Posts Tagged ‘denominator’
Thursday, November 12th, 2009
How to Find the Reciprocal of a Number
Description
A detailed tutorial on how to find the reciprocal of a number. Step by step tutorial including several examples of reciprocals for reference.
Overview
A reciprocal is a way of saying the opposite of a number, although it is not a true opposite. A true opposite of a negative number would be a positive number, and a true opposite of a positive number would be a negative number – that is why there are such things as opposite reciprocals. A more accurate name for a recirpocal would be the reverse of a number. In a fraction, the reciprocal of a number is when the numerator and the denominator are flipped. This also works for whole numbers, because you can think of the number as a numerator with denominator one.
Tags: accurate, arithmetic, denominator, flipped, fraction, integer, negative, number, numerator, opposite, positive, real, reciprocal, reverse, whole
Posted in Arithmetic | No Comments »
Thursday, November 12th, 2009
How to Solve Negative Exponents
Description
A detailed tutorial on how to solve negative exponents. Step by step tutorial including several examples of solving negative exponents for reference.
Overview
An exponent is a number representing how many times you multiply the base – the number the exponent is on – by itself. Which is why negative exponents are so confusing – how can you multiply something by itself a negative number of times? The easiest way to think of a negative exponent, is that if you take away the negative sign and put the base and exponent under the number 1 (like as a fraction), you are saying the same thing! A negative exponent simply needs to be moved to the denominator (or the numerator, if it is in the denominator) to make it a positive exponent. This can be tricky when there are other numbers or expressions found in the same fraction, but not impossible.
Tags: algebra, base, denominator, equation, exponents, expression, fraction, multiply, negative, numerator, positive, power
Posted in Algebra | No Comments »
Tuesday, November 10th, 2009
The Numerator and Denominator of a Fraction
Description
A detailed tutorial on the numerator and denominator of a fraction. Step by step tutorial including several examples of numerators and denominators for reference.
Overview
Fractions are well known in the world of mathematics. But when first starting out, you may ask yourself why the fraction appears like it does – split into two parts. You will see a fraction either written horizontal or vertical. In a horizontal fraction, the numerator is the number to the left, and the denominator is the number to the right. In the more common and proper vertical fraction, the numerator is on the top and the denominator is on the bottom. This works when there are whole equations in either the numerator and denominator as well, not just for simpler numbers. The numerator and the denominator should never be split, but algebra tricks can sometimes help to simplify them.
Tags: algebra, arithmetic, bar, denominator, equations, fraction, horizontal, number, numerator, parts, simplify, split, tricks, two, vertical
Posted in Arithmetic | No Comments »
Tuesday, October 6th, 2009
How to Find Oblique Asymptotes
Description
A detailed tutorial on how to find oblique asymptotes. Step by step tutorial including several examples of how to find oblique asymptotes for reference.
Overview
There are several different types of asymptotes. In this tutorial, we will be discussing oblique asymptotes. In order to find the oblique asymptotes of a function, you must first determine if the asymptote slants. If the numerator of a rational function has exactly one degree greater than the denominator, then the function slants and therefore has an oblique asymptote. When you divide the numerator and the denominator, the term or polynomial you get is the oblique asymptote.
Tags: algebra, asymptote, asymptotes, closer, curves, degree, denominator, distance, farther, function, horizontal, infinity, limit, linear, lines, Math, negative, nonlinear, numerator, oblique, origin, polynomial, positive, slant, straight, vertical, zero
Posted in Algebra | No Comments »
Tuesday, September 15th, 2009
An Introduction to Mixed Numbers and Improper Fractions
Description
A detailed tutorial on the solving of mixed numbers and improper fractions. Step by step tutorial including several examples of how to solve mixed numbers and improper fractions for reference.
Overview
A mixed number is a whole number and a fraction together that form one number. An improper fraction is a fraction that technically shouldn’t exist – such as 4/3, or any fraction where the numerator is larger than the denominator. They are really the same thing, written in a different way. Using the example from before, 4/3 is the same as 1 and 1/3. To convert a mixed number into a fraction, multiply the denominator by the whole number and add the product by the number in the numerator. To get a mixed number from an improper fraction, just do the opposite.
Tags: arithmetic, convert, denominator, fraction, improper, improper fractions, Math, mixed, mixed numbers, multiply, numerator
Posted in Arithmetic | No Comments »
Tuesday, September 15th, 2009
How to Solve Problems Using Long Division
Description
A detailed tutorial on how to solve problems using long division. Step by step tutorial including several examples of long division for reference.
Overview
Long division is the first method students learn to solve division problems. The process looks complicated but long division is much easier than any other method. Long division involves drawing a symbol that looks a lot like a square root symbol, putting the divisor on the outside (to the left) and the dividend on the inside (under the line of the symbol). The divisor should be smaller number than the dividend. Basically, you take each number of the dividend seperately and ask how many times the divisor will go into it. If the number is too small put the second number onto it (for example, if your number is 183, and 1 is too small, then you look at the number 18). Let’s say the divisor will go into the number 3 times. Write 3 on the top of the line and subtract your divisor * 3 from the number you used to find that. Sometimes the difference is 0, but usually it isn’t. Keep on adding the next number in the dividend with it until you get to the last number, at which point you must add on the remainder in a decimal point. Long division is also a way to convert fractions into decimals if changing the denominator to 100 is impossible. When you do this, the numerator becomes the dividend and the denominator becomes the divisor.
