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What are variables, expressions, and equations? | Introduction to algebra | Algebra I | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-equations-and-inequalities/cc-6th-intro-equations/v/variables-expressions-and-equations
Learn what variables, expressions, and equations really are.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/introduction-to-algebra/feel-for-equations-and-inequalit/e/dependent-and-independent-variables?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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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.
For free. For everyone. Forever. #YouCanLearnAnything
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How to solve equations of the form ax = b | Linear equations | Algebra I | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-equations-and-inequalities/cc-6th-one-step-mult-div-equations/v/simple-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 variable!
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/e/linear_equations_1?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription
Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/v/solving-one-step-equations-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/super-yoga/v/super-yoga-plans-solving-systems-by-elimination?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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 is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
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Solving a more complicated equation | Linear equations | Algebra I | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-2-step-equations-intro/v/equations-2
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.org right now:
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/e/linear_equations_2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/v/two-step-equations?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/v/one-step-equations?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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 is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
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Introduction to solving an equation with variables on both sides | Algebra I | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-variables-both-sides/v/equations-3
Sal solves the equation 2x + 3 = 5x - 2.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/basic-equation-practice/e/linear_equations_3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/basic-equation-practice/v/multi-step-equations-1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/linear-equation-word-problems-tu/v/application-problems-with-equation-in-one-variable?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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 is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
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Algebra: Linear equations 4 | Linear equations | Algebra I | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/algebra-linear-equations-4
Solving linear equations with variable expressions in the denominators of fractions
Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/averages?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/algebra-linear-equations-3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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 is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
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Algebra: Solving Inequalities
Solving linear inequalities. -
Algebra: graphing lines 1
Graphing linear equations
More free lessons at: http://www.khanacademy.org/video?v=2UrcUfBizyw
Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/graph-from-slope-intercept-equation?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription -
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-anmubYU -
Algebra: Slope
Figuring out the slope of a line -
Algebra: Slope 2
Second part of determining the slope of a line -
Algebra: Slope 3
Part 3 of slope -
Algebra: Equation of a line
Determining the equation of a line
More free lessons at: http://www.khanacademy.org/video?v=gvwKv6F69F0 -
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=8sz1IPjBRS8 -
Averages | Linear equations | Algebra I | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/averages
Introduction to averages and algebra problems involving averages.
Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/taking-percentages?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/algebra-linear-equations-4?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy -
Integer sums
Adding sums of consecutive integers -
Taking percentages | Linear equations | Algebra I | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/taking-percentages
Taking a percentage of a number.
Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/growing-by-a-percentage?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/averages?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
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Growing by a percentage | Linear equations | Algebra I | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/growing-by-a-percentage
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.
Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/more-percent-problems?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/taking-percentages?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
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Percent word problem example 1 | Ratios, rates, and percentages | 6th grade | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-percent-word-problems/v/another-percent-word-problem
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.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-percent-word-problems/e/percentage_word_problems_1?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade
Watch the next lesson: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-percent-word-problems/v/percent-word-problems?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade
Missed the previous lesson? https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-percent-problems/v/taking-a-percentage-example?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade
Grade 6th on Khan Academy: By the 6th grade, you're becoming a sophisticated mathemagician. You'll be able to add, subtract, multiply, and divide any non-negative numbers (including decimals and fractions) that any grumpy ogre throws at you. Mind-blowing ideas like exponents (you saw these briefly in the 5th grade), ratios, percents, negative numbers, and variable expressions will start being in your comfort zone. Most importantly, the algebraic side of mathematics is a whole new kind of fun! And if that is not enough, we are going to continue with our understanding of ideas like the coordinate plane (from 5th grade) and area while beginning to derive meaning from data! (Content was selected for this grade level based on a typical curriculum in the United States.)
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy à ªs 6th grade channel:
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More percent problems | Linear equations | Algebra I | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/more-percent-problems
Slightly harder percent problems
Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/age-word-problems-1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/growing-by-a-percentage?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
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systems of equations
systems of equations
More free lessons at: http://www.khanacademy.org/video?v=nok99JOhcjo -
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-algebra/rates-and-ratios/ratios_and_proportions/e/ratio_word_problems?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/ratios_and_proportions/v/ratios-as-fractions-in-simplest-form?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/number-sets-pre-alg/v/number-sets-3?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
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Ratio problem with basic algebra | Linear equations and inequalities | Algebra Basics | Khan Academy
A slightly more involved ratio problem with algebra. Created by Sal Khan.
