# Hot Math Posts

### How To: Solve equations with algebraic variables on both sides

In basic algebraic equations all the variables are on left side of the equation. But as the complexity of the problems increases you will find that the equations will contain variables on both sides of the equation. To solve these kinds of problems first simplify the equations on each side of the equation. You can use the distributive law to do this. Next try to cancel the variable on the right side of equation by adding the negative value of that variable to both the sides of the equation. N...

### How To: Find the surface area of an aluminum can or cylinder

This video tells us the method to find the surface area of an aluminium can or cylinder. The surface area includes the outside area of the curved portion and the aluminium top and bottom. The formula to find area is the multiple of 2, pi, r, r+h or (2)(pi)(r)(r+h). The radius of the cylinder is the radius of the circular top or bottom. In the example shown in the video, the radius is 4 inches and the height is 12 inches. Substituting the values in the formula, we get the surface area as (2)(3...

### How To: Properly read a decimal number

Decimal numbers are numbers which contain a integral part before a point and a decimal part after the point. The first step in solving decimal arithmetic is being able to understand decimal numbers. Reading a decimal number is similar to reading a whole number except for a few minor differences. In a normal number the right most digit is ones place and the place next to it is tens place and so on the value of the position increases as you move left. But a decimal number starts from a tenths p...

### How To: Simplify radicals which are not perfect squares

Need help reducing radical expressions without perfect square or cube roots? Take heart: this free math lesson will ensure that you know everything you need to know for that next big test. Examples include square roots, cube roots, and 4th roots. You'll also learn a technique to simplify n-root expressions as well as how to simplify variables in radical expressions.

### How To: Use differential equations to represent growth

This video shows the method to use differential equations to represent growth. Consider the function y=multiple of C & e raised to kx or Ce^(kx). Differentiating it with respect to x, we get dy/dx=kCe^(kx) or ky. So, the solution of the differential equation dy/dx=ky is Ce^(kx). There are two possibilities in the function y=e^(kx). It can be exponentially growth or decay function. This depends on the value of k. If k is greater than 0 or k>0, we get an exponential growth function. On the othe...

### How To: Solve math problems using proportions

Proportions or ratios are fundamental concepts of mathematics. A proportions is an equation that states that two ratios are equal. Hence proportion can be written in two ways as a:b=c:d or a/b=c/d. In these equations a and d are called as extremes and b,c are called as means. So when working with proportions we can state that product of the means is equal to the product of the extremes i.e. a*d = b*c. This is obtained by cross multiplying the second form of proportions. In mathematics you are...

### How To: Reduce a fraction by finding common factors in math

The aim of the video is to show how to reduce a fraction by factoring out prime numbers that are common to both the numerator and the denominator. The example shown in the video is 27/21. The number 27 can be achieved by multiplying 3 by 9 and the number 21 is the result of 3 multiplied by 7. The common factor, therefore in both the numerator and the denominator is 3. 3 on the top divided by 3 on the bottom is 1 and so this can be removed without affecting the value of the fraction, leaving 9...

### How To: Use cross products to solve proportions

To solve a proportion for a variable you should employ cross multiplication. The basis of cross multiplication is the property which states that the product of the numerator of one fraction and the denominator of what it is set equal to is equal to the product of the remaining denominator and numerator. For example if you have x/15=21/45 you simply need to multiply x by 45 and 15 by 21 then set them equal to each other. The result of this is 45x=315. To solve this new problem for x, divide bo...

### How To: Multiply 2 digit numbers using the grid method

This video shows the method to multiply two digit numbers using the grid method. First make a grid of three rows and three columns. Put a cross in the first row and first column or the (1,1) position. Separate the ones and the tens in the number. In our example 43 is broken into 40,3 and 56 is broken into 50,6. Put these numbers in the remaining places in the first row and first column. Now multiply every number with the other and place it in the corresponding location in the grid. In our exa...

### How To: Calculate azimuth in trigonometry

Azimuth is simply the angle of an object in the sky along the horizon. Yes, it's spherical trigonometry but it's not difficult! Check out this video and in just a few minutes you will be able to solve azimuth problems on your own.

