# Hot Math Posts

### How To: Rotate a shape about the origin 90° counter-clockwise

Davitily thinks that you can learn to rotate the images quite easily. In this video Davitily explains the process of rotating a geometrical shape about the origin. This rotation is counter-clockwise. Davitily explains the various steps involved in this process. Two steps are explained in this process. The explanation is very simple and done in a very interesting manner. This video is the perfect choice for people wanting to learn the rotation of shapes. This video is a must for people interes...

### 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 the standard error of the mean

In this video the tutor explains about the standard error of the mean. He starts explaining by drawing the diagram of a distribution and now he takes ten samples from the distribution and starts plotting them. He says that in theory if we do it infinite times then we can obtain the sampling distribution of the sampling mean. For the example he takes the number of samples as 10. Now depending on these values of n we can get different sampling distributions. Now he intends to find the mean of t...

### How To: Express inequalities using interval notation

With all the subjects offered in junior high and high school, math isn't a favorite for many. It can often times be confusing and although the results are concrete and don't require anybody to be imaginative, it can still pose a problem. In this tutorial, you'll find out how to express inequalities using interval notation. Good luck and enjoy!

### How To: Find the area of triangle using fraction measurement

This video demonstrates the way to find the area of a triangle using fraction measurements. The person presenting this video first writes the actual formula for calculating the area of the triangle. The formula is: the area of the triangle denoted by ‘A’ is equal to half of ‘b’ times ‘h’ where ‘b’ and ‘h’ are the base and height of the triangle, respectively. Now, to make it into fractions, he writes ‘b’ and ‘h’ over ‘1’. Then he asks you to calculate “what is one times ‘b’ times ‘h’” which i...

### How To: Find the determinant & area of a parallelogram

In this video, we learn how to find the determinant & area of a parallelogram. The determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix. Graph both of the equations that you are given on the vertical and horizontal axis. After you have all of the coordinates in place, you will be able to plug in the correct numbers to figure out what the answer to the equation in. This is more advanced math, so if you have not done it before, you sh...

### How To: Divide decimals

Here we are, learning how to divide decimals. So we are dividing a whole number or a fraction by a fraction. How this presenter does this is by moving the decimal two places to the right on both the top and bottom of the sum. In other words, he multiplies the two numbers by 100. So 2 becomes 200 and .25 becomes 25. So much easier to divide 200 by 25 than to divide 2 by .25. Provided you've multiplied both the top and bottom by the same amount, the result will be the same, because the relative...

### How To: Find Leg Lengths and Hypotenuse of a 45 45 90 Triangle

A 45 45 90 triangle is a special right triangle because you can use short cuts to find leg length and hypotenuse length. This video solves two problems involving leg length and hypotenuse length.

### How To: Solve angle problems in geometry

Need some help figuring out how to work with angles in geometry? Look no further. 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). With this installment from Internet pedagogical superstar Salman Khan's series of free math tutorials, you'll learn how to sol...

### How To: Draw a rectangle

In this tutorial the author shows how to draw a rectangle with given base b and height h values. First she uses a ruler to draw a horizontal base line of b cm. Now she uses a protractor and marks a 90 degree angle at one end of the line, then draws a straight line of h cm which is the height of the rectangle. Now she finishes the remaining part of the rectangle by drawing similar lines of the other sides. This video clearly explains how to draw a rectangle given the values of its base and hei...

### How To: Find the area of a rectangle

The area of a rectangle is the basis for all geometry. You will need to know how to do this in order to better understand other objects. This video tutorial will show you the formula for area of a rectangle and how to use it. Don't be confused in math class anymore.

### How To: Solve direct & inverse variation word problems

In this video the instructor teaches about direct and inverse variation. Two variables x and y are said to be in direct variation with each other if you can write them in the form y = K * x. The value of y varies directly corresponding to the value of x. Y is said to be directly proportional to x. If you have a sample value of x and y, you can substitute the values in the above equation to compute the value of the constant K. Using this formula you can always find the value of one variable x ...

