Hot Math How-Tos
How To: Graph a linear equation
In this video tutorial, viewers learn how to graph a linear equation. The linear equations example used in this video is y= 1/3x-3. The equation to graph a linear equation is y= mx+b. Now substitute each number into the equation. Therefore, m= 1/3 and b= -3. Begin by graphing the Y-intercept. M is the slope and b is the y-intercept. Plot the y-intercept on the -3 axis. Then move up once and to the side 3 times. This video will benefit those viewers who are struggling with this math unit and a...
How To: Graph linear equations with a table of values
The author teaches us how to graph the linear equations with tables. Given a set of linear equations in terms of "x and y", first we have to draw a table having a column each for x and y. We have to enter an arbitrary value of x in that table and substitute that value in the given equation to get the corresponding y value. Once you obtain both x and y values, the next step is to plot them in a graph. Consider an example: in the linear equation x=2y,on substituting an arbitrary value of x=2,we...
How To: Use the laws of logarithms
ProfessorElvisZap teaches you about the laws of logarithms. When x is positive, meaning 0<x. x times y equals y times x. This is the commutative property. x times (y times z) equals (x times y) times z. This is the associative property. x times 1 equals x. This is the multiplicative property. x times x to the power of -1 equals 1. This is the multiplicative inverse property. You can use these properties with addition: a+b=b+a, (a+b)+c=a+(b+c), a+0=a and a+(-a)=0. A logarithm is a homomorphism...
How To: Find a formula describing direct variation
In this video the instructor shows how to find a formula describing direct variation between two variables. Variation between two variables can be either direct variation or indirect variation. If a variable y is in direct variation with a variable x we can write the general equation between them as y = k * x. That is as x varies, y varies directly in relation to x, as a multiple of x. Now if you have the values of y and x, you can substitute them in this general equation which gives you the ...
How To: Use a protractor in geometry
Omar, Hayley, Gary, and Autumn teach us how to use a protractor. They give a bit of information from About.com on the history of protractors. They are used to measure angles. The first protractor was used to help with navigation and invented in 1801. To measure an angle, line up the base of the protractor with 1 line of the angle. The center circle should be on the vertex of the angle. Use the "swivel thing" to find what degree the other end of the angle lines up with. If there isn't one, you...
How To: Solve exponential and logarithmic equations
In this video tutorial the instructor shows how to solve exponential and logarithmic equations. Solving exponential equations can become very difficult if it involves large numbers. To solve these kinds of complex equations you need to get all the numbers to the same base number. The base number raised to some number should give you your original number. Now if you write the numbers as exponents of your base number you can directly equate the exponent part and solve for the missing variable. ...
How To: Factor trinomials
In this video, the instructor shows how to factor trinomials. An equation is a trinomial if it has three terms. If you factor a trinomial, you are left with two binomials which are the factors of the original trinomial. Multiplying them would result in the original trinomial. Now factor the last numerical term such that the sum or difference of those factors gives you the numerical coefficient of the middle term. Now split the middle term according to the factors obtained in the previous term...
How To: Understand parallel lines & transversals
This video explains the properties of parallel lines and transversals in geometry. The instructor, Robert Ahdoot, uses an analogy in which he compares lines and transversals to the streets of Manhattan, New York. Continuing with this comparison, he goes over corresponding angles of two parallel lines cut by the same transversal, also explaining when they're equal. He then shows where interior and exterior angles may be found, and then goes over whether two angels are same-side or alternate, d...
How To: Graph a linear equation in 3 different ways
In this video tutorial, viewers learn how to graph a linear equation in 3 different ways. The first way is to use the table of values. It is the slowest method but it always work. It is the most useful. The second way is to use the slope-intercept. It is more faster than the table of values and is very versatile. The third way is to use the intercept-intercept. It is the fastest and easiest method to do. This video will benefit those viewers who are learning about graphing in mathematics and ...
How To: Use probability of dependent events
In this video you will learn how to use probability of dependent events. The video starts with a small advertisement to there website http://www.yourteacher.com. Then its followed up by a math instructor taking you through a example problem to help you understand how you can begin solving problems of your own. The problem used in the example is: Andrea has 4 red socks and 8 blue socks in her drawer, she chooses one sock at random and puts it on, she then chooses another sock without looking, ...
