Hot Math How-Tos

How To: Derive the equation of a straight line

In this tutorial the instructor shows how to derive a straight line equation. He shows us a process that consists of two steps. In step one he uses the slope formula to obtain the slope of the line which is the ratio of difference of y-coordinates and difference of x-coordinates. Now in the step two he uses the slope he obtained in the first step and equates it two a another slope derivation which uses a generic x, y variables and a real point. Now solving this equation he arrives at the equa...

How To: Find the area of a triangle when given 2 sides & angle

This video shows you how to easily find the area of a triangle when you know the length of 2 sides and the angle between them. The first thing you have to do is mark the sides of the triangle by a, b, c, where a is the side between A and B, b is the side between B and C and c is the side between C and A. If you know 2 of these 3 sides an you know the angle between them you can find the area of the triangle very simple: Area= (a x b x sin c)/2, where a, b are the two sides and c is the angle b...

How To: Find a number given Its percent

This how-to video is about how to find a number when its percent is given. This video is really helpful and effective in finding the number when the percent is given, the following steps are explained in the video to find the number when its percent is given:

How To: Find a slope of a straight line with: Ax + By + C = 0

In this video the instructor shows how to find the slope of an equation which is in the form Ax + By + C = 0. He says that the formula to find the slope of a line in the above form is slope m = -A/B, where A and B are the numeric constants of the variables x and y in the given equation. He goes on and further shows how to do this with a couple of examples. He shows how to reduce any equation into the general form and how to apply the slope formula then. This video shows how to find the slope ...

How To: Divide small numbers by big numbers

This is a mathematical educational video on how to divide a small number by a larger number. You are aware that it is easy to divide a larger number by a small number. For example, if you want to divide 379 by 9 it is easy to do so. But if you have to divide 9 by 379 it is a bit difficult. You have to add a zero and see if you can divide. You need to add one more zero so that you can divide 900 by 379. But you should know that the answer would start like this 0.0 as we have added 2 zeros alre...

How To: Identify characteristics of a sample during a survey

To identify characteristics of a sample in your survey, there are many factors to consider of your samples. The first four characteristics you need to focus on are gender, age, income level, and education level. All four of these characteristics must be proportional to that of the population. You also need to consider the geographic location. Only take samples from the immediate geographical area. Finally, an important characteristic of the survey is the sample size. You do not want to ask to...

How To: Calculate the area of a triangle using a basic formula

Free Math Tutoring teaches you in this video how to calculate the area of a triangle using a basic formula. The area of a triangle is (b times h)/2. B is the base of the triangle and h is the height. This formula works for all kinds of triangles. Sometimes you won't have the height in the triangle, so you need to draw a line from one angle to the base opposite that, at a 90 degree angle. Measure that and you have your height. It might seem difficult at first, but practice helps you understand...

How To: Use ">" (greater than) and "<" (less than) symbols

In this video the author explains how to identify the less than (<) and greater than (>) symbols and when to use them. She explains to us to relate the numbers to animals stating that the smaller numbers are smaller animals and bigger numbers are bigger animals. Now she tells us to imagine that smaller animals are eaten up by the larger animals. So she shows a smaller number comes on the left side of '<' sign and bigger number comes on the right side of '<' sign stating that the bigger number...

How To: Derive the basic area of a triangle

In this video tutorial, viewers learn how to solve the area of a triangle. The formula for the area of a triangle is A = ½ x b x h or bh/2. The base of the triangle is always at the bottom; it is the side that the triangle sits on. The height is the length between the base and the highest point of the triangle. Multiply the base and height of a triangle; then divide by two or multiply by half. The measurement unit of the answer should be squared. This video will benefit those viewers who need...

How To: Simplify a quadratic formula result

In this video the tutor shows how to simplify a quadratic formula result. You can solve a quadratic equation using the quadratic formula. The first thing you have to do when given the quadratic equation is bring all the terms to one side so that you have a zero on the other side of the equals to sign. Now the formula to calculate the roots of the quadratic equation ax*x + bx + c = 0 is x = (-b + root of(b*b - 4*a*c) ) / 2 * a. The other root can be obtained by using the minus sign before the ...

