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How To: Find a 95% confidence interval for a proportion in statistics

From Ramanujan to calculus co-creator Gottfried Leibniz, many of the world's best and brightest mathematical minds have belonged to autodidacts. And, thanks to the Internet, it's easier than ever to follow in their footsteps (or just study for that next big test). With this installment from Internet pedagogical superstar Salman Khan's series of free math tutorials, you'll learn how to find a 95% confidence interval in statistics.

How To: Multiply decimals together

In this tutorial we learn how to multiply decimals together. Start off by ignoring the decimal points on the equation and just imagining you have normal numbers. Then, multiply the two numbers that you wrote down together. Once you figure that out, it will be time to reintroduce the decimals. Look at the place the decimal is in each number in the beginning equation. Then, add the decimal places together between each of them. From here, place the decimal on the end of the answer you came up wi...

How To: Graph an equation

In this video, we learn how to graph an equation. First, pick a point out of the equation and see if it's a solution to the equation. This equation shows where two lines cross in the math problem. See if the two coordinates are part of the line that is on the equation. The two numbers are going to be the 'x' and 'y' that you plug into the equation. Once you have these written out, you will be able to graph them using the coordinates on the graph. Once finished, you will have graphed the equat...

How To: Multiply and simplify square roots

In this tutorial we learn how to multiply and simplify square roots. When you multiply square roots, you will first need to put them under one radical. From here, you will need to factor out what you have. Once you find a perfect square, find the square root of it. You can either write these as all separate equations or pull the perfect root on the outside of the other parts of the equation. Do the math until you find what you are left with. From here, you can do basic math to find what's lef...

How To: Graph a circle

In this tutorial, we learn how to graph a circle. When given an equation to graph the circle, you will first need to find the vertex of the circle. Once you find this, you can use those coordinates to mark the vertex on the graph. Follow the negatives and positives to go up, down, left, and right on the graph. Next, you will need to find the 'r' value of the equation. After this, you will use this to continue to graph the rest of the points around the vertex. When finished, draw the outline o...

How To: Subtract decimals

In this video, we learn how to subtract decimals. If you can subtract using basic numbers, then you will be able to subtract decimals. First, you will line up the tens and the other units of the numbers. Once this is finished, you will start to take away the top number from the bottom number. Borrow from the number to the left if you need to, then write down what you are left with on the bottom. Once you come up with your number, make sure you place in the decimal point where it goes. All you...

How To: Subtract rational expressions

In this video, we learn how to subtract rational expressions. To start, you will need to find common denominators. To do this, factor out the denominators in the fractions on both sides of the equations. Now you need to build the lowest common denominator for these two fractions. To do this, take the first denominator and take whatever is missing from the second. After you do the math for this, you will build new fractions with the common denominator as the denominator. Leave the denominator ...

How To: Understand angle relationships

In this tutorial, we learn how to understand angle relationships. Start out by drawing an angle out and looking at the different parts of it. From here, you will start to find where the different angles are. Linear pairs equal 180 degrees and are on a straight line. Once you learn this, you can write them out on the paper. Supplementary angles equal 180 degrees as well. Two angles that add up to 90 degrees are complimentary angles. Once you learn the relationships between angles, you can bett...

How To: Understand completing the square

In this video, we learn how to understand completing the square. First, you will write the quadratic expression out. Then, you will write the open bracket so you write it out in the correct format. Now, find the number in front of the 'x' term, which is the coefficient. Then, write this number on the other side of the equation in the parenthesis. From here, you will need to follow the proper rules of math to find out what the square is equal to. When you are finished, make sure you label the ...

How To: Understand negative exponents

In this video, we learn how to understand negative exponents. The one rule you have to remember is when you have a number with a negative power, then you need to divide it over one. You can take this term and put it in the denominator of your fraction to make it a positive exponent. For example, if you have 5 to the -1, then you can move the 5 to the denominator and get 1/5, which is the same exact thing! This is one of the most basic rules in math. Once you understand this, simplifying fract...

How To: Convert numbers in and out of standard form

In this video, we learn how to convert numbers in and out of standard form. Standard form is a useful way of writing down very large numbers and very small numbers. To do this, you will look at the number you have and ignore the zeros that are just at the end. Then, write down the basic numbers. Put a decimal point in this number to make it between one and ten. Now, write down x 10 and put the power for how many places the decimal point moved to get to the new number. This will help you write...