Tags: arithmetic, denominator, divide, dividend, divisor, fractions, long division, Math, numerator, quotient
Posted in Arithmetic | No Comments »
Thursday, September 10th, 2009
How to Rationalize the Denominator
Description
This video is a quick tutorial of how to rationalize the denominator in both normal expressions and binomial expressions. Many example problems are provided in this video.
Overview
Rationalizing the denominator refers to something you must do in math when you are given a fraction with a square root of a number like 2 or 3, that comes out to be a very long decimal. Instead of giving up and saying you can’t solve the problem, you can use a math trick to help you. This math trick is multiplying by one. Nothing happens to a number when you multiply it by one. 1 * n = n, and so on. But, here\’s the trick: write one as something different. The fractions 2/2 or sqrt(6)/sqrt(6) are also equal to one. You need to look at your denominator. If the number in your denominator is sqrt(5), then the number you will multiply the fraction by is sqrt(5)/sqrt(5). Follow your rules for fraction multiplication, and you will see that there is now no radical in the denominator! It is okay to have a radical in the numerator after doing this.
Tags: algebra, denominator, fractions, irrational numbers, Math, multiply, radicals, rationalize, rationalizing the denominator, square roots
Posted in Algebra | No Comments »
Tuesday, September 8th, 2009
How to Solve Subtraction Problems with Fractions
Description
This video show how to subtract fractions and mixed numbers that have different denominators. The process is clearly explained. One example problem is provided in the video.
Overview
Subtracting fractions is very similar to adding fractions. The most important part of subtracting fractions is making sure you have an LCD – Least Common Denominator. If your denominators are already the same, then that makes is much easier.
Example: (a/b) – (c/b) = (a – c) / b
The one problem with subtraction is that unlike addition, it does matter which number is bigger. If you are subtracting a smaller number from a bigger number, there is no problem. But if you are subtracting a larger number from a smaller number, you may not know what to do. However, all this does is create a negatuve number. Pretend that your numbers are flipped. Subtract the smallest number from the biggest number. That number is still your answer, but if you had to flip the numbers to get it then you need to put a negative sign in front of it.
Example: (1/2) – (5/2) = (1 – 5) / 2
1 – 5 is obviosuly a bigger number subtracted from a smaller number. Now, to flip these. 5 – 1 = 4. So, 1 – 5 = -4. The answer to our sample problem is -4/2.
Tags: algebra, arithmetic, denominator, fractions, LCD, least common denominator, Math, negative, numerator, positive, subtract, subtraction
Posted in Algebra, Arithmetic | No Comments »
Tuesday, September 8th, 2009
How to Solve Addition Problems with Fractions
Description
This video is a tutorial on how to add fractions that have different denominators. Several examples are provided in the video and all steps are laid out in an organized manner.
Overview
Adding fractions is not too complicated, but can sometimes be a bit of a problem if the fractions have different denominators. If the fractions have the same denominators then it is easy to add – you are only doing one problem.
Example: (a/b) + (c/b) = (a + c) / b
However, this method only works if you have both denominators set equal to each other. So if you are given fractions with different denominators, you must make them the same. You do this by finding the LCD – the Least Common Denominator. The LCD would be a multiple of both 4 and 6, and it is wisest to go with the lowest number you can find that fits that description. If you are working with small numbers, sometimes the best way is to simply multiply them together, and the number you get would be your LCD, and therefore the number you would use in your denominator. Now, when the numbers in the denominator change you must also change the number in the numerator. You do this by multiplication – whatever you do to the top must be done to the bottom.
Example: (1/2) + (2/3)
The LCD w0uld be 6, because 2 * 3 = 6.
(1/2) + (2/3) = [(1 * 3) / (2 * 3)] + [(2 * 2) / (3 * 2)] = (3/6) + (4/6)
Now you can solve this problem like a normal fraction addition problem.
Tags: add, addition, algebra, arithmetic, denominator, fractions, LCD, least common denominator, Math, multiply, negative, numerator, positive
Posted in Algebra, Arithmetic | No Comments »
Tuesday, September 8th, 2009
How to Solve Divison Problems with Fractions
Description
This video explains how to properly divide fractions and shows several different methods that can be used. Many example problems are scattered throughout the video and solutions are presented in an organized manner.
Overview
Dividing fractions is really no different than multiplying fractions, because division is the inverse of multiplication. While we can\’t see this when using whole numbers, it is very easy to show with fractions. When you see a divison problem with fractions, it will often look like this:
(a/b) / (c/d)
Notice how if you wrote that out on paper, that would look like one giant fraction, with a fraction in the denominator and a fraction in the numerator. Now, remember that multiplication is the inverse of division. Continuing on with our example, this is our next step:
(a/b) / (c/d) = (a/b) * (d/c)
You can see that on the second fraction, the numerator and the denominator have been swapped, and we are now multiplying instead of dividing. When you do this, you are actually multiplying the first fraction by the reciprocal of the other. Now you may solve this problem just like you would solve a multiplication problem.
Tags: algebra, arithmetic, denominator, divide, division, fractions, Math, multiplication, multiply, negative, numerator, positive
Posted in Algebra, Arithmetic | No Comments »