### How To: Multiple and divide rational expressions

This video walks you through the steps of multiply and divide rational expressions. This excellent video shows you a clean board, with the instructors voice showing exactly what to do. Don't fret, any question you may have, will be answered. Watching this video will make you feel like your back in the classroom but rather comfortably from your home.

### 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: 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: 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: 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 linear absolute value equations & inequalities

In this video the instructor shows how to solve linear absolute value equations and inequalities. You need to remember basic rules to solve these kind of problems. When the absolute value is equal to a number then the real value of it is equal to either the positive value of that number or negative value of that number. In case the absolute value is less than or equal to a number, then the real value lies in between the positive and negative values of that number. In the third case, if the ab...

### How To: Determine the age of a fossil using carbon-14

If you have a fossil, you can tell how old it is by the carbon 14 dating method. This is a formula which helps you to date a fossil by its carbon. If a fossil contains 60% of its original carbon, how old is the fossil? The half life of carbon 14 is 5600 years. That means this is how long it takes for half the nuclei to decay. After 5600 years, if we start with a gram, we end up with half a gram. This rather complex formula shows you how to solve this puzzle using accepted scientific methods.

### How To: Find the area of a right triangle using simple math

It is easy to find out that right triangle is only half of the square. And again there is a rectangle with a triangle shaded in red color. The red triangle is half the area of the rectangle. But to calculate just the area of triangle, we can calculate the area of the rectangle whose area is length times width. When we have a rectangle with its length and width as 4u and 2u respectively then the area of that rectangle will be equal to 8u(squared). But we already know that the triangle is half ...

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

To write the sum or difference of logarithms as a single logarithm, you will need to learn a few rules. The rules are ln AB = ln A + ln B. This is the addition rule. The multiplication rule of logarithm states that ln A/b = ln A - ln B. The third rule of logarithms that deals with exponents states that ln (M power r) = r * ln M. Using these three rules you can simplify any expression that involves logarithms to arrive at a single logarithm. The instructor shows how to apply these rules to a f...

### 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 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: Translate a sentence into math symbols

We will be translating the sentence "twice y differs from 5 by more than two, “into a mathematical equation. The word twice generally means two times, so 2*y (because y comes next in the sentence). Differs normally means is different and a difference from something in a mathematical sentence means subtraction most of the time, thus minus five. We don't know if we’re talking about below 5 or above 5 on the number line, so we put absolute value around the equation. More than implies a greater t...

### How To: Calculate a limit by getting a common denominator

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 limi...

### How To: Add or subtract fractions with math

Learn how to add or subtract fractions with math in simple steps. First convert any story line you have into a fraction. Now you have to convert the denominators so that both the fractions have the same. To do so multiply both the numerators and denominators with the same number. Now when you have the same denominators add the numerators to get the answer. Reduce the fractions to a lower value if you wish. Try this out with some other examples.

### How To: Convert percents into fractions and decimals

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.

### How To: Find the sum of reciprocals of complex numbers

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 denom...

### How To: Find the area of an oblique triangle using formulas

In this tutorial the instructor shows how to find the area of an oblique triangle using different formulas. To find the area of an oblique triangle there are different formulae. The first formula to calculate the area of a triangle is area A = (1/2) * a * b * Sin(C), where a and b are the lengths of the two sides of the triangle and C is the value of the angle of the triangle that lies in between the two sides a, b. Now substitute these values in the given formula to find the area if you have...

### How To: Do algebraic long division

In this video, you can learn how to do algebraic long division. Take an easy example, such as 88 divided by 4. You are actually dividing 4 into 88. You take the 4 and divide it into the 80, and your answer is 20. Multiply (20 x 4) and you get 80, then subtract the 80 from 88 and you get 8. You then divide 4 into the remaining 8 and your answer is 2, giving you a final answer of 22. Try a harder problem, such as 2105 divided by 12. You are dividing 12 into 2105. The easiest way to handle this ...