How To: Graph inequalities on a number line

In this video, we learn how to graph inequalities on a number line. Inequalities have a greater than or less than sign instead of an equal signs. Remember that these are no different than figuring out how to graph normal equations. First, you will need to remove the single numbers from each side of the equation. Continue to do math on the equation until you figure out what 'x' is. From here, draw the numbers on your graph and then find the number that 'x' is greater to or less than. Use an op...

How To: Add rational expressions

In this tutorial, we learn how to add rational expressions. When you have two rational expressions, you will first need to factor every denominator. After this, find the lowest common denominator from all of them. After this, rewrite every fraction so it has the lowest common denominator for the denominator. Leave it in factored form for the denominators. Multiply the top and the bottom to find the answer for each of the fractions in the equation. When finished, make sure you find the most si...

How To: Rationalize square roots

In this tutorial, we learn how to rationalize square roots. You cannot have square roots in the denominator of an equation. You need to multiply so the square root goes away. You can do this by multiplying the top and bottom of the equation by the bottom denominator. From here, this will make the square root go away, so your equation will be normal numbers. After you have done this, you will have the equation answered and you will be able to simplify it to find the end answer. You can do this...

How To: Graph a parabola

With this tutorial, we learn how to graph a parabola. The way you can tell it's parabola is that the 'x' value will be squared. With a line, 'y' and 'x' are not squared. The 'a' is the number in front, which will also be the coefficient in the graph. 'B' will be the number following that and 'c' will be the last number. Once you identify these, remember that they are always numbers. From here, you can draw out your graph. Follow the numbers that you just listed and then you can graph it out c...

How To: Calculate a limit at infinity with a radical

In this video, we learn how to calculate a limit at infinity with a radical. The idea is to take out the higher power of 'x' in the denominator first. If the x squared is under a radical, take that out so you're left with just 'x'. After this, divide every term by 'x'. Once you are finished with this, you can rewrite the equation. Next, you will use the rules of math to find the answer of the equation. This is hard math to do if you aren't used to it! Make sure you practice with the samples i...

How To: Use inductive reasoning

In this tutorial we learn how to use inductive reasoning. Start out with your equation that is giving you your statement. You need to prove whether this is true or not by figuring out the equation. Look at the different angles to see if they are a linear pair and then see if they are the same. Compare them to see if they add up to 180 degrees and use your mathematical logic. Once you understand the backbone to doing this type of math and what the exceptions are, then you will be able to figur...

How To: Understand the properties of real numbers

In this video, we learn how to understand the properties of real numbers. Natural numbers start at one and continue on and on. Zero is not a natural number. A whole number is just like a natural number, except it includes zero. Integers are the negatives included with whole numbers. There are no decimals included in integers. Integers also include positive numbers and no decimals with them, just whole numbers. Rational numbers are fractions and all decimals that end at a certain point. Once y...

How To: Find the arc length of a function

In this tutorial, we learn how to find the arc length of a function. All you're doing when finding arc length is finding the curve between 'a' and 'b'. Imagine this as a string you're pulling straight to see how long it is going to be. The formula says if your function is in 'y=x' you have to take one times the derivative squared. This is a basic formula that you will use to find the arc length. When you plug in your values to this equation, you will find the answer. Practice with the example...

How To: Graph a parabola

In this tutorial, we learn how to graph a parabola. Quadratic functions are parabolas. To graph these, you will first need to look at the function, which is the set of outputs for a set of inputs. Write this out on a t-chart to find what your 'x' and 'y' values are. Once you find these, you will plug in the coordinates to a graph. After you have written down the coordinates, you can graph your parabola. This is easy to do if you are familiar with quadratic functions and good at math. Just pra...

How To: Determine if lines are parallel or perpendicular

In this tutorial, we learn how to determine if lines are parallel or perpendicular. You will be given two straight line equations. First, remember that parallel lines have equal slope, identical to each other. Perpendicular lines have negative reciprocal slopes. For example, 2/3 and -3/2 would be a perpendicular line. If you think of parallel lines, then you can graph them to see what they look like when written down. Then, graph the other lines to see what they look like as well. Once you un...