### How To: Find surface area and volume of a sphere

In this how to video, you will learn how to find the volume of a sphere and surface area. Let's say you need to find the volume of a sphere with a surface area of 200 cm cubed. You will need to know the formulas for surface area and volume of a sphere. The formula for surface area is 4 pi r squared. The formula for volume is 4/3 pi r cubed. Plug in the surface area of 200 cm cubed and plug it into the formula. You should get an answer of about 3.99 cm. Now you just have to solve for the radiu...

### How To: Find the percent increase or decrease in a quantity

This video shows us the method to find the percent increase or decrease in a quantity. This can be done in 30 seconds. The formula states that the percentage increase or decrease is equal to the product of the ratio of amount (increase or decrease) and the original amount and 100. This is explained by two examples. In the first example the amount of increase of the price of groceries is found by taking the difference of the new price and the old price. This is divided by the original price an...

### How To: Solve a rational equation with no solution

This is a very interesting mathematical instructional video on how to find rational equation with no solution. How to solve the equation and check the answer. Let us take the example m over m-3 minus 4 is equal to 3 over m-3. In this equation we get m-4m+12 over m-3 is equal to 3 over m-3. When we simplify it further we get -3m +12 = 3. Or -3m = -9 and m = 3. This video teaches you very clearly how to solve a rational equation with no solution.

### How To: Find the highest common factor (or HCF) of two numbers

Need to figure out the highest common factor of two numbers? 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: Find the area of a triangle quickly and easily

Finding the area of a triangle is essential in mathematics. This video will show you how to ace that geometry test in a few simple steps. Not only will you learn how to find the area of a triangle in this video, you will learn to do so quickly and improve your test scores. Finding area is not difficult once you learn the basics.

### 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: Find if a point lies on a line in point slope form

In this tutorial, the author shows how to determine if a point lies on a given line which is in Point Slope Form. To show the method he takes a sample point order pair and an equation of a line in its point slope form. Now he substitutes the value of the x, y order pair and the equation of the line, and solves the equation on both the sides. If both sides match it means that the point lies on the given line, or else it does not lie on the current line. In this video, the instructor shows how ...

### How To: Solve word problems that require dividing fractions

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 unpack and solve word problems that require you to divide two or more fractions.

### How To: Multiply three or more fractions or mixed numbers

Want to multiply three or more fractions or mixed numbers? It's easy: Turn the mixed numbers into improper fractions. Cross cancel where you can. Multiply straight across. (simplify and reduce if you did not completely cross cancel). This free video math tutorial presents a complete walkthrough of the process. 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...

### How To: Simplify expressions involving absolute value

Need to know how to simplify expressions involving absolute values? It's an absolute cinch. 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). With this free math tutorial, you'll learn how to divide one fraction into an...

### How To: Evaluate expressions involving absolute value

Need to know how to evaluate expressions involving absolute values? It's an absolute cinch. Learn how with this free video math 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). With this free math tutorial, you'll learn how to solve problems with ab...

### How To: Graph inequalities

Learn the correct method for graphing inequalities on a number line. Inequalities are, simply, mathematical comparisons between numbers or expressions. Numbers and other expressions can be greater than, less than, and/or equal to other numbers or expressions. Typically, this is indicated in mathematics through the use of the less-than (<) and greater-than (>) signs, along with the greater-than-/less-than-or-equal-to signs. Using other special notations, which you will learn in this video, the...

### How To: Do long division without a calculator

This video shows you step by step how to do long division without the use of a calculator. The video shows viewers two different ways to solve a division problem. It first shows how to do the problem the traditional way, then it shows how to do it according to the long division process. The long division process is where you write the whole division, multiplication, and subtraction process out showing all your work. Long division is mainly used when dividing large numbers. There are three com...

### 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: Calculate percent composition for chemistry

To calculate percentage composition we will take the example CO2 it stands for Carbon-Di-Oxide. It is the composition of Carbon and Oxygen. We have one carbon and its weight is 12.01 and 2 oxygen. So, we will multiply 2 with 16.00 which is the weight of the oxygen.