How To: Find the equation of a line given 2 points

This tutorial teaches you how to find a mathematical equation of a line given 2 points that exists on the line. The tutorial starts off with 2 points labeled (2,-4) and (3,6). The first step is to determine the slope of the line using the formula given in the tutorial in blue. The slope is then solved as 'm'. Plug the slope and the points into another formula given in green. The tutorial maker provides a tip that one can use x1 and y1 or x2 and y2, however, it must be consistent. After, solve...

How To: Find and sketch the domain of a multivariable function

Looking for a primer on how to find and sketch the domain of a function z = f(x, y) in calculus? Learn how with this free video calc lesson. 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 finish your homework or study for that next big test).

How To: Prove a triangle inscribed in a circle is right angled

When a triangle is inserted in a circle in such a way that one of the side of the triangle is diameter of the circle then the triangle is right triangle. To prove this first draw the figure of a circle. Now draw a diameter to it. It can be any line passing through the center of the circle and touching the sides of it. Now making this as the side of a triangle draw two lines from the ends of the diameter to a point on the circle. Now join the center of the circle to the other vertex of the cir...

How To: Calculate probability in "at least one" problems

Calculating probablities can be used to help us make decision. PatrickJMT explains how to calculate probability in an "either A or not A" scenario. The probability of A plus the probability of not A is equal to one. Therefore, the probability of A is equal to one minus the probability of not A ; P(A)= 1 - P(not A). The probability of a major earthquake in San Francisco over a period of time is used as an example. The probablity of an earthquake of a magnitude of 7.5 or greater in San Francisc...

How To: Write a sum/difference of logarithms as a logarithm

To write the sum or difference of logarithms as a single logarithm, you will need to learn a few rules. The rules are ln AB = ln A + ln B. This is the addition rule. The multiplication rule of logarithm states that ln A/b = ln A - ln B. The third rule of logarithms that deals with exponents states that ln (M power r) = r * ln M. Using these three rules you can simplify any expression that involves logarithms to arrive at a single logarithm. The instructor shows how to apply these rules to a f...

How To: Calculate circular velocity & acceleration

In this video the tutors explain about the concepts of Circular Velocity and Acceleration. She explains the concepts using a real world small experiments. She shows that the equation to calculate circular velocity is v = (2 * Pi * r) / T, where r is the radius of the circle the object moves in, and T being its time period. Now she takes the values from the experiment and calculates the velocity of the other tutor who is the object that runs around in the circle for the experiment. She even co...

How To: Prove Rank(A) = Rank(transpose of A) in linear algebra

Learn how to prove that the rank of a matrix, A, is equal to the rank of its transpose in linear algebra. 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 finish your homework or study for that next big test).

How To: Find standard deviation

In this video tutorial, viewers learn how to calculate the standard deviation of a data set. The standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. To calculate the standard deviation, users will need to follow these steps. 1) Find the mean of the data. 2) Subtract the mean from each data point. 3) Square each of the values you got in step 2. 4) Then find the mean of the values you get from step 3. 5) Finally, square r...

How To: Write a slope-intercept equation given an X-Y table

In this tutorial the author shows how to derive a slope-intercept equation of a line given an X-Y table. He explains that the general form of slope intercept form which is y = m*x + b. Now he intends to find value of slope, i.e. m first. Now slope is change in y over change in x. He computes the slope using the X-Y values from the table. Next he substitutes a pair of x, y value in the equation to compute the value of y intercept b. Now finally substituting the values in the equation the slop-...

How To: Find a slope of a line parallel/perpendicular to it

This video tells you how to find a slope of a parallel / perpendicular to it. In the equation y = mx + c, m is the slope. To calculate the slope of a line that is parallel to another line, you have to consider the rule m1 = m2 which means slope of the first line m1 is equal to the second line m2, if both the lines are parallel. Take the equation y = 2/3x - 7.2/3 is the slope. According to the rule m1 = 2/3 and so m2 = 2/3.Now to calculate the slope of perpendicular line you have another rule ...

How To: Find how many toothpicks will be needed to form the nth figure in a sequence

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. With this installment from Internet pedagogical superstar Salman Khan's series of free math tutorials, you'll learn how to employ inductive reasoning to determine the number of toothpicks you'll require to generate the nth (e.g., the 50th) figure in a sequence of figures.