How To: Complete the square

Quadratic equations are easy to solve when they can be factorized. This video teaches another method of solving a quadratic equation when its not easy to find factors for it.

How To: Subtract rational expressions

In this tutorial, we learn how to subtract rational expressions. If they have different denominators, you will first need to get them the same denominator. To do this, you will need to find the lowest common denominator. Factor the denominators that you have and figure out what the lowest common denominator of each of them are. From here, you can simplify the rational expressions in your equations. Next, you can go across the board and subtract the fractions from each other. To finish this up...

How To: Add fractions together

In this video, we learn how to add fractions together. First, try doing a simple equation like 1/2 + 1/2. From here, you will simply just add together across the board. Once you get the answer, it will be 2/4, but you must simplify this so it's lower. Check this and do the reverse to make sure it's correct. Do this for all of the fractions that come your way and you will be doing fractions more easily each time! Just make sure you simplify when you reach the end, or the answer will not be cor...

How To: Find the formula of a given sequence

In this tutorial, we learn how to find the formula of a given sequence. First, you need to decide what you're starting with. Start with a1, then continue on with a2, a3, and a4. Eventually, you will have an "An". You will have an "n" in your numerator and the denominator will start between the numbers of your fractions. Look to see if that works, then you have to see where the signs alternate on the fractions. Write in any negatives that you have, then figure your power out. Once you follow t...

How To: Identify number types

In this video, we learn how to identify number types. You will need to figure out what numbers from a list is a rational numbers in your math equations. A natural number is a counting number (1,2,3). A whole number is a natural number and zero (0,1,2,3). An integer is a whole number and a negative whole (-2,-1,0,1,2). A rational number is any number that can be expressed as a ration of integers. An irrational number is any number that's not rational and non-perfect. Once you understand these ...

How To: Determine if you have a function

In this tutorial, we learn how to determine if you have a function. You will start off with two functions and their points. The 'x' values make up the domain of the function and the 'y' values make up the range. The input values are the domain and the output are the range. If you're checking to see if you have a function, you will need one 'y' for every 'x'. This means that each value has another one that goes with it. Each of the points need to have one partner with them, no more and no less...

How To: Rationalize the denominator

In this video, we learn how to rationalize the denominator. This says that if there is a square root or any type of root, you need to get rid of them. Look at the examples given in the video to get an idea of what types of roots you will be removing and how to do it. To get rid of a square root, all you really have to do is to multiply the top and bottom by that same square root. Do this on all of your problems with a square root and they will be gone in just a matter of minutes!

How To: Multiply a number by zero in basic mathematics

With this free video math lesson, you'll learn how to do multiply any number by zero. With mathematics, as with anything else, not everyone progresses at the same rate. Basic math is no exception. Happily, in the age of Internet video tutorials, this isn't a problem. Those who progress quickly can go beyond what's being taught them and those who are struggling likewise have all the time in the world to catch up.

How To: Divide a two-digit number into a three-digit number

With this free video math lesson, you'll learn how to do long division with double and triple-digit numbers. With mathematics, as with anything else, not everyone progresses at the same rate. Basic math is no exception. Happily, in the age of Internet video tutorials, this isn't a problem. Those who progress quickly can go beyond what's being taught them and those who are struggling likewise have all the time in the world to catch up.

How To: Explore and decipher fractal geometry and self-similar mathematics

There wouldn't be any chaos in the world without Benoit Mandelbort— chaos theory, that is. Mandelbrot, who just passed away at the age of 85, pioneered fractal geometry and greatly influenced chaos theory. He spent most of his life working in physics, biology and astronomy, and is best known for his Mandelbrot Set, a mathematical set of points in the complex plane (the boundary of which forms a fractal).

How To: Interpret a standard deviation

A rough definition of standard deviation is that it is a measure of expressing the observed variations about the average in statistical data i.e. by how much do the observed values vary from the mean. This video continues from the previous solved example and demonstrates the mathematical interpretation of the standard deviation that was calculated. We begin with stating the mean and standard deviation values and then calculating the upper and lower bounds of the data based on the standard dev...