BASIC ALGEBRA FACTS

1. common denominator:   1/8 + 5/8  = 6/8     =  (2 x 3) / (2 x 4) = 3/4          1/x + 5/x = 6/x      y/x + c/x = (y + c)/x  

                                        y/x - 5y/x = (y - 5y)/x = -4y/x

2. multiplication: same signs multiplied equals a positive         different signs multiplied equals a negative

    2 x 3 = 2/1 x 3/1 = 6/1 = 6       2/5 x 7/12 = (2 x 7)/(5 x 12) = 14/60 = 7/30          (a/b) (c/d) = (a x c)/(b x d)          (-a/b) (-c/d) = (a x c)/(b x d)

3. addition / subtraction        Positive + positive = positive        3 + 2 = 5         3x + 2x = 5x

                                           Negative + negative = negative (add the numbers and use a negative sign)   -3 -2 = -5     -3x - 2x = -5x

                                          Positive + negative = sign of larger numeric value    -3 + 7 = 4     -3x + 7x = -4x      -18x + 6x = -12x

4. distributive:     a(b + c) = ab + ac       a(b - c) = ab - ac      (b+c)a = a(b+c) = ab + ac      -a(b+c)= -ab - ac      -(a + b) = -a - b

                         -a(-a -b) = a + b

5. addition and subtraction of polynomials:    combine like terms only!!

6. exponents:           Y = Y¹    (F)(F) = F²    (F²)(F³)=F⁵   (X⁵)(X^-12)=X^-7   ADD EXPONENTS WHEN MULTIPLYING     

                      For addition or subtraction only combine like terms = do not alter exponents:     X² + 3X² = 4X²

 B⁶ = BxBxBxBxBxB          (B²)³=B²xB²xB²=BxBxBxBxBxB=B⁶        (4b³y^-7)³=4³b⁹y^-21   =(64b⁹)/y²¹   

x⁵/x⁹ = x^(5-9) = 1/x⁴ = 1/x^(9-5)     x^ax^b = x^(a+b)        x^a/x^b = x^(a-b)

7. Equations:  ISOLATE the variable -- GET IT BY ITSELF ---  use GASR

        group anything you can [get rid of parenthesis] - get rid of added things - get rid of subtracted things - get rid of multiplied things

(a/b)x +c -d =e        x=(e+d-c)(b/a)

8. Order of operations:     Parenthesis, exponents, (multiplication or division), (addition or subtraction)

9. Natural numbers:  1,2,3,4,5...   Whole numbers: 0,1,2,3,4,5.....   Integers:   .......-3,-2,-1,0,1,2,3,4..................

10. Translating to words:   subtraction and division is not straight forward:   a number is 4 less than 9  -------     n = 9 - 4

                                        8 less than a number is 16 ---------   n - 8 = 16

11. Adding two negatives = subtracting a positive from a negative :  Add the digits together and the answer is negative:  -7 - 9 = -16

12. Subtracting a negative from a positive or adding a negative to a positive:  Add the digits together and the answer has the sign of the largest number:   8x - 19x = -(19x - 8x)=-(11x) = -11x

13. prime factorization: create a factor tree by starting with 1 then 2 then 3 ....