Math How-Tos
How To: Graph linear inequalities
In this video the instructor shows how to graph linear inequalities. A linear in a equation is almost similar to a linear equation except for the sign in the equation. Now treat the in equation as a linear equation and graph the line. So substitute the lesser than or greater than symbol in the liner in equation with the equals to sign and graph the equation. Find the slope of the equation and identify the points that the line passes through. Now take a point on the either side of the pointed ...
How To: Solve percent equations
In this tutorial the instructor shows how to solve percent equations. The general form of a percent equations is that a is b% of c. As there can be three kinds of variables a, b, c, the questions involving percent equations can be of three types having one of the three variables unknown. These kind of percent statements can be solved easily by setting up an equation. So, to convert percent statement into a equation replace the unknown term with n, the 'is' term with equals sign and the '%' si...
How To: Factor the GCF and difference of squares
In this video the instructor shows how to factor the GCF and difference of squares. When you are asked to factorize a number or monomial or a polynomial, the way to do is break it down into individual terms. When asked to factorize a binomial, try to pull out any common terms and factorize the simplified equation. When you are asked to factorize the difference of squares use the general formula which states that the factors of (a*a - b*b) is (a-b) * (a+b). Now substitute the given values in t...
How To: Use the distance formula
YAYMATH. This video is a demonstration of usage of the distance formula to find the distance between two given (x,y) points. In this video, the tutor guy who is teaching the distance formula to his students takes an example of two (x,y) points such as (5,-1) and (11,7). He then writes the distance formula on the board. The formula goes like this, the distance between two points, denoted by 'd' is equal to the square root of the sum of the square of (x2-x1) and the square of (y2-y1) where (5,-...
How To: Understand why you cannot divide by zero
This video discusses the number zero in division. When dividing numbers, there are ways to check your math, like multiplying the two numbers. When you multiply zero with any other number, it still is zero. The video goes on to discuss indeterminate answers. If you were to divide a zero by a zero, your calculator would come up with an error message. But there are real results to these odd equations and they are indeterminate. The indeterminate doesn’t really show up in everyday living, but in ...
How To: Solve rational equations
In this video the instructor shows how to solve rational equations. If you have fractions in your equation, then you need to factorize the denominators first. Now compute the least common denominator of all the denominators of the fraction. Next multiply both sides of the equation with the least common denominator. This cancels out all the denominators of all the fractions and you are left with a linear equation. Now simply multiply the remaining terms in the numerator and add common terms to...
How To: Do long division with decimals
Video Nerd thinks that when your doing long division with decimals you should first take out the decimal. Write the number as if it didn't have a decimal. For example if the problem was 12.5 divided by 5 then you will just use 125 and divide that by 5. Next divide the first digit of the dividend by the divisor an write the number up top. Next you multiply, after your done multiplying the numbers subtract, and when your done subtracting the numbers drop the reaming numbers in the dividend down...
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: Find circumference and area of a circle
In this video tutorial, viewers learn how to solve for the circumference and area of a circle. The circumference is the distance around a closed curve. The formula for circumference is C= pi x d. The diameter is two times the radius (d= 2r or r= d/2). The value of pi is approximately 3.14. The formula for the area of a circle is A= Pi x r^2. This video provides examples and demonstrations on how to use and solve with both the formulas. This video will benefit those viewers who are struggling ...
How To: Use line segments in pre-Algebra
This video shows the way to name a line segment. A line segment begins and ends with an end point. We can name a line segment by naming the two end points of the line segment. The example shown in the video shows a line segment that ends with points named 'A' and 'C'. So, we can name this line segment as segment 'AC'. This can also be named as segment 'CA'. The example shown consists of a point 'B' in between 'A' or 'B'. We cannot name the line segment as segment 'AB' or 'BA' and segment 'BC'...
How To: Graph square root functions & inequalities
On Yay Math, Robert Ahdoot, founder of Yay Math, will show you some square root functions and some inequalities. He begins with the problem y=x². Then he makes a sketch with two intersecting lines in a t shape. The problem is illustrated by a curved U shape, the U's bottom resting on the horizontal bar, which represents x, while the center takes the vertical line. The vertical bar represents y. This U is directed up because the x² is a positive number. If the number were negative, the U would...
How To: Graph half an ellipse
If you are given an equation of ellipse in the form of a function whose value is a square root, you may need to simplify it to make it look like the equation of an ellipse. Now equate the function to a variable y and perform squaring on both sides to remove the radical. Now simplify the equation and get it in the form of (x*x)/(a*a) + (y*y)/(b*b) = 1 which is the general form of an ellipse. Now you will have the x and y intercepts which are a and b respectively. Using this values graph the eq...
