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# Rule for Algebra- Understanding Why they exsist

Lubna Naseem
30-40 mins
Critical thinking, Problem Solving
Remember, Understand, Application

Explaining the three rules of signs in algebra and why they exist like thatMaking them comfortable with using signs at the end of the class and apply it in algebra
Make them understand that the operations are the core principles of arithmetic and algebra and they remain same for both. Coz in algebra numbers get replaced by variables bt the end results remain same. Students have to understand that subtle/ hidden concept abt algebra
Blackboard and chalk

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 )  .

## Situation 1:  ++ =+

When we add two  plus numbers we get a plus number

Ex   :   3+6=9.

## Situation 2:  –  – =+

When we add two minus numbers we get a minus number  but the value of the answer is more than the two additives that’s why its  Plus sign

Ex :  -5 + – 6 = – 11 .

Example 5 + 6 + 8 = 19  .   Example    -5  +  –  8   +  –  6 =   –  19 .

Rule 2Addition of two numbers with different signs  the result is the difference between the numbers with the sign of the” bigger number ” .

## Situation 3: – + = –

Ex  6 + – 9 = – 3 :  Ex  19 + -5 =  14 .  Ex   -15   + 13 = – 2 .

In the above example the answer is decreasing therefore negative sign applies.

Note  Ex :  14    – 9  is the same as 14  +  –  9  =  5 . and –  7 –  5 is really -7  + – 5 = – 12

Example simplify –  6 +   9    –   7  +  3 +   6 –  8 = –  6  – 7 – 8 + 9 + 3 + 6 = – 21 + 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 .   ( Minus )  x  ( Plus )  = Minus ,  (Plus )  x  (Plus )  =  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  ,   -7  x  5  = -35  .  Example  – 7. x  –  4  x  3 =  28  x  3 =  84 .

Brainstorming Questions: Can you tell why in the above conditions of rule 3 results are like that

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 .

You can give them sums with the above three rules for practice to be done at home link to follow: http://www.leavingcertsolutions.com/junior_cert_maths_higher_algebra.htm
Can you explain why the results are like that for Rule 3
Accurate, Complete, Methodical, Precise, Organized

this class shud be taken up before the teacher begins with algebraic expressions.