Perform industry calculation

1. Perform Industry Calculation

Perform four fundamental operations

The four basic mathematical operations--addition, subtraction,

multiplication, and division--have application even in the most

advanced mathematical theories. Thus, mastering them is one of the

keys to progressing in an understanding of math and, specifically, of

algebra. Electronic calculators have made these (and other)

operations simple to perform, but these devices can also create a

dependency that makes really understanding mathematics quite

difficult. Calculators can be a handy tool for checking answers, but if

you rely too heavily on one, you may deprive yourself of the kind of

rigorous mental exercises that will help you not just to do math, but

to fully understand what you are doing.


Perform conversion of units

How to Safely Convert Between Units

We can convert from km/h (kilometers per hour) to m/s (meters per

second) like this:

A kilometer has 1000 meters, and an hour has 3600 seconds, so a kilometer

per hour is:

1000

3600 = 0.2777... m/s

How did I know to make it 1000 and not 3600 (the other way around)? The

3600 1000 do the conversions

as fractions!

Example 1:

Let's start with a simple example: convert 3 km to m (3 kilometers to

meters). There are 1000 m in 1 km, so the conversion is easy, but let's

follow a system.

The system is:

Write the conversion as a fraction that equals 1

Multiply it out (leaving all units in the answer)

Cancel any units that are both top and bottom




Perform calculations on algebraic expressions

Perform calculations on algebraic expressions

 An algebraic expression is a mathematical phrase that contains numbers and/or variables.

•Understand the difference between an algebraic expression and an algebraic equation. An algebraic expression is a mathematical phrase that can contain numbers and/or variables. It does not contain an equal sign and cannot be solved. An algebraic equation, however, can be solved, and does include a series of algebraic expressions separated by an equals sign. Here are some examples:
•Algebraic expression: 4x + 2
•Algebraic equation: 4x + 2 = 100 
•2. Know how to combine like terms. Combining like terms just means adding up (or subtracting) the terms of the same degree. This means that all x2 terms can be combined with other x2 terms, that all x3 terms can be combined with x3 terms, and that all constants, numbers that are not attached to variables, such as 8 or 5, can be added up, or combined, as well. Here's an example:
•3x2 + 5 + 4x3 - x2 + 2x3 + 9 =
•3x2 - x2 + 4x3 + 2x3 + 5 + 9 =
•2x2 + 6x3 + 14

3. Know how to factor a number. If you're working with an algebraic equation, which means there is an expression on either side of an equals sign, then you can simplify it by factoring out a common term. Look at the coefficients of all of the terms (the numbers before the variables, or the constants) and see if there is a number that you can "factor out" by dividing each term by that number. If you can do this, then you have simplified the equation and are on your way to solving it. Here's how:

•3x + 15 = 9x + 30

You can see that each coefficient can be divisible by 3. Just "factor out" the number 3 by dividing each term by 3 to get your simplified equation.

•3x/3 + 15/3 = 9x/3 + 30/3 =
•x + 5 = 3x + 10

4. Know the order of operations. The order of operations, also known by the acronym PEMDAS, explains the order in which you should perform different mathematical operations. The order is: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Here's an example of how the order of operations works:

• (3 + 5)2 x 10 + 4
•First, follow P, the operation in the parentheses:
•= (8)2 x 10 + 4
•Then, follow E, the operation of the exponent:
•= 64 x 10 + 4
•Next, do multiplication:
•= 640 + 4
•And last, do addition:
•= 644

5. Learn how to isolate a variable. If you're solving an algebraic equation, then your goal is to get the variable, often known as x, on one side of the equation, while placing the constant terms on the other side of the equation. You can isolate x by division, multiplication, addition, subtraction, finding the square root, or other operations. Once you've isolated x, you can solve for it. Here's how:

•5x + 15 = 65 =
•5x/5 + 15/5 = 65/5 =
•x + 3 = 13 =
•x = 10


How to Find the Percentage for a Ratio

Ratios are often expressed in the form m:n or m/n. To convert a ratio
into the form of a percentage, simply divide m by n and then multiply
the result by 100.

For example, If the ratio is 12:4, convert it to the form 12/4, which is an
equation we can solve. After that multiply the result by 100 to get the
percentage.

12 ÷ 4 = 3
3 × 100 = 300%

A proportion is simply a statement that two ratios are equal. It can be
written in two ways: as two equal fractions a/b = c/d; or using a colon,
a:b = c:d. The following proportion is read as "twenty is to twenty-five
as four is to five."