How To: Change Fahrenheit to Celsius
This video is a tutorial on how to convert Celsius to Fahrenheit. The title of the film says it will teach you how to convert Fahrenheit to Celsius, but it does not. It does just the opposite. The video begins by comparing Fahrenheit and Celsius. He points out that Fahrenheit measures water to freeze at 32 and water to boil at 212. Celsius measures water to freeze at 0 and water to boil at 100. To convert Celsius to Fahrenheit, multiply the Celsius temperature by 1.8 and add 32. Many countrie...
How To: Sketch the graph of a piecewise function
This video teaches us to draw the graph of a piecewise function. This is shown using two examples. In the first example we have 'y' equal to 'x + 2' for x less than zero and '1 - x' for x greater than equal to zero. We plot two points on the function for x less than zero and do the same for the function with x greater than equal to zero. The graph for the first function is erased for x greater than equal to zero, and the same is done for the second function for x less than zero. Note that the...
How To: Find the distance between 2 points w/ distance formula
Algebra – The Distance Formula.
How To: Find the order of operations with fractions & decimals
In this video, the instructor shows how to find the order of operations with fractions and decimals. If you have an equation with both fractions and decimals, you can convert the decimals to fractions, or fractions to decimals to have the entire equation in either decimals or fractions. In this video, the instructor shows how to do this in either way. To convert fractions to decimals, just divide the numerator with the denominator. This method cannot be used if the decimals are repeating deci...
How To: Draw the "y=A|x-h|+k" graph
In this video, one teacher talked in detail about how to solve absolute value functions and how to translate different absolute value functions from one point in the matrix to another one horizontally and vertically. If the function is y=A|x-h|+k, generally, the diagram is symmetric based on the line of X and can be moved vertically based on k. The teacher gave several examples to explain how to illustrate the absolute value function. He started with a simple one: y=|x-h|, then continued with...
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: Divide numbers using long division
This video focuses on how to do long division. She starts by dividing 1548 by 26, going incrementally between each value. She first take 26 into the first three numbers of 1548 (154) and gets 5, then takes the remainder of 24 (154-130) and brings down the 8 to get 248. She then divides 248 by 26 to get 9 with a remainder of 14. She then goes into some detail as to how to extract the decimal from the remainder by continuing the long division and adding zeros to the end of the divisor. At the e...
How To: Graph the absolute value of a function
This video shows the method to plot the graph of the absolute value of a function. The video shows the example of the function of cube root of 'x'. The demonstrator first plots the graph of a cube root function. This is done by taking the reference point of positive one and positive eight. The graph is drawn for both negative and positive values of 'x'. After this the graph of absolute function is drawn by taking the absolute value of the cube root function. The resultant graph comes out to b...
How To: Square expressions involving radicals
Here we look at squaring expressions that involve radicals because people tend to make some common mistakes while solving such expressions. Take 5 times the square root of y quantity squared, the answer here is not 5y. Here's the reason, square means to multiply something with itself so the square of 5 root y would be 5 root y into 5 root y. So 5 x 5 is 25 and under root y into under root y equals just y so the answer will be 25y.
How To: Solve a quadratic equation
In this video the instructor shows how to solve a quadratic equation. If you have a quadratic equation with complex fractional terms and you find that a particular term is repeating then equate that term to a new variable and replace the variable in the given equation. Now try to get the equation a*x*x + b*x + c = 0, and solve for the roots of the equation which gives the values of the intermediate variable. But this variable was replaced instead of another term. So equate that term to the va...
How To: Solve radical equations easily
In this video, the instructor demonstrates how to solve radical equations and inequalities. If you have an equation that contains radicals, re-,arrange the equation so that all the radicals are on one side and the integers are on the other side. To cancel a square root from an equation, square both sides of the equation. The square of the equation cancels out the square root, thereby removing the radical. Even after squaring if you still have a radical left, treat it as a new problem and appl...
How To: Factor a number
The following are the steps to describe how-to factor a number: 1. First we go into factoring a number we first need to know the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23 etc.
How To: Apply the Pythagorean Theorem to right triangles
In this video the instructor talks about Pythagorean theorem and how to apply it to right triangles. Pythagorean theorem states that in any right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse the sum of the squares of the lengths of the legs is equation to the square of the length of the hypotenuse. That is a*a + b*b = c*c. This theorem works only for right angled triangle. So if you have the lengths of the two legs of a right triangle substitute the va...
How To: Find the equation of a line
In this video the instructor shows how to find the equation of the line given its slope and a point that lies on it. If the slope of the line is m and the point that lies on it is (x,y) then you can find the equation of the line by substituting the values in the slope-intercept form of an equation which is y = mx + b. Now substitute the values in the above equation and solve it for the value if the y-intercept y. Now you have the slope m and y intercept b. Substitute these values in the gener...
