Math: Page 22

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 is...

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 simple...

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. The...

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...

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 slope...

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...

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...

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...

In order to solve a quadratic equation by completing the square, take a quadratic equation and make sure that the coefficient of the first squared term in one. If it is not factor it by pulling the term out to get it to one. Now just write down the first two terms in side a bracket and after it add the third term. Now take the coefficient of the x term and take one half of it and square it and put that number back into the bracket. Now as you added a new number, to cancel it out subtract it...

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 or...

To simplify a complex fraction, turn it into one fraction on the top divided into a fraction on the bottom. Once this is complete, you will turn the division into the two into a multiple by the reciprocal, factor, and then cancel. To make a division, find the lowest common denominator of both the top and the bottom. Once you get this division equation, look carefully at the equations. If something can be easily canceled, go ahead and cancel it out at this time. If you cannot cancel anything at...

This videos explains how one can easily find the parallel line to a given mathematical equation. He starts by explaining what it means for two lines to be parallel mathematically speaking. Defining two lines, then comparing the slope of both lines you can mathematically determine that they are in fact parallel. He then moves to common math problems found on tests where you are given a point and a linear equation. He then forms a T-table with one column being line one and line two and...

This clip shows how you can draw a hypercube, which is a complex shape composed of cubes. You start with a series of equally spaced horizontal lines. Then you draw a vertical line from the origin (o, o, o). From the same point, you draw a horizontal line of the same length and two more lines at 45 degrees and 135 degrees from the horizontal. The vertical line and the 45 degree line form two of the vertices of one of the cubes. The vertical line and the 135 degree line form two of the vertices...

Need to figure out the area of a trapezoid for a household project? Even if you just want to sound smart, there is a simple formula that can be used every time you need to find the area of a trapezoid. Try the formula and see how good you are at geometry.

This video shows us how to draw a linear equation using the slope and intercept technique. First, the narrator explains how to simplify the equation in order to get the slope and intercept out. He then shows how the coefficient of x equals the slope and the constant term tells us the y position of the intercept point. The technique for drawing the final line is plotting the intercept at the right height on the y axis, then running for some distance along the x axis and rising some amount. This...

This video shows the method to add rational expressions with different denominators. The first step in this process involves finding the LCD. After this is done, the numerator and denominator are multiplied by a specific number so that the fractions are rewritten with common denominators. In the second step the numerators are added or subtracted according to the problem with LCD in the denominator. Simplify the numerator by adding or subtracting like terms. After this, we get a rational...

In this video you learn how to understand the basics of matrices. The video includes how to do matrices with addition, subtraction and multiplication. The teacher explains in this exercise that you will need to know the number of rows and columns. He breaks down all of the steps required to solve these problems. Not only does he show how to understand the basics of matrices, but he does it dressed up like a king and with a little reggae music. You can hear the class's reactions to his jokes in...

In this video, the instructor shows how to find the equation of a circle given its center point and a tangent line to it. To do this, take a graph and plot the given point and the tangent on that graph. Now, from the center of the circle, measure the perpendicular distance to the tangent line. This gives us the radius of the circle. Using the center point and the radius, you can find the equation of the circle using the general circle formula (x-h)*(x-h) + (y-k)*(y-k) = r*r, where (h,k) is the...

This video shows the method to change a word problem into algebra and to identify rational numbers among a group of numbers. In the first part of the video we take a word problem namely - The product of 9 and seven, less than a number. 9 multiplied by something can be expressed as 9(). The unknown number can be expressed as 'x'. Seven less than a number can be expressed as x - 7, so that the final equation becomes 9(x - 7). In the second part we are given a list of numbers. A rational number...

This video will demonstrate exactly how to shift a graph on a x,y axis. When shifting a graph on the x axis you will need to replace x with x-h; where h is the variable to shift the graph. No matter how far you need to shift a graph, h is always the number of units you are shifting; shifting up or right is represented as a positive and down or left is negative. Just plug in your units into your equation and you will have your shifted graph.

This is video on mathematics. It specifically deals with geometry. The video describes how to determine where the y-intersects are when a point and distance to the y-intersect are given. The author starts out by giving an example ordered pair. The speaker next shows an example of how to solve such a problem. The speaker uses the distance formula along with the given distance and x-coordinate in order to solve for the y-intersect values in question. Most of the video entails solving this...

This is a video tutorial on how to simplify square roots. To simplify square roots, one must have the knowledge of splitting numbers into prime factors. For example,12 can be split into 4*3 and further more into 2*2*3. Here we see that all the factors are prime numbers. So the square root of 12 can be written as 2*square root of 3(as shown in the video). The method used in the video is applicable for simplifying any square roots as any number can be split into prime factors. Follow the video...

In this tutorial you are shown exactly how to do algebraic long division when terms are missing in the polynomial. Follow these steps and you can divide whatever you'd like:

In this video the instructor shows how to divide rational expressions. To divide rational expressions follow this simple four step approach. In the fist step change the division to multiplication by flipping the second fraction. Now the original division simplifies to multiplication. In the second step factor the terms of numerators and denominators in the two fractions. In the third step cancel the common terms in the numerator and the denominator. Now finally in the fourth step multiply all...

This video explores how to get the limit by getting a common denominator. When you try and plug in a limit, for example when the denominator goes to zero, you can get yourself into a situation where you get the answer (0/0) which is mathematically irrelevant. To solve this problem, you must find a common denominator and split the problem up into its various parts. By setting common denominators in the numerator, you can then flip the fraction around allowing you to properly calculate the...

