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Rules for Algebra

Rule 1 Addition of two Numbers with the same sign The result is the sum of the numbers with the given sign ( the sign of the two numbers ) . When we add two plus numbers we get a plus number When we add two minus numbers we get a minus number . Example 5 + 6 + 8 = 19 . Example -5 + - 8 + - 6= Ex : 3+6=9.

Ex : -5 + - 6 = - 11

- 19 .

Rule 2 : Addition of two numbers with different signs the result is the difference between the numbers with the sign of the" bigger number " . Ex 6 + - 9 = - 3 : Ex 19 + -5 = 14 . Ex Note Ex : 14 12 -15 + 13 = - 2 .

- 9 is the same as 14 + - 9 = 5 . and - 7 - 5 is really -7 + - 5 = 9 7 + 3+ 6 - 8 = - 6 - 7 - 8 + 9 + 3 + 6 = - 21 +

Example simplify - 6 + 18 = - 3 .

Note we add the minus numbers ,we add the plus numbers then tidy it up . Rule 3 : Multiplication and signs : The basic rules for multiplication and signs are as follows (Minus ) x ( Minus ) = Plus . ) = Plus . ( Minus ) x ( Plus ) = Minus , (Plus ) x (Plus

This can be expressed as follows that (a) when we multiply two numbers with the same sign we get plus ( b) when we multiply two numbers with difference signs we get a minus . Example : - 7 x - 5 = + 35 , = 84 . -7 x 5 = -35 . Example - 7. x - 4 x 3 = 28 x 3

Example : - 5 x - 6 x - 2 = 30 . x. - 2 = - 60 . Note if we are asked to multiply three or more numbers remember you can only multiply two numbers at a time . Example - 4 x -3 x 5 x -2 = 12 x 5 x - 2 = 60 . x - 2 = - 120 .

Rule 4 : Letters

Letters are often used in place of numbers , letters are often referred to as variables or unknowns . Rules 1,2,3 above apply to all calculations with letters , we have to remember one further rule which applies to letters that is we can only add things

together that are the same ie we can only add x's to x's and y's to y's etc . Note also 5a means 5 times a . Example 5a - 7a = - 2a , Example - 3x + 7x = 4x, Example 5a + 6b - 4a - 11b ,= 5a 4a + 6b - 11b = a - 5b . Multiplying letters by...

Rule 1 Addition of two Numbers with the same sign The result is the sum of the numbers with the given sign ( the sign of the two numbers ) . When we add two plus numbers we get a plus number When we add two minus numbers we get a minus number . Example 5 + 6 + 8 = 19 . Example -5 + - 8 + - 6= Ex : 3+6=9.

Ex : -5 + - 6 = - 11

- 19 .

Rule 2 : Addition of two numbers with different signs the result is the difference between the numbers with the sign of the" bigger number " . Ex 6 + - 9 = - 3 : Ex 19 + -5 = 14 . Ex Note Ex : 14 12 -15 + 13 = - 2 .

- 9 is the same as 14 + - 9 = 5 . and - 7 - 5 is really -7 + - 5 = 9 7 + 3+ 6 - 8 = - 6 - 7 - 8 + 9 + 3 + 6 = - 21 +

Example simplify - 6 + 18 = - 3 .

Note we add the minus numbers ,we add the plus numbers then tidy it up . Rule 3 : Multiplication and signs : The basic rules for multiplication and signs are as follows (Minus ) x ( Minus ) = Plus . ) = Plus . ( Minus ) x ( Plus ) = Minus , (Plus ) x (Plus

This can be expressed as follows that (a) when we multiply two numbers with the same sign we get plus ( b) when we multiply two numbers with difference signs we get a minus . Example : - 7 x - 5 = + 35 , = 84 . -7 x 5 = -35 . Example - 7. x - 4 x 3 = 28 x 3

Example : - 5 x - 6 x - 2 = 30 . x. - 2 = - 60 . Note if we are asked to multiply three or more numbers remember you can only multiply two numbers at a time . Example - 4 x -3 x 5 x -2 = 12 x 5 x - 2 = 60 . x - 2 = - 120 .

Rule 4 : Letters

Letters are often used in place of numbers , letters are often referred to as variables or unknowns . Rules 1,2,3 above apply to all calculations with letters , we have to remember one further rule which applies to letters that is we can only add things

together that are the same ie we can only add x's to x's and y's to y's etc . Note also 5a means 5 times a . Example 5a - 7a = - 2a , Example - 3x + 7x = 4x, Example 5a + 6b - 4a - 11b ,= 5a 4a + 6b - 11b = a - 5b . Multiplying letters by...

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