ALGEBRA:

Whole numbers and Integers:

1. Zero is neither Positive nor Negative number. It’s neutral
2. Whole number starts from 0, 1, 2, 3 (Positive Numbers)
3. Whole number starts from -3, -2, -, 0, (Integers)

Understand:

    Natural Numbers: 1,2,3,…

    Whole numbers: 0,1,2,3,….

    Integers Z: …-2,-1,0,1,2,….

    Rational number: -2,-1.5,-1,-0.5,0,0.5,1,1.5,2….

  Algebraic numbers square root…

    Irrational number is the PI… 3.14

An irrational number cannot be expressed as a fraction. 
Irrational numbers cannot be represented as terminating or repeating decimals.
Irrational numbers are non-terminating, non-repeating decimals.

Examples of irrational numbers are: 

Either you are adding/subtracting/multiplying/dividing –

(Keep this formula in mind):

Factor              *          Factor              =          Product

Positive    *    Positive  =   Positive   (+a * +b = +ab)

Negative  *    Negative =  Positive   (-a * -b = +ab)

Negative  *    Positive  =   Negative (-a * +b = -ab)

Positive   *    Negative =  Negative (+a * -b = -ab)

Another Explanation:

A friend is +, an enemy is −

Algebra Word Expressions:

Writing Phrases as Algebraic Expression:

The variable x is usually used to represent “a number” in these expressions.

            Just as a phrase ten more than five is written as 10 + 5

                                                Or

            The phrase ten more than a number is written as 10 + x

Unknown Variables:

We usually use x to represent the first number and y to represent the second number. Twice a number plus four times and other number would be written as 2x + 4y

1. Negative nine times a number

2. A number combined with six

3. Eight take away a number

4. A number shared by ten

5. Two plus one-half of a number (or a number divided by 2)

6. The total of number and negative one times another number 

7. The quotient of seven and a number minus a second number 

8. Eighteen less than a number multiplied by another number 

9. The difference between the square of a number and ten times another number (x -10y)

    10. The total of six times a number and the difference between another number and nine

Answer Key:

1. -9x or -9(x)
2. x + 6
3. 8 – x
4. x/10
5. 2 + x/2

6. x + -1y  simplifies to x-y

7. 7/x-y8.   

8. xy - 18

9.  x² -10y

10. 6(x) + (y-9)

Subtracting Negative and Positive Integers Word Game:

To subtract integers, change the sign on the integer that is to be subtracted.

• If both signs are positive, the answer will be positive.
  Example: 14 - (-6) = 14 + 6 = 20
• If both signs are negative, the answer will be negative.
  Example: -14 - (+6) = -14 - 6 = -20
• If the signs are different subtract the smaller absolute value from the larger absolute value. The sign will be the sign of the integer that produced the larger absolute value.
  Example: 14 - (+6) = 14 - 6 = 8
  Example: -14 - (-6) = -14 + 6 = -8

Minute Word Game:

Key:

            -6 - 1 =        9 -  -8 =         -4 - 2 =

            5 - -6 =         3 – 7 =         2 - -10 =

            11        17        -4         -6         12        -7         11

            __        __        __        __        __        __        __