How To: Simplify rational expressions
When you need to compute the square root of a number you can do it by breaking it into perfect squares. When you can split the given number into small perfect squares you can cancel out the square root of the expression to the square of the perfect squares. You cannot always write the number inside the square root as a perfect square, but try to write this number as a product of a perfect square and another number. Now you can pull out the perfect square out of the radical and leave the remai...
How To: Find the equation of a perpendicular line
In this video the instructor shows how to find out an equation of a perpendicular line. If you need to find the equation of a line passing through the given point and perpendicular to another line, the first thing you need to do is compute the slope of the given line. Obtain the slope of the equation by writing it in the form of y = mx + b. Now the product of slopes of two perpendicular lines is negative one. So the slope of our required line will be negative inverse of the slope of given lin...
How To: Understand nth roots and operations on radicals
This video teaches us the concept of nth roots. The video starts with the square root of constants. We find the number which when multiplies by itself for two times results in the constant inside the square root. Then we find the square root of variables. Here again the same concept is used. We find the variable which when multiplied by itself for two times results in the given variable. Then we find the cube root. Here we find the number which when multiplied by itself for three times result...
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: Simplify complex fractions in math
In this tutorial the instructor shows how to simplify complex fractions. A complex fraction is the same as a normal fraction, but has a fraction problem in the numerator and a fraction problem in the denominator. The first thing to do is arrive at a simple fraction both in the numerator and the denominator. To do this take the lcm of the denominators of the fractions in the numerator and simplify it. Similarly do this in the denominator. Now both the numerator and the denominator have a simpl...
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: Interpret a graph
YouTube user NotesCollegeAlgebra teaches you how to interpret a graph. You will learn how to read it and extract information. You go to the graph to see that f(-4)=-2. f(1.5)=2, so it's positive. You then have the question: For what x-values is f(x)<0? You go to the graph and see that you come up with (-5,3). The x-int is (3,0) (4,0). The y-int is (0,4). The domain is (-5,4) and the range is (-4,4). You then have the question: how often does y=7/5 intercept the graph? The answer is 4 times. T...
How To: Solve an equation using the point slope form
In this video the instructor shows how to derive a general equation for a line in Point-Slope form. The slope of an equation is the ratio of difference of y coordinates to the difference of x coordinates. In other words, slope is the change of y up on change of x. So you have the basic slope equation m = (y2 - y1)/(x2 - x1). When you have fractions you can simplify them by multiplying the denominator to the numerator on both sides. So multiply the equation by (x2-x1) on both sides. This gives...
How To: Prove congruent triangles with SSS and SAS
This is a video tutorial on how to prove congruent triangles with SSS and SAS test. SSS means side-side-side and SAS means side-angle-side. For applying the SSS test of congruency, each side of one triangle must be congruent to the corresponding side of the other triangle. For applying the SAS test of congruency, two corresponding sides of the two triangles must be congruent as well as the angle between those two sides of each triangle must be congruent. Follow the rest of the video to unders...
How To: Convert temperature using a point slope equation
In this video the instructor shows how to convert temperature using the point slope form. In this kind of problem sometimes you are given a temperature in Fahrenheit and its equivalent in Celsius and an other temperature similarly in both Fahrenheit and Celsius. Now you are asked to find a linear equation for these pair of temperatures. To solve these kind of problems assume that the given temperatures represent the point (x, y). Now you have two points. Substitute this value in the point slo...
How To: Figure out the area and circumference of a circle
Bill, Bobbie, and Drew present information on a circle. The presentation defines the key points of a circle. The area of a circle is Pi (3.14) x radius x radius. The diameter of a circle is the line drawn from one end to another inside the circle. The radius is the center of the circle to the edge. To find Pi, one simply takes the circumference/diameter. Circumference/diameter will always equal Pi (3.14) no matter the circle’s size. The final point is “what makes a circle a circle”? It is a b...
How To: Solve problems about linear equation
In this video the instructor shows how to write a linear equation. If you need to find the equation of a line that passes through the two given points then you need to find the linear equation of that line. The first step is to find the slope of the line that passes through these points. The slope can be calculated by finding the ratio of the difference of y coordinates to the difference of the x coordinates i.e. the change in y up on the change in x. Now substitute the value of slope and any...
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: Do Celsius to Fahrenheit temperature conversion
The video teaches how to convert degrees Celsius to degrees Fahrenheit. First the boiling points of 32 degrees Fahrenheit and 100 degrees Celsius are plotted on the Y and X axis. Then a line is drawn to join them both. The value m is delta Y (boiling point minus freezing point, i.e., 212-32)/ delta X (boiling point minus freezing point, i.e., 100-0). So m works out to 180/100 or 1.8. Then the formula y=mx+b (intercept of y = 32) is used, substituting X with Celsius and y with Fahrenheit, to c...