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To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There's also a nice graphical way to add vectors, and the two ways will always result in the same vector.​​

Subject:
Algebra
Material Type:
Lesson
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Author:
Salman Khan
02/07/2018
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This arithmetic lesson demonstrates more long division problems with remainders.[Arithmetic playlist: Lesson 26 of 38]

Subject:
Mathematics
Material Type:
Lecture
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Author:
Salman Khan
12/15/2011
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You get the general idea of decimal is and what the digits in different places represent (place value). Now you're ready to do something with the decimals. Adding and subtracting is a good place to start. This will allow you to add your family's expenses to figure out if your little brother is laundering money (perhaps literally). Have fun! Common Core Standard: 5.NBT.B.7

Subject:
Numbers and Operations
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Activity/Lab
Homework/Assignment
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Author:
Khan
Salman
06/25/2014
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You get the general idea of decimal is and what the digits in different places represent (place value). Now you're ready to do something with the decimals. Adding and subtracting is a good place to start. This will allow you to add your family's expenses to figure out if your little brother is laundering money (perhaps literally). Have fun! Common Core Standard: 5.NBT.B.7

Subject:
Numbers and Operations
Material Type:
Activity/Lab
Homework/Assignment
Lecture
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Author:
Khan
Salman
06/25/2014
Conditions of Use:
Remix and Share
Rating

You get the general idea of decimal is and what the digits in different places represent (place value). Now you're ready to do something with the decimals. Adding and subtracting is a good place to start. This will allow you to add your family's expenses to figure out if your little brother is laundering money (perhaps literally). Have fun! Common Core Standard: 5.NBT.B.7

Subject:
Numbers and Operations
Material Type:
Activity/Lab
Homework/Assignment
Lecture
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Author:
Khan
Salman
06/25/2014
Conditions of Use:
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The real world is seldom about whole numbers. If you precisely measure anything, you're likely to get a decimal. If you don't know how to multiply these decimals, then you won't be able to do all the powerful things that multiplication can do in the real world (figure out your commission as a robot possum salesperson, determining how much shag carpet you need for your secret lair, etc.). Common Core Standards: 5.NBT.B.5, 5.NBT.B.7

Subject:
Numbers and Operations
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Activity/Lab
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Lecture
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Author:
Khan
Salman
06/25/2014
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The real world is seldom about whole numbers. If you precisely measure anything, you're likely to get a decimal. If you don't know how to multiply these decimals, then you won't be able to do all the powerful things that multiplication can do in the real world (figure out your commission as a robot possum salesperson, determining how much shag carpet you need for your secret lair, etc.). Common Core Standards: 5.NBT.B.5, 5.NBT.B.7

Subject:
Numbers and Operations
Material Type:
Activity/Lab
Homework/Assignment
Lecture
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Author:
Khan
Salman
06/25/2014
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The real world is seldom about whole numbers. If you precisely measure anything, you're likely to get a decimal. If you don't know how to multiply these decimals, then you won't be able to do all the powerful things that multiplication can do in the real world (figure out your commission as a robot possum salesperson, determining how much shag carpet you need for your secret lair, etc.). Common Core Standards: 5.NBT.B.5, 5.NBT.B.7

Subject:
Numbers and Operations
Material Type:
Activity/Lab
Homework/Assignment
Lecture
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Author:
Khan
Salman
06/25/2014
Conditions of Use:
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Rating

The real world is seldom about whole numbers. If you precisely measure anything, you're likely to get a decimal. If you don't know how to multiply these decimals, then you won't be able to do all the powerful things that multiplication can do in the real world (figure out your commission as a robot possum salesperson, determining how much shag carpet you need for your secret lair, etc.). Common Core Standards: 5.NBT.B.5, 5.NBT.B.7

Subject:
Numbers and Operations
Material Type:
Activity/Lab
Homework/Assignment
Lecture
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Author:
Khan
Salman
06/25/2014
Conditions of Use:
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Rating