### 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: Find the slope of a line given 2 points with fractions

In this video tutorial the instructor shows how to find the slope of a line given two points with fractional values. To do this first name your two points as point 1 with coordinates as x1, y1 and point 2 with coordinates x2, y2. Then substitute the values in the equation of the slope which is slope m = (y2 - y1) / (x2 - x1). Now all you have to do is simply the fraction after substituting the point values. Be careful about the signs while substituting in the formula. Now finally after solvin...

### How To: Convert between diameter and radius

To convert between diameter and radius just follow a few steps. Sometimes we aren't given the number directly so first we need to find the diameter.

### How To: Find extra points for a parabola (quadractic equation)

This is a mathematical educational video on how to find extra points for a parabola. In the first two examples there is no need for finding extra points as they have five points and have zeros of the parabola. In example 3 we need to find extra points. The equation is y=4xsquare-4x+4. You can take x= -1 and get the value for y. You will get a point now. Similarly you can substitute -2 for x in the same equation and get the value for y. Now you get another point. Now you can draw the parabola.

### How To: Find the area of a parallelogram using geometry

The video shows us how to find the area of parallelogram using geometry. Here in this video it is done by using an example where the parallelogram is given ABCD. The area of the parallelogram is base times height (bh). Here the base is given as 15 but the height is not known but it is represented by the segment BD. To find the value of h, let’s use right triangle BDC on the right side of the figure. Since base is 15 and the opposite side of the parallelogram is congruent, the hypotenuse of th...

### How To: Find the Slope Given 2 Ordered Pairs

Slope is the change in Y over the change in X. Written out, the formula looks is as follows: (y2-y1)

### How To: Write a logarithm as a sum or difference of logarithms

This video shows the method to write a logarithm as a sum or difference of logarithms. The square root of the term given is taken out as half according to the rule. Then the numerator and denominator is divided into product of factors. This is broken into the difference of numerator and denominator according to the rule. Finally, the product of factors is expressed as the sum of factors. Now we see the domain of the term. As the term is a square root of the term it should be greater than zero...

### How To: Find the area & perimeter of triangles & squares

When you are figuring the area of a square, you only need to know the height and width of the shape. Once you know the height and width, multiply them to get the area of the square. To find the perimeter of the square, add all four sides together. To find the area of a triangle, multiply together two of the sides (not the hypotenuse) and then multiply that figure by 1/2. To find the perimeter of the triangle, add all three sides together.

### How To: Find a missing side of a triangle, similar to another

In this tutorial the author shows how to find out the missing side of a triangle which is similar to an other triangle. He explains the concept of similar triangle using diagrams and by showing that similar triangles have equal corresponding angles and parallel sides. Now he labels sides of similar triangles and intends to find out the length of unknown side. Now in similar triangles, as the lengths of sides are proportionate he shows how to write a equation of proportion and solve it finding...

### 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: Factor a trinomial with negative leading coefficient

In this video the instructor shows how to factor a trinomial with negative leading coefficient. Most of the students are confused when they have to factor a trinomial with a negative leading coefficient. But there are many ways to solve these kind of problems as shown in this video. One way you can do is that take out the greatest common factor (GCF) of -1 from the equation. So pulling the -1 gives you the original trinomial with all the signs of the terms changed. Now go on and factor the ne...

### How To: Find the Volume of Composite Figures (Also Called Composite Shapes)

Composite figures are composed of several geometric shapes and are three-dimensional shapes. The first composite shape is a combination of a rectangular prism and a pyramid. To find the volume of the entire shape you find the volume of each individual shape and add them together. The second figure consists of a cylinder and a hemisphere. Check out the video below for the full lesson.

### How To: Find the 100th term in a sequence

Need to find the nth term in a given arithmetic sequence? See how it's done with this free video math lesson. Need help finding the 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). With this installment from Internet pedagogical superstar Salman Khan's seri...