How To: Add and subtract integers
In this video the instructor teaches how to add and subtract integers. When adding or subtracting two numbers there can be four kind of situations depending on the signs between the numbers. When you are adding two numbers which are both positive then you move forward on the number line adding the two numbers together to give the result. Similarly when adding two negative numbers together then you move left side of the number line. Go to the left by the value of first number and go further le...
How To: Get the radius and area of a circle with circumference
This video from Your Teacher is one of a range of math solutions. (which is the measurement from the center to the edge when drawn in a straight line) and also the area of the circle, is the amount of total space within its perimeter. The circumference of this circle is 20 pi. The circumference is 2 pi r. So 20 pi is 2 pi r. Which factors down to show that 10 is the radius (10=r). The area is pi r squared. As we know the radius is 10, we can work out the area - 100 pi.
How To: Multiply integers together
In this video the instructor shows how to multiply and divide integers. When multiplying or dividing two numbers if the signs of the two numbers are same then the sign of the result is a positive number. When multiplying or dividing two numbers if the signs of the two numbers are not same then the sign of the result is a negative number. So a positive number multiplied by a positive number gives a positive number. Similarly a negative number multiplied by a negative number gives a positive nu...
How To: Solve 3 different types of percent problems
In this video the instructor shows how to compute percentage problems. Percentage was first used in ancient Rome when the emperor Augusts levied a 1/100 of a tax on goods sold. To solve percentage problems you need to know how to convert between percentages and decimals. When you have a value in decimal, to convert it into percentage, shift the point two decimals to the right. To convert from percentages to decimals, shift the decimal two places to the left. For example to convert .50 to perc...
How To: Graph a quadratic function in factored form
This video deals with solving quadratic functions. It does not involve the use of the quadratic equation; rather, only factored equations are used. The speaker starts out with a factored quadratic equation. The speaker goes on to do the mathematical steps necessary to find both the x and y intercepts of the quadratic function at hand. The author then continues on with the example to find the function's minimum. Next all of the points that have been solved for are plotted and the function is s...
How To: Understand integers and the number line
User DayTeacher helps you understand integers and the number line. When numbers were conceived, man had the basic concept of small numbers. The first things you learn in a language are numbers. The weather might have had an impact on numbers, as temperatures dropped below 0. When talking about years Before Christ (BC), you could say 1000 B.C. is actually -1000. Being in debt means negative money. Two days ago is -2 days from the time we are talking about. Integers are positive whole numbers, ...
How To: Factor a trinomial
In this video the instructor shows how to factor a general quadratic polynomial. Here the first step is to identify the coefficient of the squared term. Write the reciprocal of the numerical coefficient of the squared term out side and write two separate parenthesis which are going to contain the binomials which are the factors of the original equation. The first term of both the binomials is the first term numerical coefficient times the unknown variable. Now multiply the first term numerica...
How To: Simplify complex fraction
In this video the instructor shows how to simplify a complex fraction. A complex fraction is a fraction that has fractions in both the numerator and the denominator of the original fraction. Complex fractions can look intimidating but are generally simple to solve, as shown in this video. A fraction is nothing but a division of its numerator and its denominator. So in a complex fraction basically you are dividing two fractions. Now you can turn this division into multiplication by multiplying...
How To: Solve a 3x3 linear system using Cramer's Rule
In this video the instructor shows how to solve a 3 x 3 linear system using the Cramer's rule. In this kind of problem you are given three equations in three variables x, y, z and you need to solve for the values of these equations. You can solve this using the Cramer rule which says that the value of x is Dx/D, where Dx and D are two different determinate. Now you have to figure out the determinate to get the value of variable x. The determinate D is called the foundation determinate and is ...
