Posts Tagged ‘operations’
Thursday, November 5th, 2009
Linear Subspaces Explained
Description
A detailed tutorial on linear subspaces and how to identify linear subspaces. Step by step tutorial including several examples of linear subspaces for reference.
Overview
A linear subspace is usually referred to as simply a subspace, when it needs to be distinguished from other types of subspaces. Linear subspaces are also sometimes referred to as vector subspaces. In mathematical terms, to identify a linear subspace, we say that K is a field (or a set, like of real numbers), and V is a vector space over K. Elements of V are vectors and elements of K are scalars. W is said to be a subset of V. If W is a vector space itself, with the same vector space operations as V, then it has a subspace of V.
Tags: algebra, element, field, k, linear, number, operations, real, scalar, set, space, subset, subspace, v, vector, W
Posted in Algebra | No Comments »
Tuesday, October 20th, 2009
Families of Sets in Set Theory
Description
A detailed tutorial on families of sets. Step by step tutorial including several examples of families or collections of sets for reference.
Overview
Families of sets are closely linked with indexed sets – the only sets that can be indexed are families of sets. A family of sets is basically a set of sets. An example would be a power set (the set of all subsets of a set). Unions and intersections can also be performed with families of sets. Instead of concerning just two sets, they concern every single set in the family of sets. The union and intersection over a family of sets are known as extended set operations.
Tags: collections, discrete math, elements, extended, families, index, indexed, intersection, operations, power set, set, set theory, subset, union
Posted in Discrete Math | No Comments »
Tuesday, September 15th, 2009
How to Dividing Decimals
Description
A detailed tutorial on how to divide decimals. Step by step tutorial including several examples of dividing decimals for reference. It is a requirement to know how to divide decimals for all math classes.
Overview
Decimals are really no different from regular numbers when you perform operations on them, but sometimes the numbers in the decimal places can be a little tricky to figure out. The operation we will be talking about is division. With division, you set it up just like any long division problem. Move the decimal over to the right on the divisor so that there is no decimal, and then you must move the decimal point over exactly that many spaces on the dividend. Then solve it just like you would any other division problem, and don’t forget about the decimal point.
Tags: arithmetic, decimal points, decimals, divide, division, Math, operations, point, quotient
Posted in Arithmetic | No Comments »
Tuesday, September 15th, 2009
How to Multiply Decimals
Description
A detailed tutorial on how to multiply decimals. Step by step tutorial including several examples of multiplying decimals for reference. It is a requirement to know how to multiply decimals for all math classes.
Overview
Decimals are really no different from regular numbers when you perform operations on them, but sometimes the numbers in the decimal places can be a little tricky to figure out. The operation we will be talking about is multiplication. Normally, when performing an operation on decimals, you match up the decimal points. However, in multiplication you pretend that the decimal points don’t exist. You multiply as you normally would. However, you do need a decimal point in your final answer. You you need to perform a second operation. Count how many decimal places are in your first decimal, and then count how many there are in your second decimal. Add them together. When you get your final answer, count that many numbers (starting from the right) and then put down your decimal point that many places over.
Tags: arithmetic, decimal points, decimals, Math, multiplication, multiply, operations, point, product
Posted in Arithmetic | No Comments »
Tuesday, September 15th, 2009
How to Subtract Decimals
Description
A detailed tutorial on how to subtract decimals. Step by step tutorial including several examples of subtracting decimals for reference. It is a requirement to know how to subtract decimals for all math classes.
Overview
Decimals are really no different from regular numbers when you perform operations on them, but sometimes the numbers in the decimal places can be a little tricky to figure out. The operation we will be talking about is subtraction. The most important thing to remember when doing anything with decimals is to match up the decimal points and add zeros onto the end if you need to. Then just subtract like you normally would, and remember to put your decimal point back in the right place.
Tags: arithmetic, decimal points, decimals, difference, Math, operations, point, subtract, subtraction
Posted in Arithmetic | No Comments »
Tuesday, September 15th, 2009
How to Add Decimals
Description
A detailed tutorial on how to add decimals. Step by step tutorial including several examples of adding decimals for reference. It is a requirement to know how to add decimals for all math classes.
Overview
Decimals are really no different from regular numbers when you perform operations on them, but sometimes the numbers in the decimal places can be tricky to figure out. The operation we will be talking about is addition. The most important thing to remember when doing anything with decimals is to match up the decimal points and add zeros on the end if you need to. Then just add like you normally would, and remember to put your decimal point back in the right place.
Tags: add, addition, arithmetic, decimal points, decimals, Math, operations, point, sum
Posted in Arithmetic | No Comments »
Thursday, September 10th, 2009
How to Perform Operations of Functions
Description
Step-by-step video tutorial on how to solve various operations of functions. Several example problems are provided. Knowledge of functions and operations of functions are required for grade-school algebra.
Overview
I’m sure you are familiar with the normal form of a function – f(x) = (equation or number). If you have a second one, it will be expressed as g(x) = (equation or number). But what happens if you are told to combine the functions through an operation? You follow these basic patterns:
(f + g)(x) = f(x) + g(x)
(f – g)(x) = f(x) – g(x)
(f * g)(x) = f(x) * g(x)
(f / g)(x) = f(x) / g(x)
These are all very basic, and very easy to solve. There is one other pattern, which can seem rather confusing. This pattern is (f o g)(x) = f[g(x)]. The circle means “of”, so you would read that to be “f of g of x”. This means that for every x you see in the f function, you replace it with the entire g function.
Tags: addition, arithmetic, division, functions, Math, multiplication, operations, operations of functions, subtraction
Posted in Algebra, Arithmetic | No Comments »
