Posts Tagged ‘fraction’
Friday, November 20th, 2009
How to Identify a Perfect Square
Description
A detailed tutorial on how to identify a perfect square. Step by step tutorial including several examples of how to identify perfect squares for reference.
Overview
A perfect square is a number that is the square of a non-negative integer – in other words, a positive whole number. The way you can identify a perfect square is that when you take the square root, you should not end up with a fraction or decimal – you should get the non-negative integer. There are many perfect squares, but most of them are large numbers, so many people do not know more than the squares of the numbers one through twelve.
Tags: arithmetic, basic, decimal, fraction, identify, integer, inverse, negative, non-negative, number, perfect, positive, root, square, squareroot, whol
Posted in Arithmetic | No Comments »
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 »
Friday, October 30th, 2009
How to Determine the Point of Discontinuity
Description
A detailed tutorial on determining the point of discontinuity. Step by step tutorial including several examples of how to determine the point of discontinuity for reference.
Overview
A point of discontinuity is where the graph of a function is discontinuous – this means the graph has a breaking point in it, it break off for a while and starts again somewhere else, or there is a small open circle somewhere on the graph, which would be an actual point of discontinuity. In mathematical terms, the point of discontinuity is the point at which the graph of the function is undefined. Simply look a value of x that will make the function undefined, and that is your point of discontinuity. This is easiest to determine when your function is a fraction.
Tags: a, algebra, break, discontinuity, discontinuous, fraction, function, graph, point, start, stop, undefined, x
Posted in Algebra | No Comments »
Tuesday, October 6th, 2009
How to Test for Convergence Using the Alternating Series Test
Description
A detailed tutorial on testing for convergence using the alternating series test. Step by step tutorial including several examples of testing for convergence using the alternating series test for reference.
Overview
The alternating series test, like all convergence and divergence tests, is fairly easy. The hardest part is figuring out if you should use the AST, or a different test. An easy way to tell is, is the equation negative? What would happen if you pulled a negative one out? Or maybe, there is already a negative one outside of the equation. If you see any fraction, function, or any equation at all with a -1 to an odd power at the front (or at the front of the numerator, in a fraction) then you should use the alternating series test for it. If the series is decreasing over time, and the limit is approaching zero, then the series is convergent. The alternating series test is normally used in conjunction with another test for convergence.
Tags: -1, alternating, AST, Calculus, converge, convergence, decreasing, diverge, divergence, fraction, function, limit, Math, negative, one, series, test, zero
Posted in Calculus | No Comments »
Friday, September 25th, 2009
How to Find the Domain & Range of a Function
Description
A detailed tutorial on finding the domain and range of a function. Step by step tutorial including several examples of how to find the domain and range of a function for reference.
Overview
Finding the domain and range is very important when given the graph of a function. The domain is the set of all possible x values of the function, and the range is the set of all possible y values of the function. When given a function, the first one you want to find is the domain. You want to figure out what is allowed for the x value. Typically, the domain ends up being the set of all real numbers, expressed a R. If the x is found in a fraction, it can be the set of all real numbers excluding 0. If the x is found in a square root, it is the set of all real positive numbers. It’s rare for there to only be a few values allowed for the domain. The next one you want to find is range. Very often, range also ends up being the set of all real numbers. But say you know that something has to come out negative, then it would only be the set of all negative numbers. Each function is a little bit different, but finding the domain and range is typically a very straightforward process.
Tags: algebra, domain, fraction, function, graph, Math, negative, positive, possible, range, real numbers, set, square root, values, x, y
Posted in Algebra | No Comments »
Tuesday, September 22nd, 2009
Definition of a Prime Number
Description
A detailed tutorial on the solving of prime numbers. Step by step tutorial including several examples of what a prime number is and the definition of a prime number for reference.
Overview
A prime number is a type of number you will hear a lot about. It is any number greater than 1 that is not divisible by anything other than itself and one. This also tells us that it must be a positive number – there are no negative numbers that are greater than 1. Also, except for one prime number, only odd numbers can be prime numbers. This is because all even numbers are divisible by 2. So the only even prime number is 2, which is only divisible by itself and 1. Examples of prime numbers are 2, 3, 5, 7, 11, and 13. You can easily check to see if a larger number is a prime number by using algebra tricks for divisibility. Remember that it must divide evenly – if you get a known fraction or decimal then it is considered to not be divisible by that number.
Tags: decimal, divisibility, even, fraction, greater than 1, Math, non-divisible, number, odd, positive, prime, prime numbers, real, whole
Posted in Arithmetic | No Comments »
Tuesday, September 15th, 2009
Finding the Slope of a Line
Description
A detailed tutorial on how to find the slope of a line. Step by step tutorial including several examples of how to find the slope of a line for reference.
Overview
Finding slope isn’t all that difficult. The slope of a line is the numerical expression of the slant of a line on a graph. The slope is represented by the letter m and is written in the format of rise over run – in other words, from point to point, how many spaces up the line goes and how many spaces over. Negative numbers are used if the slope runs either down or to the left instead of up and to the right. If the graph is already provided, the slope can be found by counting. But the correct way to find slope is to use a formula.
m = (change in y) / (change in x)
In order to use this formula, you need to have two points on the line. The change in x is the first x-coordinate minus the second x-coordinate, and the change in y is the first y-coordinate minus the second y-coordinate. The equations in the numerator and denominator are solved seperately and will form one fraction, which will be the slope.
Tags: algebra, change in x, change in y, formula, fraction, graph, graphing, line, m, Math, rise over run, slope, x-coordinate, y-coordinate
Posted in Algebra | 1 Comment »
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 »