How To: Add consecutive odd numbers
Professor ElvisZap teaches you about adding consecutive odd numbers. You can learn this faster by drawing squares near the numbers themselves. If you are doing 2x2, draw 4 squares. They will be arranged in columns of two. For 9 you will draw 3 columns of 3. 16 are 4 columns of 4. 16 is also 1+3+5+7, which are all odd consecutive numbers. 25 are 5 columns of 5, but also 1+3+5+7+9. If you start counting 1 as the zeros odd number, then 3 as the first odd number, the nth odd number will be (2xN+1).
How To: Factor a trinomial, GCF, then unfoil
In this video the instructor shows how to factor a polynomial. A polynomial having three terms is called as trinomial. Now if you factor it you will obtain two binomials whose product will be the original polynomial. Before factoring a polynomial you need to find out if the polynomial has a GCF. Look out for the common variables in all the three terms and pull them out which is the GCF of the polynomial. This simplifies the original equation to a polynomial which is of lower degree. Now facto...
How To: Solve quadratic equations by factoring
This is a great educational video on how to solve quadratic equations by factoring. Let us take an example and try to learn the method. Here is a quadratic equation: (r+7) (r-9) = 0. Consider zero-factor property. For real a and b, if a.b = 0, then a = 0 or b = 0 or both are equal to zero. So r+7 = 0 or r-9 = 0 > r = -7 or r = 9. Hence, r = -7, 9. Similarly to solve a quadratic equation (13r+7) (6r-18) = 0, we will get 13r = -7 or r = -7 over 13. Also 6r = 18 or r = 3. So r= -7over 13, 3. Thi...
How To: Fill a cone
This is a very interesting instructional video on how to fill a cone. Pour oil into a cone of diameter 30 inches and depth 40 inches. Now find the volume of the oil as a function of its depth. Volume = 1 over 3 phi rsquare h. We don't know the height and depth of the oil poured into the cube. Draw similar right angled triangles. In one right angled triangle the height is 40 inches and in the other triangle it is h. Similarly the height is 40 inches and h respectively. Now rover h =15 over 40....
How To: Stretch, shift & reflect the graph of a square root
Professor ElvisZap teaches you how to stretch shift and reflect the graph of a square root. A square root function is the opposite of a squared function. You start with y=square root of (x-1) it becomes 0<=x-1. then 1 <=x. You use the graph and solve it as you would for any function using small values first, then you have y=square root of x - 1, the domain 0<=x. This shifted the graph down 1 unit. 0=square root of x - 1, 1=square root of x, 1=x. Then the range is [-1 + infinity). Continue in ...
How To: Discover the area of a triangle
Before you can find the area of any geometrical figure, recall what you are finding when you solve for the area. The area is the surface of a 2-dimensional shape. When trying to find the area of a right triangle, the easiest way is to first double the triangle so that it resembles a square. This is particularly important if you don't know the length of the hypotenuse. Using the knowledge that the area of a square is the length multiplied by the height, calculate the area of the square you cre...
How To: Find the area of triangles and other geometric shapes
The video shows us how to find the area of triangles and other geometric shapes. First, before starting to find the areas, we need to know the basics of what do those shapes actually mean and we need a little bit of vocabulary to back us up. First, the parallelograms are four sided figures with two sets of sides which are parallel to each other. The rectangles and the squares qualifies the parallelograms and also the parallelograms except that they have slanted sides and the triangles are thr...
How To: Do long division with remainders
This video goes through the step by step process of doing long division with remainders. Multiple examples are used throughout the video to give the viewer a better idea of how to properly complete the difficult task. Perfect for anyone learning long division for the first time, or for anyone attempting to relearn long division after forgetting how to do the process (an all to common occurrence in a world with calculators on every cell phone).
How To: Multiply binomials with the FOIL method
Multiplying polynomials is a distributive property. If you are given with two binomials and asked to multiply them, you need to apply the distributive property and multiply the terms of binomial with the terms of second binomial. To do this first take a term of first binomial and multiply it with the second complete binomial. Now take the second term of first binomial and multiply it with the second binomial adding or subtracting it from the previous result depending on the sign between the f...
