Math

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Author:
Hanoverstreet
ID:
197006
Filename:
Math
Updated:
2013-01-31 20:50:17
Tags:
Algebra
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Description:
SIGNED NUMBERS
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  1. What are the two parts of a signed number?
    Its algebraic sign, + or − , and its absolute value, which is simply the arithmetical value, that is, the number without its sign.

    |−3 = 3.

     

    |3| = 3.
  2. What is the only difference between  8 − 5  and  5 − 8 ?
    The algebraic signs. They have the same absolute value.
  3. What is a number line?
    The number line is a kind of "ruler" centered on 0.  The negative numbers fall to the left of 0; the positive numbers fall to the right.
  4. What is an
    integer?
    Any positive or negative whole number, including 0.

    0, 1, −1, 2, −2, 3, −3, etc.
  5. What is "The negative of −a is a."?
    • A formal rule.
    • whenever we see something that looks like this
    •   −(−a)

     then we may rewrite it in this form:

    a
  6. Evaluate the following

    a)  −(−10) 
         
    b)  −(2 − 6) 

         
    c)  −(1 + 4 − 7) 

    d)  −(−x)  =
    a)  −(−10)  = 10 

    •      
    • b)  −(2 − 6)  = 4 

    •      
    • c)  −(1 + 4 − 7)  = 2 

    d)  −(−x)  = x
  7. What is the algebraic definition of the negative of a number
    a + (−a) = −a + a = 0

    5 + (−5) = 0.
  8. What is the rule for "adding" a negative number?
  9. a + (−b)  =  a − b
  10. What are the terms? 1 + (−2) + 3 + (−4)  =  1 − 2 + 3 − 4
    1 − 2 + 3 − 4
  11. If the terms have the same sign...
    add their absolute values,and keep that same sign.

    2 + 3 = 5.

    −2 + (−3) = −5.

    −2 − 3 = −5.
  12. If the terms have opposite signs...
    subtract the smaller in absolute value from the larger, and keep the sign of the     larger.



    2 + (−3) = −1.


    −2 + 3 = 1.
  13. What is the fundamental rule for 0?
    a + 0 = 0 + a = a

    Adding 0 to any term  does not change it.

    • 0 + 6 = 6
    • 0 − 6 = −6
    • 0 + (−6) = −6
    • −6 + 0 = −6
  14. What is the rule for subtracting a negative number?
    a − (−b)  =  a + b

    Any problem that looks like this,

    a − (−b)

    rewrite so that it looks like this:

    a + b.

    ex

    −(−5) = +5


    ex

    2 − (−5)=  2 + 5=  7.
  15. What is the Rule of Signs for multiplying, dividing, and
    fractions?
    Like signs produce a positive number; unlike signs, a negative number.

    −5(−2 =  10.  

    5(−2) =  −10.

    −12/−4 =  3.

    12 /−4 =  −3.
  16. An even number of negative factors produces a
    positive number. 

     


    (−2)(−2) = 4 
  17. While an odd number of negative factors produces a
    negative number.


    (−2)(−2)(−2) = −8
  18. Multiplication is always simpler if factors will produce 10, or 100, or any power of 10.

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