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Basic Algebra/Introduction to Basic Algebra Ideas/Solving Equations Using Properties of Mathematics

VocabularyEdit

Associative Property of Addition
Associative Property of Multiplication
Commutative Property of Addition
Addition Property of Equality
Subtraction Property of Equality

LessonEdit

It is very important to show math in the simplest way. For example,   is the same as  , but   is better because it is easier to understand. The simplest answer is usually the best.

Associative Properties mean that you can do the problem in any order, and the answer will always be the same.

Commutative Properties mean that you can change the order of numbers around, and the answers will always be the same.

Equality Properties state that if two numbers on either side of the equation are equal, and the operation processed is the same, as well having the same variables in the operations, the result will be the same for both sides of the equation. Read the section devoted to the Addition and Subtraction Properties of Equality for more information.

Associative Property of AdditionEdit

The associative property of addition shows us that when adding multiple values together, the outcome will always be the same. You can group numbers together in parenthesis, and it will still end up having the same outcome. For example,  . The order remains the same, but the grouping has changed. The result, however, is consistent.

Associative Property of MultiplicationEdit

The associative properties work for both addition and multiplication. Think of grouping   together. You end up with 9. What about  ? If we change the grouping here, the result will be the same. Try to visualize why this is. When multiplying, you're often building objects in rows and columns.

For example, a 2 inch   4 inch block will be 2 inches across, and 4 downward. If you had a block 4 inches across and 2 inches downward, it would be the same size overall. When you put objects in parenthesis, remember to do those operations first. You may end up with certain "sides" of the operation or object being larger or smaller, but the total area will always have the same outcome.

Commutative Property of AdditionEdit

The commutative property of addition shows that no matter what order numbers are in when we add them, the result will always be the same. For example,  , just how  . Even though the order in which we added has shifted, the result doesn't change, and the statements on both sides of the equal sign remain true.

Addition Property of EqualityEdit

The addition property of equality states that if two variables or numbers are equal to each other on each side of the equation, and the operation they go through is alike, the resulting sum will be the same. If for example, both   and y are 6, and you add   to each of them, that is,

if   then  

or if   then  

Subtraction Property of EqualityEdit

The subtraction property of equality states that if two variables or numbers are equal to each other on each side of the equation, and the operation they go through is alike, the resulting difference will be the same. If for example, both   and y are 6, and you subtract   from each of them, that is,

if   then  

or if   then  

Example ProblemsEdit

Find   where  .


  •  
 
Substituting 6 for y using the given y
 
By multiplying the denominator on either side simplifies it
 
Taking down the parentheses
 
Subtracting 6 on both side does not affect the property of the given formula but again simplifies it
 
To arrive at the answer


  •  
 
Again taking the hints as given,  
 
Dealing with the parentheses
 
Taking down the parentheses is the most natural next move using PEMDAS
 
Adding  
 
Adding 18 to either side
 
Taking down the parentheses
 
Divide the multiplier to either side to emerge the solution
 
And simplify to get the answer


  •  
 
Substitute  
 
Parentheses
 
Multiply by the denominator (x) on either side
 
Divide the multiplier on either side
  or  
Simplify or divide fraction

Practice GamesEdit

Practice ProblemsEdit

Answer should be correct to two decimals - round up or down accordingly until the answer is correct to two decimals

Find   where  

1

 

Answer:

2

 

Answer:

3

 

Answer:

4

 

Answer:

5

 

Answer:

6

 

Answer:

7

 

Answer:


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