How To: Find a missing coordinate given: coordinate & equation
In this video, the instructor shows how to find an unknown coordinate given the other coordinate of that point and the equation that passes thought the point. A point is said to lie on the graph, if the point can satisfy that equation of the line. To check if a particular point satisfies an equation, all you have to do is substitute the value of the point in that equation and check if it validates the equation. Now, substitute the given point with an unknown coordinate in that equation. If th...
How To: Find the area between curves
This video shows how to find areas between curves. The basic idea is that we find the space trapped between two curves on a graph. The formula for finding this is top curve, subtract bottom curve and then integrate. The presenter shows a parabola that goes through the origin. Then he draws a line that runs through the origin. We try to find the area trapped between the two. You take your smallest x co-ordinate to the largest x co-ordinate, you take the curve on top (2x) and subtract the curve...
How To: Simplify complex fraction w/ single fraction on bottom
This is a great instructional video on education. This educational video teaches you how to simplify a complex fraction with a single fraction on bottom. Let us learn this with an example. Let us assume we have to simplify the complex fraction 5 by x-4 divided by 5-4x by 5. When you simplify this you will get 5-4x over x divided by 5-4x over 5. You will now get 5-4x over x multiplied by 5 over 5-4x. This is equal to 5 over x. This is how we have to simplify a complex fraction with a single fr...
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: Understand the Pythagorean Theorem
In this video Ken teaches you about the Pythagorean Theorem. The Pythagorean Theorem is used to find the missing length of a side of a right triangle. By watching this video, you will learn how to find any the length of any side by using a simple mathematical formula. Ken walks you through various examples changing the dimensions of the triangle you are solving as well as changing the side you are solving. Ken even includes a real world application to further your understanding of the Pythago...
How To: Multiply and divide three rational expressions
In this video, the instructor shows how to multiply and divide rational expressions. To solve a rational expression that contains many terms, solve step by step by following the order of operations. Order of operations advises one to work the parenthesis part first; so solve the equation inside the parenthesis first. If you have a fraction multiplied by another fraction, first factorize the numerator and denominator of both the fractions. Cancel out any common factors simplifying it. In case ...
How To: Simplify fourth roots
In this video the instructor shows how to find out the fourth roots of a number. The properties of fourth root says that for any positive number of a, its fourth roots are real. And for any negative value a, its fourth roots are not real. So split the number inside the fourth root as the product of two perfect squares and then cancel out the power with the fourth root giving its roots. As the fourth roots of a positive number are real, the answer you get is correct. But you cannot find out th...
How To: Find the area of a circle with pi
This video shows how to find the area of a circle using a formula. The formula for area of circle is pie multiplied by square of radius. Pie is actually an infinite number but for the sake of convenience we consider the value of pie as 3.14. So we multiply the square of radius with 3.14. Radius is the distance between the center point of the circle to any of the outside arcs. It is actually half of the diameter (diameter is the distance between two arcs of a circle). As an example here the ra...
How To: Solve quadratic equations by square root method
In this video the instructor shows how to solve quadratic equation by the square root method. The square root property of equations states that if k is positive and a*a = k, then a is equal to square root of k or -1 times the square root of k. So to solve a quadratic equation by square root property first get the equation in the form of a*a = k. Now apply the square root property explained in the previous step to get the result. The instructor now demonstrates these concepts by solving some e...
How To: Convert from cubic yards to cubic feet and inches
brettman6533 teaches you how to convert from cubic yards to cubic feet and inches. The volume of a cube is side cubed. If the side of a cube is 1 foot, then the volume would be 1 foot squared. Knowing that a foot equals 12 inches, you transform that into 1 times 12 in times 12 in times 12, which equals 1728 inches squared. If you want to convert a cubic yard, you have to remember 1 yard equals 3 feet. So now 1 yard squared is 1 times 3 feet times 3 feet times 3 feet, which is 27 feet squared....
How To: Solve equations with fractions and decimals
In this tutorial the instructor shows how to solve equations with fractions and decimals. When you have a fraction first try to simplify it by canceling out the common factors in the numerator and the denominator. If there are any decimals convert them into fractions. Now if you have a number multiplying a equation apply distributive law and simplify the equation. Now finally try to get the variables on one side and numerical terms on the other side of the equation and finally solve for the u...
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...