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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:

 = 3.141592654….. = 1.414213562….. and 0.12122122212…

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 −

 + + = + a friend of a friend is my friend + − = − a friend of an enemy is my enemy − + = − an enemy of a friend is my enemy − − = + an enemy of an enemy is my friend

Algebra Word Expressions:

 Addition Subtraction Multiplication Division Combine Take away Times Share Together Difference Product Quotient Total Minus Factors Percent Plus Decrease Each Out of Sum Left Every Average Altogether Less than Increase Each And Fewer than Of per increase Double, triple…

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

1. A number combined with six

1. Eight take away a number

1. A number shared by ten

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

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

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

1. Eighteen less than a number multiplied by another number

1. 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

__        __        __        __        __        __        __