The real world is seldom about whole numbers. If you precisely measure anything, you're likely to get a decimal. If you don't know how to multiply these decimals, then you won't be able to do all the powerful things that multiplication can do in the real world (figure out your commission as a robot possum salesperson, determining how much shag carpet you need for your secret lair, etc.). Common Core Standards: 5.NBT.B.5, 5.NBT.B.7

Subject:
Numbers and Operations
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Lecture
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Author:
Khan
Salman
06/25/2014
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Anything you can do with whole numbers, you can do with decimals. Subtraction is no exception. In this tutorial, you'll get some good practice subtracting decimals! Common Core Standard: 5.NBT.B.7

Subject:
Numbers and Operations
Material Type:
Activity/Lab
Homework/Assignment
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Author:
Khan
Salman
06/25/2014
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Anything you can do with whole numbers, you can do with decimals. Subtraction is no exception. In this tutorial, you'll get some good practice subtracting decimals! Common Core Standard: 5.NBT.B.7

Subject:
Numbers and Operations
Material Type:
Activity/Lab
Homework/Assignment
Lecture
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Author:
Khan
Salman
06/25/2014
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This lesson explains leverage and insolvency and why it is good or bad. [Banking, Money, Finance playlist: Lesson 10 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson provides an analysis of the federal reserve balance sheet as of February 2007. [Banking, Money, Finance playlist: Lesson 21 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson discusses how open market operations effect the rate at which banks lend to each other overnight. [Banking, Money, Finance playlist: Lesson 14 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson presents more information on the mechanics of the Federal Funds rate and how it increases the money supply. [Banking, Money, Finance playlist: Lesson 15 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson talks about the gold standard and is a short discussion on the meaning of wealth. [Banking, Money, Finance playlist: Lesson 17 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson tells how banks can give out loans without ever giving out gold. [Banking, Money, Finance playlist: Lesson 7 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson talks about how money is created in a fractional reserve banking system. [Banking, Money, Finance playlist: Lesson 4 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson explains reserve requirements and how they limit how much lending a bank can do. [Banking, Money, Finance playlist: Lesson 8 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson introduces bank notes and how you are more familiar with them than you realize. [Banking, Money, Finance playlist: Lesson 5 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson discusses government debt and treasuries. It explains what it means that Federal Reserve Notes are issued by the Reserve Bank but are not an obligation on the government. [Banking, Money, Finance playlist: Lesson 12 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson introduces the ways that banks make money. [Banking, Money, Finance playlist: Lesson 1 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson is an introduction to the income statement of a bank, and to income statements, in general. [Banking, Money, Finance playlist: Lesson 2 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson discusses the idea of a reserve bank. [Banking, Money, Finance playlist: Lesson 11 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson discusses the mechnics of repurchase agreements, reposession transactions and loans. [Banking, Money, Finance playlist: Lesson 20 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson idiscusses how bank notes and checks can be used. [Banking, Money, Finance playlist: Lesson 6 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson talks about the pros and cons of various banking systems and talks more about using gold as a standard. [Banking, Money, Finance playlist: Lesson 18 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson explains how reserve ratios limit how much lending an individual can do. [Banking, Money, Finance playlist: Lesson 9 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson discusses the discount rate and window and the concept of lender of last resort. [Banking, Money, Finance playlist: Lesson 19 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson explains the rationale for targeting interest rates instead of directly having a money supply target. [Banking, Money, Finance playlist: Lesson 16 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson reviews tools of the Central Bank to increase the money supply [Banking, Money, Finance playlist: Lesson 13 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson explains the weak points of fractional reserve banking. [Banking, Money, Finance playlist: Lesson 22 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson continues the discussion of fractional reserve banking. It further discusses the FDIC, deposit insurance and its side effects. [Banking, Money, Finance playlist: Lesson 23 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This lesson is a summary of thoughts of why Fractional Reserve Banking is a subsidy to banks and allows them to arbitrage the yield curve. [Banking, Money, Finance playlist: Lesson 24 of 24]

Subject:
Finance
Economics
Material Type:
Lecture
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Author:
Khan, Salman
01/17/2012
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This 17-minute video lesson looks at understanding the structure of a muscle cell. [Biology playlist: Lesson 50 of 71].

