Posts Tagged ‘fractions’
Tuesday, September 29th, 2009
Introduction to Magnitude
Description
A detailed tutorial of how to solve for magnitude. Step by step tutorial including several examples of how to solve for magnitude for reference.
Overview
The magnitude refers to size – in mathematical concepts, what is larger? What has a greater value or quantity? This is what you look for when arranging things in order of magnitude. Several different measurements are considered to be types of magnitude – examples are volume, area, and length. Things that can be ordered by magnitude are fractions, line segments, planes, solids, and angles. Magnitude is considered to be measured only in positive, not in negative – not to say that the absolute value is taken, just that negative numbers are not included.
Tags: angles, area, arithmetic, fractions, greater, length, line segments, magnitude, Math, measurement, planes, positive, solids, value, volume
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Friday, September 18th, 2009
How to Order Numeric Expressions
Description
A detailed tutorial on the ordering of numeric expressions. Step by step tutorial including several examples of how to order numeric expressions for reference.
Overview
Ordering numeric expressions is something most of you should be familiar with. When you order numbers, or numeric expressions, you either order them from the lowest number to the highest number or from the highest number to the lowest number. It’s not difficult if you know how to count. But what if you’re faced with an array of decimals, percents, mixed numbers, and fractions? How do you know which number goes where? You need to convert them all to the same – decimals are the easiest when you are converting numbers so you can order them. Then after you order them, simply replace the ones you converted back to the values that were given.
Tags: arithmetic, convert, decimals, expressions, fractions, highest, lowest, Math, mixed numbers, numbers, numeric, order, ordering numeric expressions, percents
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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
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Thursday, September 10th, 2009
How to Solve a Fractional Exponent
Description
This video shows two different ways of solving fractional exponents and explains what to do if the exponents are negative as well as fractional. Several example problems are scattered throughout the video to make learning easier.
Overview
All of you are probably familiar with exponents by now, but what do you do if the exponent is a fraction? What a fractional exponent is, is a square root, cube root, or any other root function. The number in the denominator is your root function, and the number in the numerator is the power you are raising it to. For example, if you have a 3/2 power, then you have the square root of 4 to the third power. While roots, also called radical functions, can be confusing, often it is a great improvement from the fractional exponent you had previously. If for some reason you need a fractional exponent, this process also works in reverse – radical functions can be changed into exponents. Normally there is no need to do that until calculus, but it is good to know anyway.
Tags: algebra, exponents, fractional exponents, fractions, Math, negative, negative exponents, positive, radicals, roots, to the power
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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
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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
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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
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Tuesday, September 8th, 2009
How to Solve Multiplication Problems with Fractions
Description
This video explains how to multiply different kinds of fractions and shows what to do when you have a negative fraction in the equation. Many sample problems are provided in the video and instructions on how to solve are laid out in an organized manner.
Overview
Fractions are viewed as one of the most difficult subjects of math, but once you know how to solve equations with them they become less difficult. Multiplying fractions are very easy. It is always the numerators multiplied over the denominators multiplied. It follows the basic form of:
(a/b) * (c/d) = (a * c) / (b * d)
If you have a negative fraction, the same rule applies, with only a slightly different format, as the numerator is the only one of the numbers that gets affected by the negative. It doesn\’t matter what numbers you have in multiplication – this works just as easily on problems with different denominators as it does with problems with the same denominators.
Tags: algebra, arithmetic, denominator, fractions, Math, multiplication, multiply, negative, numerator, positive
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Thursday, September 3rd, 2009
How to Convert Between Fractions, Decimals, and Percents
Description
This video gives one simple example of how to convert a percent into a fraction, and then into a decimal. It covers the decimal place chart and what to do if the number in the numerator of a fraction is a multiple of 10. Easy to follow instructions are provided.
Overview
Fractions, decimals, and percents all display the same thing, just in a different way. Depending on what you are doing, it may be easier to work with one or the other. Often, decimals are converted into fractions, fractions are converted into percents, and percents are converted into either decimals or fractions. To start out with decimals, you need to know your decimal places. 1 decimal place means 10, 2 means 100, 3 means 1000. The decimal place refers to the denominator in a fraction. The numbers that are in your decimal are the numbers in the numerator. For example, 0.28 would be written as 28/100. When you have a number over 100, it can be written as a percent. Unless otherwise specified, percents are always out of 100. That means that 28/100 would be 28%. Remember, with fractions, always convert it to be something over 10, 100, or any other multiple of 10. 100 is usually best. Once you know the system of decimals, fractions, and percents, it is not difficult to convert any of them.
Tags: arthmetic, conversion, decimal place, decimal point, decimals, denominator, fractions, Math, numerator, percents
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