Active Math Posts
How To: Figure out a tip without a calculator
To figure out a tip without a calculator, first remove the pennies amount in the bill. For example, if your bill is $23.76 becomes $23.70. To figure out a 10% tip, move the decimal point one place to the left. So, 23.70 becomes 2.370 or $2.37. Bump up that number to $2.30 or $2.40 or $2.50 cents, depending on your preference. Since 20% equals two times 10%, double the figure you computed for 10%. So, $2.30 becomes $4.60, or $2.40 becomes $4.80 or $2.50 becomes $5.00. Using this method, you wo...
How To: Add and subtract radicals
Radicals are square roots which are not integers; the square roots of 2 or 3 are examples of radicals. The presenters show simple ways of how to add and subtract such radicals. They explain that by using the method of factoring, the addition or subtraction is made very easy. If the square root of 8, for instance, is in some addition sum, it can be factored into the square root of 4 times the square root 2. Since we know that the square root of 4 is 2 this can be simplified to be 2 times the s...
How To: Solve 3 equations with 3 variables
You can solve 3 equations having 3 variables. Here are the 3 equation examples: x+2y+z=10. 2x-y+3z=-5. 2x-3y-5z=27. The goal is to reduce to 2 equations having 2 variables. Multiply bottom equation by (-1). Rewrite 2nd and 3rd equation. 2x-y+3z=-5. Add -2x+3y+5z+-27. Equals 2y+8z=-32. Go back to original equations and multiply by (-2). Then you have -2x -4-2z=-20. plus 2x -y +3z. When you add these 2 equations, the answer is -5y +z = -25. You have now reduced the equations from 3 equations do...
How To: Graph a hyperbola
This video is one in a series of videos dealing with conic sections, in mathematics. This particular video deals with hyperbolas. The teacher, Robert Ahdoot, gives an example of a hyperbola, during which he emphasizes some key points. A hyperbola is identified by an equation containing x squared and y squared, with a minus sign between them. If x is larger, the hyperbola will open to the sides, and if y is larger it will open up and down. He creates hyperbolas, demonstrating where to make asy...
How To: Factor trinomials with the "swing method"
This is a very interesting educational video on how to find the factor trinomials using the swing method. Let us take an example and find the factor trinomials for 2xsquare-13x-45. Let us use the swing method. So now we will get 2xsquare -13x-45. You have to find the suitable factors of 90. It is 18 and 5. If you multiply 18 by 5 you will get 90. You will get (x-18over2)(x+5over2). The final answer is (x-9)(2x+5). Now we have found out the factor trinomials of 2xsquare-13x-45. This swing meth...
How To: Use math rotations in pre-Algebra
On yourteachermathhelp teaches you how to use math rotations in pre-algebra. In this example, the shaded object represents the original one, while the empty object is the new, rotated one. Here, the original object has suffered a quarter of a turn, or a 90 degree turn. You can see that the top of the shaded figure or object has been turned to the left. This is in the opposite direction in which the hands of a clock move. This translates to a 90 degree turn in the counter-clockwise direction. ...
How To: Solve a linear system with no solution
A method for solving a linear system with no solution is described. The method is described in 4 steps. The first step in the method is designed to solve a linear system that is described consist of “solving by graphing”. Details for “solving by graphing” first consist of finding points to graph using two different equations. The second step in the method consist of placing the points from both equations on the same graph in order to find out if bo...
How To: Solve rational equations easily
This video revolves around solving rational equations in Algebra 2. When you are given a rational equation, you have to find the greatest common factor and multiply all fractions to get that common factor. If a fraction already has that common factor, then no further step is necessary for that one. Next, you have to multiply all fractions by the greatest common factor to get rid of all denominators. Finally, the remaining equation is simple math and you only need to solve the equation for the...
How To: Find a percentage of a number
This video in the Education category will show you how to find a percentage of a number. For example, what is 12% of 56? The simple way to do this is to find 10% of 56; which is 5. 6. Then you find 1% of 56 is .56. Then you add 10% plus 1% plus 1%, that is, 5. 6 plus .56 plus .56; which is 6. 72. And that’s the answer. The other way to do this is to make decimal out of 12; which is .12. Now multiply .12 by 56 and the product is 6. 72. These are the two methods of finding out a percentage of a...
How To: Simplify expressions involving algebraic radicals
In this video tutorial, viewers learn how to simplify expressions involving algebraic ratios. In some ways, simplifying algebraic radicals is easier than numeric radicals. When we are working with square roots, we need to find the highest even power of a variable to act as out perfect square. When working with cube roots, we look for the highest multiple of 3 as an exponent for our perfect square. This video is very descriptive and clearly explains all the functions of the formula. This video...
How To: Understand parabolas
The instructor in this video uses humor to teach people math, which is not a favorite subject for many. The video goes on to teach the students in the video different ways to cut the conic sections into different shapes. The teacher then focuses on parabolas and defines the formulas. The formula is y = x^2. The rest of the video dissects the equation breaking it down into much more meaningful statements so that the average human being who is not very good at math can understand the equation. ...
How To: Add and subtract fractions with different denominators
This video is a simple math video showing how to add and subtract fractions using different denominators. It begins with a man explaining briefly and sitting in front of a piece of paper. He writes out a group of fractions each one with different denominators, ending in three and five. To add appropriately, on must find a common denominator, which is fifteen. So he multiplies each by five and three, raising the denominators to fifteen. This will raise the fractions to six-fifteenths and twent...
How To: Find the area of a circle when you know the diameter
In this video, it is shown how to calculate the area of a circle where the diameter is given. The formula for calculating the area of a circle is pi multiplied by square of radius. Radius is actually half of the diameter. In this video, the diameter is given as 10.6 meters. Hence, the radius will be half of 10.6 which is equal to 5.3 meters. Now, to find the area we shall multiply pi with the square of 5.3. Square of 5.3 is 28.09. If we multiply 28.09 with pi we shall get the area of the circ...
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: 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: 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: Find the volume of a sphere with radius r
Are you slightly rusty on your math skills? This video demonstrates how to find the volume of a sphere with a given radius. The first step is to sketch a solid and cross-sectional view of your sphere to get an understanding of the process to come. Next, find a formula for the area of this cross-section. Third, find the limits of integration. This will allow you to take the area of each cross-section in the sphere, not just the singular one you are viewing. Lastly, integrate this formula from ...
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: Graph a line using slope intercept form
A basis of algebra, slope intercept form can easily bring your equation to a graph with ease. This video will show you exactly how to graph equations using the slope intercept form.
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: Complete a proof involving segments
This video from Yay Math! is a geometry lesson on how to complete a proof involving segments. He draws a line segment with four points labeled A, B, C and D. The problem is as follows: Given: AC is equivalent to BD. Prove that AB is equivalent to CD. The first statement of proof is the given. Next, you need to define the congruent segments and state that they're equal in measurement. Next, break down the segments: AC=AB+BC, and BD=BC+CD. This is called segment addition postulate. The end of t...
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: 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: 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 ...