conics! |

## 65) Foci of an ellipse | Conic sections | Algebra II | Khan Academy## Calculating the foci (or focuses) of an Ellipse. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 66) Foci of a hyperbola | Conic sections | Algebra II | Khan Academy## Introduction to the foci (focuses) of a hyperbola |

## 67) Proof: Hyperbola foci | Conic sections | Algebra II | Khan Academy## Proof of the hyperbola foci formula |

## 68) Partial fraction expansion 1 | Partial fraction expansion | Precalculus | Khan Academy## Introduction to partial fraction expansion Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ... |

## 69) Partial fraction expansion 2 | Partial fraction expansion | Precalculus | Khan Academy## A more complex problem Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ... |

## 70) Partial fraction expansion 3 | Partial fraction expansion | Precalculus | Khan Academy## Dealing with repeated factors Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ... |

## 71) Parabola Focus and Directrix 1## Parabola as the locus of all points equidistant from a point and a line More free lessons at: http://www.khanacademy.org/video?v=ZJf9s |

## 72) Focus and Directrix of a Parabola 2## Finding the focus and directrix of a parabola More free lessons at: http://www.khanacademy.org/video?v=1Jm9r |

## 73) Two Passing Bicycles Word Problem## Algebra word problem involving two bicycles passing each other. More free lessons at: http://www.khanacademy.org/video?v=Nx4Xk |

## 74) Passed Bike Word Problem## Fun algebra word problem involving a train passing a bike. More free lessons at: http://www.khanacademy.org/video?v=P03lj |

## 75) Passing Trains## Trains passing at different rates. More free lessons at: http://www.khanacademy.org/video?v=qLLjD |

## 76) Overtaking Word Problem## 3 people overtaking each other at different rates More free lessons at: http://www.khanacademy.org/video?v=LYWUH |

## 77) Early train word problem | Linear equations## Fun word problem that is almost a brain teaser. |

## 78) Officer on Horseback## Not quite a brain teaser but fun nonetheless! More free lessons at: http://www.khanacademy.org/video?v=IPJAi |

## 79) Rational inequalities | Polynomial and rational functions | Algebra II | Khan Academy## Two ways to solve a rational inequality (or an inequality involving a fractional expression) |

## 80) Rational inequalities 2 | Polynomial and rational functions | Algebra II | Khan Academy## Slightly harder rational inequality problem |

## 81) Interesting Polynomial Coefficient Problem## Finding the coefficients of a third degree polynomial given 2 roots and the y-intercept More free lessons at: http://www.khanacademy.org/video?v=hypi8 |

## 82) Geometric series sum to figure out mortgage payments | Precalculus | Khan Academy## Figuring out the formula for fixed mortgage payments using the sum of a geometric series Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/preca ... |

## 83) Introduction to function inverses | Functions and their graphs | Algebra II | Khan Academy## Introduction to Function Inverses Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 84) Function inverse example 1 | Functions and their graphs | Algebra II | Khan Academy## Function Inverse Example 1 Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 85) Function inverses example 2 | Functions and their graphs | Algebra II | Khan Academy## Function Inverses Example 2 Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 86) Function inverses example 3 | Functions and their graphs | Algebra II | Khan Academy## Function Inverses Example 3 Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 87) Direct and inverse variation | Rational expressions | Algebra II | Khan Academy## Understanding direct and inverse variation Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 88) Recognizing direct and inverse variation | Rational expressions | Algebra II | Khan Academy## Examples of variables varying directly and inversely Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 89) Recognizing odd and even functions | Functions and their graphs | Algebra II | Khan Academy## Even and odd functions Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 90) Connection between even and odd numbers and functions | Algebra II | Khan Academy## A possible reason why even functions are called "even" and odd functions are called "odd" Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 91) New operator definitions | Functions and their graphs | Algebra II | Khan Academy## Getting comfortable with evaluating newly defined function operators Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algeb ... |

## 92) Proof by induction | Sequences, series and induction | Precalculus | Khan Academy## Proving an expression for the sum of all positive integers up to and including n by induction |

## 93) Alternate proof to induction for integer sum | Precalculus | Khan Academy## Another way to prove the expression for the sum of all positive integers up to and including n |

## 94) Setting up proportions to solve word problems | 7th grade | Khan Academy## Some examples of writing two ratios and setting them equal to each other to solve proportion word problems Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/ma ... |

## 95) Converting repeating decimals to fractions 1 | Linear equations## Examples of how to convert basic repeating decimals to fractions Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/a ... |

## 96) Converting repeating decimals to fractions 2 | Linear equations## Converting more interesting repeating decimals to fractions Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/a ... |

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