Despite what we all argued in school, math does come up in daily life. When those dreaded fractions are staring you in the face remember these steps and you will be multiplying in no time. Practice always helps.

In this video the instructor shows how to graph a piecewise defined function. A piecewise defined function is a function that is defined in separate pieces. In these kind of functions, for different ranges of the value of x, you are given different small functions, all of which together make the whole function. This means your equation of the function is given in the form of smaller functions. Now to graph these kind of equations all you have to do is graph the individual equations in the same...

A pyramid is a three dimensional version of the triangle. In this video, learn how to find the volume of a pyramid. Finding volume is the next step after you learn how to find 2D area. Check out this tutorial and soon you will be tackling 3D objects just as easily as you learned their 2D cousins.

This video teaches how to convert a value in Celsius to Fahrenheit in simple steps. First take a paper and marker and keep in mind a Celsius value (e.g-32) to convert into Fahrenheit. Now use the formula to convert Celsius to Fahrenheit which is F=1.8(32)+32. Use a calculator to calculate the formula and you will get the result as 89.6 Fahrenheit. Now round it off the and your final result will be 90 degree Fahrenheit.

This video shows us how to multiply mixed numbers with the whole numbers. First thing you need to do is to change the mixed number into an improper fraction by multiplying the denominator with the whole number and add the resulting number with the numerator. The resulting number will be placed as a numerator with the denominator being the same. Next, is that we can't multiply a fraction with a whole number. So we need to change the whole number into a fraction and this is done by putting the...

This video demonstrates how to solve a linear function with rational coefficients by multiplying by the reciprocal of the coefficient. The reciprocal is just a fancy way of saying the numerator and denominator are swapped. Two sample problems are solved using this method. Multiplying each side of the equation by the reciprocal of the rational coefficient of the variable 'x' is an allowed operation, but only because both sides are multiplies by the the same amount. The teacher then demonstrates...

To do this, there are many ways to approach this problem. One way is to look at the change in Y over the change in X by looking at the points on the graph. Another way is to use the equation Y2-Y1 over the equation X2-X1. In other equations where you are given a graph, you may be asked if the slope is positive, negative, or zero. To determine this, look at the line in the context of moving from left to right along the graph. If the line graphed is going down as you move from left to right, the...

The video describes the basic process of multiplying two rational expressions. The problem illustrated in this video involved multiplying rational expressions of monomial terms with integer coefficients. As with the other example problems, we follow the steps of: factoring, canceling, and multiplying. Because these terms are monomials, no factoring is required (but we still state it as a step for similarity to solving other problems). We then find the greatest common divisor for both terms to...

Use a simple mathematical formula to find the circumference of a circle. The circumference of a circle can be determined by using the formula 2 times pi times the circle's radius. Pi is equal to 3.14. If a circle's radius is 10 centimeters, first multiply pi times 2. Pi, or 3.14, times 2 is 6.28. The next step then is to multiply 6.28 times the circle's radius. Since the circle's radius is 10 centimeters, multiply it by 6.28. This gives you 60.28. 60.28 inches, then, is the circumference of the...

NotesCollegeAlgebra teaches you how to find intercepts on a calculator TI-83. You start with y plus 1.7 equals .8 times x squared plus 1.4 times x. First you subtract 1.7 from both sides, you get y alone on one side. The window should be set to -5...5, -5...5. X scale should be at 1, y scale at 1 and x rez at 1. Make a graph for it, like a parabola. Use trace to get y intercept at negative 1.7. The x intercept is about .85. Continue to use the calculator to get all the values that you need.

In this video the tutor shows how to compare exponential expressions and judge if they are equivalent. He shows how to do this using examples to simply exponential expressions. Now after simplifying the numerator and denominator separately he reduces the fraction to arrive at a simple value. Now using this simple values we can compare them and judge if both their values are equivalent. This video gives a good introduction on how to simplify the exponential expression and how to compare them...

This video shows you how to convert percents to fractions and decimals To convert percent to decimal or fraction it is important that we know the meaning of percent which is per 100. So to convert a percent to fraction is simply to put in over 100 and simplify. Now to convert percent to decimal is to move the decimal point two spots to the left. if you don't see a decimal point, it is understood that is behind the last digit of the number.

In this video, the narrator presents the viewer with a quick, painless way of simplifying cube roots. The narrator presents many methods to simplify square roots to appeal to different learning styles. By doing things like dividing the power by the root to figure out the power of a number x, the viewer is better able to tackle square-rooting numbers that may not have friendly roots. The video gets more complex as it goes on, eventually teaching the viewer to split the inside of a root up if the...

The gentleman, acting as the Instructor, starts the session immediately by suggesting that to teach early multiplication all parents should practice a method of "Count-by's" with their children when they are very young using ones to ten, twos to twenty, threes to thirty, fours to forty, and so forth. The Instructor then demonstrates this method of counting by tens using a grid behind him on a chalkboard which depicts columns of ten elements. He counts each column from 10 to 100, and then writes...

In this tutorial the instructor shows how to calculate the sum of reciprocals of complex numbers. If you have to find out the sum of the reciprocals of two complex numbers first you will have to find out the least common multiple of the denominators. To do this multiply the numerator and denominator of the first fraction by the second complex number. Similarly multiply the numerator and denominator of the second fraction by the first complex number. Now you will have two fractions whose...