### How To: Find the equation of an ellipse given a graph

Notes College Algebra teaches you how to find the equation of an ellipse given a graph. You first want to find out the center of the ellipse, which in the video is (2, -3). The major axis is parallel to the X axis. The equation is (x - h) squared/a squared plus (y - k) squared/a squared equals 1. A is the distance from the center to either of the vertices, which is 5 over here. B is the distance from the center to the top or bottom of the ellipse, which is 3. You then use these values to find...

### 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 the slope from a set of points

To find the slope of a line you must have two points and then you must plug in the two points into the slope formula. The slope formula is m= y2-y1 over x2-x1. If the slope is a fraction be sure to reduce to the lowest. Remember if a number is divided into zero it is zero, if zero is divided into the number it is undefined. A calculator can help one remember this. Horizontal lines have slopes and vertical lines do not. Drawing the lines on a graph can help you see the actual slopes and which ...

### How To: Find the x & y intercepts of rational functions

In this tutorial the instructor shows how to find the x and y intercepts of rational functions. Finding the intercepts of a rational function is similar to finding the intercepts of other normal equations. You can find the x intercept of the equation by setting the value of y to zero and solving the equation. Similarly you can solve the y intercept by setting the value of x to zero and solving the equation. Now while solving this rational function for intercepts if you face a situation where ...

### How To: Use a mean and scatter plot for Statistics

Wondering how to use a mean and scatter plot for statistics? Just follow the few simple steps as below.

### How To: Solve multi-step equations with absolute values

This educational math video describes the steps necessary to solve an equation involving absolute values. "Absolute value" refers to the magnitude of a quantity and is always expressed as a positive number. You can think of absolute value as the distance a number would be from zero if plotted on a number line. Positive 17 and negative 17 both have the same absolute value because both are 17 units from zero on a number line. Because of this, all absolute value problems have two answers, one wh...

### How To: Do multiplication

For people who are learning how to multiply, this video will show you easily how to multiply numbers with more than one decimal place. Starting with your rightmost digit on your bottom number, multiply with your top number as if you were doing a simple multiplication problem. After you have finished, place a 0 below the rightmost number of your product as a place holder and continue to multiply with your next digit in the bottom number. After you have completed this for all your numbers, you ...

### How To: Calculate the acceleration of a car on inclined plane

In this video tutorial the instructor shows how to calculate the acceleration of a car on an inclined plane. He goes on to solve a problem he came across which is based on the acceleration of a car on an inclined plane. He shows how to solve this problem by showing how to extract the data from the question and draws a diagram to get a clear understanding of the problem. Now he marks the forces acting on the vehicle and goes on to specify his axes and how to split the components of force along...

### How To: Do a rotation in Geometry

Learn how to do a rotation in geometry with this video! First step is to pout the pencil into the compass. Adjusting the pencil and compass needle is same. Suppose you want 165 degree size circle. Measure the reading with compass in protractor. Note the point and adjust the compass. After place the sharp end of the compass at the point and rotate the compass the circle will enabled. Next use protractor. We see 75 degree acute angle. Place the protractor on the line and mark the reading we wan...

### 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: Use the percentile formula in Statistics

In this tutorial the instructor explains the percentile formula. He says that the percentile formula is used to find the percentile rank of a data point in a group of data. He takes an example that consists of the lengths of puppies. Now he intends to find out the percentile rank of any puppy in the group. He shows that the formulate to compute a percentile rank of a particular puppy is rank R = 100 * (N< + (1/2)N= )/ Nt, where N< is the number of puppies whose length is less that the length ...

### How To: Graph a line in slope-intercept form

Graphing a line in slope-intercept form is easy in simple after watching this video. In this math tutorial, you'll be guided step-by-step how to graph a line from an equation in the y=mx+b format. The steps include determining the slope and the y-intercept, plotting the y-intercept on the graph, and finally applying the slope to connect the points. The video guides you through the entire process by illustrating and demonstrating all the necessary steps, thus making graphing a snap.