How To: Solve an equation with a radical under a radical

In this video the instructor shows how to solve an equation with a radical under a radical. If you have an equation with a square root on both sides, with one of the sides having another inner square root under the original square root, it can be a little tricky to solve it.

How To: Find the equation of a tangent line

This is the video about how to find the equation of a tangent line. As you may recall, a line which is tangent to a curve at a point a, must have the same slope as the curve. Therefore, the slope of the tangent is m = lim f(a + h) - f(a) h-->0 h Since the slope equation of the tangent line is exactly the same as the derivative definition, an easier way to find the tangent line is to differentiate using the rules on the function f. For example, Find the slope of a line tangent to the function ...

How To: Use probability to predict weather

In this video, we learn how to use probability to predict weather. Probability is the chance of something happening. If you want to know what the weather is going to be like, you can look at the weather report and see what each day is going to do throughout the week. Ask yourself what the probability is that the weather will be cloudy, judging from what the current work week weather is. First, figure out how many days there are total and then find out how many are cloudy versus how many are s...

How To: Do long division in your head

In this video, we learn how to do long division in your head. Start off by trying to do a division problem in your head that divides evenly. This will help you start to get used to doing division in your head. If you come across a problem where you have to carry a number, don't forget to remember it. If you can see a pattern in any division problem, you will be able to solve any problem that you come across. This can be used for small division problems as well as extremely long division probl...

How To: Multiply fractions with unlike denominators

With this free video math lesson, you'll learn how to multiply fractions that posess unlike denominators. 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: Do matrix algebra on a TI-83 calculator

Looking for a primer on how to solve matrix problems using a TI-83 graphing calculator? See how it's done with this free video algebra lesson. 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 finish your homework or study for that next big test).

How To: Simplify exponential expressions in basic algebra

The video shows how to solved mixed property problems using the exponent rules. See if there are any rules you can apply to the problem until you get to a point where you can't simplify anymore. The instructor shows in the example problem that the two bases are the same, but there is extras happening the numerator. The power to power multiply rule is applied removing the extra issues from the numerator. Next the quotient rules is applied as there is the exact same base to the power so we keep...

How To: Find the formula of a piecewise function given a graph

This video shows how to find the formula of a piecewise function when given a graph. The first step is to write a definition for the graph, which is done by identifying the different domains shown in the graph. The second step is writing formulas for each domain specified by the lines in the graph. The point-slope formula is used to identify the slope and y-intercept for the leftmost domain, which has a sloped line. A point and horizontal line make for simpler equations in the other pieces of...

How To: Write the equation of a circle in standard form

Here you'll be shown how to take the equation of a circle, and convert it into standard form. Also, it will be explained just what standard form is, while running through the process of conversion. You'll be able to use techniques to quickly work off the numbers on the equation, one by one, until it's simplified enough to understand. Complicated algebra functions become much simpler when you see these easy to use techniques, that will help you rearrange the equation into a form that is actual...

How To: Solve an equation by the distributive property

In this simple tutorial the tutor shows how to solve equation by the distributive property. He states that when there is a number which is multiplied to a full equation, we have to multiply each and every term of that equation by that multiplying number. This is called the distributive property as the value is distributed to each and every term inside the equation. He goes on and solves a problem based on this property to give a clear idea of the property. This video shows how to solve equati...

How To: Solve multi-step equations with absolute values

This educational math video describes the steps necessary to solve an equation involving absolute values. "Absolute value" refers to the magnitude of a quantity and is always expressed as a positive number. You can think of absolute value as the distance a number would be from zero if plotted on a number line. Positive 17 and negative 17 both have the same absolute value because both are 17 units from zero on a number line. Because of this, all absolute value problems have two answers, one wh...

How To: Figure out the domain & range of a piecewise function

Need to calculate the domain and range of a graphed piecewise function? Learn how with this free video lesson. 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 finish your homework or study for that next big test).

How To: Determine the age of a fossil using carbon-14

If you have a fossil, you can tell how old it is by the carbon 14 dating method. This is a formula which helps you to date a fossil by its carbon. If a fossil contains 60% of its original carbon, how old is the fossil? The half life of carbon 14 is 5600 years. That means this is how long it takes for half the nuclei to decay. After 5600 years, if we start with a gram, we end up with half a gram. This rather complex formula shows you how to solve this puzzle using accepted scientific methods.

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