Khan Academy on a Stick
Ratios and proportions
What ratios and proportions are. Using them to solve problems in the real world.
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Ratio problem with basic algebra
A slightly more involved ratio problem with algebra
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Writing proportions
As opposed to actually solving ratio word problems, in this video we'll practice just setting up the equations to solve them. Watch as we set up proportions to get at the answers.
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Solve a proportion with unknown variable
Here's a great video where we explain the reasoning behind solving proportions. We'll put some algebra to work to get our answers, too.
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Solve a proportion with unknown variable word problem
Need to increase a recipe by 2 or 3 times in order to feed more guests? Ok, to do that you would need to construct proportions and solve for variables. We'll demonstrate here.
- Proportions 2 exercise examples
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Constructing equations from proportions to solve problems
We're putting some nifty thinking to work as we use proportions to create equations which then tell us how much tip to leave for dinner.
Ratios and proportions
You remember a thing or two about ratios and proportions from your pre-algebra days. Well, how can we use these same ideas to solve problems in algebra? This tutorial re-introduces ratios in an algebraic context and helps us solve some awesome problems!
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The golden ratio
An introduction to one of the most amazing ideas/numbers in mathematics
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Advanced ratio problems
More advanced ratio problems
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More advanced ratio problem with algebra
More advance ratio problem with algebra.
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Another take on the rate problem
Another Take on the Rate Problem
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Alternate solution to ratio problem
An alternate solution to the advanced ratio problem in the last video.
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Mountain height word problem
Using some basic algebra to solve what looks like a hairy word problem that involves proportions.
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Multiple rates word problem
Sometimes you'll need to solve for multiple parts of the equation before getting at the answer. Here we solve for average speed, but first we have to determine total distance and total time.
Advanced ratios, proportions, and rates
In this tutorial, we will explore more advanced examples involving ratios, proportions, and rates.
- Introduction to rational and irrational numbers
- Recognizing irrational numbers
- Sum and product of rational numbers
- Proof that rational times irrational is irrational
- Proof that sum of rational and irrational is irrational
- Proof that square root of 2 is irrational
- Proof that square root of prime number is irrational
- Proof that there is an irrational number between any two rational numbers
- Recognizing rational and irrational expressions example
Rational and irrational numbers
In this tutorial, we'll use the powers of algebra to actually prove what we've always suspected to be true of rational and irrational numbers!