Practice this yourself on Khan Academy right now: https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/ratios-core-algebra/e/constructing-proportions-to-solve-application-problems?utm_source=YT&utm_medium=Desc&utm_campaign=algebrabasics
Watch the next lesson: https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebra-direct-inverse-variation/v/direct-and-inverse-variation?utm_source=YT&utm_medium=Desc&utm_campaign=algebrabasics
Missed the previous lesson? https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/ratios-core-algebra/v/constructing-proportions-to-solve-application-problems?utm_source=YT&utm_medium=Desc&utm_campaign=algebrabasics
Algebra basics on Khan Academy: Topics covered in a traditional college level introductory macroeconomics course
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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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_hhRtUuw -
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=-xyTz0WZ1W4 -
Introduction to Ratios
Basic ratio problems. (from KhanAcademy.org) -
Advanced ratio problems
More advanced ratio problems
More free lessons at: http://www.khanacademy.org/video?v=PASSD2OcU0c -
Age word problems 1 | Linear equations | Algebra I | Khan Academy
Age word problems
Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/age-word-problems-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/more-percent-problems?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
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Age word problems 2 | Linear equations | Algebra I | Khan Academy
Second set of age word problems
Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/age-word-problems-3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/age-word-problems-1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
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Age word problems 3 | Linear equations | Algebra I | Khan Academy
Part 3 of the presentation on age word problems
Watch the next lesson: https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-using-multiplication-and-division?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/age-word-problems-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
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Level 1 multiplying expressions
(Ax+By)(Ax+By)
More free lessons at: http://www.khanacademy.org/video?v=Sc0e6xrRJYY -
Solving a quadratic by factoring | Quadratic equations | Algebra I | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratics-solve-factoring/v/example-1-solving-a-quadratic-equation-by-factoring
Factoring quadratics
Watch the next lesson: https://www.khanacademy.org/math/algebra/quadratics/quadratic_odds_ends/v/ca-algebra-i-factoring-quadratics?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/quadratics/quadratic_inequalities/v/quadratic-inequalities-visual-explanation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
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Introduction to i and imaginary numbers | Imaginary and complex numbers | Precalculus | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/v/introduction-to-i-and-imaginary-numbers
Introduction to i and imaginary numbers
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/i_precalc/e/imaginary_unit_powers?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Watch the next lesson: https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/i_precalc/v/calculating-i-raised-to-arbitrary-exponents?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/parametric_equations/polar_coor/v/polar-coordinates-3?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Precalculus channel:
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Calculating i raised to arbitrary exponents | Precalculus | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/v/calculating-i-raised-to-arbitrary-exponents
Calculating i raised to arbitrarily high exponents
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/i_precalc/e/imaginary_unit_powers?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Watch the next lesson: https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/i_precalc/v/imaginary-roots-of-negative-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/i_precalc/v/introduction-to-i-and-imaginary-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Precalculus channel:
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i as the principal root of -1 (a little technical) | Precalculus | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/v/i-as-the-principal-root-of-1-a-little-technical
i as the principal square root of -1
Watch the next lesson: https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/complex_num_precalc/v/complex-number-intro?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/i_precalc/v/imaginary-roots-of-negative-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Precalculus channel:
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Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy -
Complex Numbers (part 1)
Introduction to complex numbers. Adding, subtracting and multiplying complex numbers. -
Complex Numbers (part 2)
Dividing complex numbers. Complex conjugates. -
Introduction to the quadratic equation | Quadratic equations | Algebra I | Khan Academy
Introduction to using the quadratic equation to solve 2nd degree polynomial equations
Watch the next lesson: https://www.khanacademy.org/math/algebra/quadratics/quadratic_odds_ends/v/quadratic-equation-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/quadratics/quadratic_odds_ends/v/ca-algebra-i-completing-the-square?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
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Quadratic equation part 2 | Quadratic equations | Algebra I | Khan Academy
2 more examples of solving equations using the quadratic equation
Watch the next lesson: https://www.khanacademy.org/math/algebra/quadratics/quadratic_odds_ends/v/quadratic-formula-proof?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/quadratics/quadratic_odds_ends/v/introduction-to-the-quadratic-equation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy -
Completing the square
Solving a quadratic by completing the square. -
Quadratic formula (proof) | Quadratic equations | Algebra I | Khan Academy
Deriving the quadratic formula by completing the square.
Watch the next lesson: https://www.khanacademy.org/math/algebra/quadratics/quadratic_odds_ends/v/ca-algebra-i-quadratic-equation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/quadratics/quadratic_odds_ends/v/quadratic-equation-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy -
Quadratic inequalities | Polynomial and rational functions | Algebra II | Khan Academy
Solving quadratic inequalities using factoring
Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_ineq/v/quadratic-inequalities-visual-explanation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/v/discriminant-for-types-of-solutions-for-a-quadratic?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
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Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy -
Quadratic inequalities (visual explanation) | Algebra II | Khan Academy
How to solve a quadratic inequality. Visual intuition of what a quadratic inequality means.
Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial_tutorial/v/terms-coefficients-and-exponents-in-a-polynomial?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_ineq/v/quadratic-inequalities?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
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Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy -
Introduction to functions
An introduction to functions.
More free lessons at: http://www.khanacademy.org/video?v=VhokQhjl5t0 -
Functions Part 2
More examples of solving function problems
More free lessons at: http://www.khanacademy.org/video?v=XEblO51pF5I -
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=5fcRSie63Hs -
Functions (part 4)
An example of a functions problem submitted by a youtube viewer
More free lessons at: http://www.khanacademy.org/video?v=rbt51hXmzig -
Domain of a function | Functions and their graphs | Algebra II | Khan Academy
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Figuring out the domain of a function
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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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Proof: log a + log b = log ab | Logarithms | Algebra II | Khan Academy
Proof of the logarithm property: log a + log b = log ab
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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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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)
Watch the next lesson: https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_properties/v/change-of-base-formula-proof?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_properties/v/proof-log-a-log-b-log-ab?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
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Proof: log_a (B) = (log_x (B))/(log_x (A))
Proof of the logarithm property
log_a (B) = (log_x (B))/(log_x (A))