Subject:
Anatomy/Physiology
Biology
Material Type:
Lecture
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Author:
Salman Khan
05/18/2012
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This 6-minute video lesson provides an introduction to the neuron and its anatomy. [Biology playlist: Lesson 41 of 71].

Subject:
Anatomy/Physiology
Biology
Material Type:
Lecture
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Author:
Salman Khan
05/18/2012
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This 14-minute video lesson provides an overview of B cells (B lymphocytes) and how they are activated and produce antibodies. [Biology playlist: Lesson 53 of 71].

Subject:
Biology
Material Type:
Lecture
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Author:
Salman Khan
05/18/2012
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This 18-minute video lesson provides an introduction to bacteria. [Biology playlist: Lesson 18 of 71].

Subject:
Biology
Material Type:
Lecture
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Author:
Salman Khan
05/18/2012
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This 17-minute video lesson looks at C-4 Photosynthesis: How some plants avoid photorespiration. [Biology playlist: Lesson 33 of 71].

Subject:
Biology
Material Type:
Lecture
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Author:
Salman Khan
05/18/2012
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This 9-minute video lesson looks at how CAM Plants are able to fix carbon at night so they don't have to keep their stomata open during the day. [Biology playlist: Lesson 34 of 71].

Subject:
Biology
Material Type:
Lecture
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Author:
Salman Khan
05/18/2012
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This 13-minute video lecture provides an introduction to what cancer is and how it is the by-product of broken DNA replication. [Biology playlist: Lesson 13 of 71].

Subject:
Biology
Material Type:
Lecture
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Author:
Salman Khan
05/18/2012
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This 18-minute video lesson looks at the the vocabulary of DNA: chromosomes, chromatids, chromatin, transcription, translation, and replication. [Biology playlist: Lesson 8 of 71].

Subject:
Biology
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Lecture
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Author:
Salman Khan
05/18/2012
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This 15-minute video lesson provides an introduction to the circulatory system and the heart. [Biology playlist: Lesson 39 of 71].

Subject:
Biology
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Lecture
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Author:
Salman Khan
05/18/2012
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This 7-minute video lesson provides a correction to Sodium and Potassium Pump Video. [Biology playlist: Lesson 43 of 71].

Subject:
Biology
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Lecture
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Author:
Salman Khan
05/18/2012
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This 10-minute video lesson discusses how cytotoxic T-Cells get activated by MHC-I/antigen complexes and then proceed to kill infected cells. [Biology playlist: Lesson 56 of 71].

Subject:
Biology
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Lecture
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Author:
Salman Khan
05/18/2012
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This 28-minute video lesson provides an introduction to DNA. [Biology playlist: Lesson 6 of 71].

Subject:
Biology
Genetics
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Lecture
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Author:
Salman Khan
05/18/2012
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This 19-minute video lesson looks at diffusion and osmosis. [Biology playlist: Lesson 36 of 71].

Subject:
Biology
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Lecture
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Author:
Salman Khan
05/18/2012
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This 17-minute video lesson presents an overview of the Electron Transport Chain. [Biology playlist: Lesson 26 of 71].

Subject:
Biology
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Lecture
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Author:
Salman Khan
05/18/2012
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This 2-minute video lesson provides an overview of early development of a zygote to an embryo. It also discusses embryonic and somatic stem cells. [Biology playlist: Lesson 12 of 71].

Subject:
Biology
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Lecture
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Salman Khan
05/18/2012
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This 13-minute video lesson provides an overview of glycolysis. [Biology playlist: Lesson 24 of 71].

Subject:
Biology
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Lecture
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Salman Khan
05/18/2012
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This 21-minute video lesson provides an introduction to helper T-Cells and their role in activating B cells. [Biology playlist: Lesson 55 of 71].

Subject:
Biology
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Lecture
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Salman Khan
05/18/2012
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This 15-minute video lesson examines hemoglobin and its role in the circulatory system. [Biology playlist: Lesson 40 of 71].

Subject:
Biology
Material Type:
Lecture
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