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Learn How To Improve Your Math Skills!

Not all of us are born with math skills, but it’s not a bad news. The good thing is that we all can learn mathematics and be good at this important subject.

Fourteen advice to studying math well

1. Always read math problems completely before beginning any calculations.

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Math is beautiful, useful and as valuable a part of our common culture as music or poetry .

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Some students who are good at math and enjoy solving math problems don't seriously consider majoring in the subject

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Friday, June 29, 2012

Identity Elements

Identity Elements

An identity element is a number which, when combined with a mathematical operation on a number, leaves that number unchanged. For example, the identity element for addition and subtraction is zero, because adding or subtracting zero to a number doesn’t change the number. And zero is also what you get when you add together a number and its opposite, like 3 and -3.

The inverse operation of addition is subtraction—when you add a number and then subtract that same number, you end up back where you started. Also, adding a number’s opposite is the same as subtracting it—for example, 4 + (-3) is the same as 4 - 3.
 

Multiplication and division are also inverse operations to each other—when you multiply by a number and then divide by the same number, you end up back where you started. Multiplication and division also have an identity element: when you multiply or divide a number by one, the number doesn’t change.

Just as the opposite of a number is the number you can add to it to get zero, the reciprocal of a number is the number you can multiply it by to get one. And finally, just as adding a number’s opposite is the same as subtracting the number, multiplying by a number’s reciprocal is the same as dividing by the number.

Order of Operations







Order of Operations:                               

Introduction

Look at and evaluate the following expression:
 2 + 4 \times 7 - 1 = ?
How many different ways can we interpret this problem, and how many different answers could someone possibly find for it?
The simplest way to evaluate the expression is simply to start at the left and work your way across:


& 2 + 4 \times 7 - 1\\
&= 6 \times 7 - 1\\
&= 42 - 1\\
&= 41
This is the answer you would get if you entered the expression into an ordinary calculator. But if you entered the expression into a scientific calculator or a graphing calculator you would probably get 29 as the answer.
In mathematics, the order in which we perform the various operations (such as adding, multiplying, etc.) is important. In the expression above, the operation of multiplication takes precedence over addition, so we evaluate it first. Let’s re-write the expression, but put the multiplication in brackets to show that it is to be evaluated first.
2 + (4 \times 7) - 1 = ?
First evaluate the brackets: 4 \times 7 = 28. Our expression becomes:
 2 + (28) - 1 = ?
When we have only addition and subtraction, we start at the left and work across:
& 2 + 28 - 1\\
&= 30 - 1\\ 
&= 29
Algebra students often use the word “PEMDAS” to help remember the order in which we evaluate the mathematical expressions: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

Order of Operations

  1. Evaluate expressions within Parentheses (also all brackets [ \ ] and braces { }) first.
  2. Evaluate all Exponents (terms such as 3^2 or x^3) next.
  3. Multiplication and Division is next - work from left to right completing both multiplication and division in the order that they appear.
  4. Finally, evaluate Addition and Subtraction - work from left to right completing both addition and subtraction in the order that they appear

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