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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.

What is the only difference between 8 − 5 and 5 − 8 ?
The algebraic signs. They have the same absolute value.

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.

What is an
integer?
Any positive or negative whole number, including 0.
0, 1, −1, 2, −2, 3, −3, etc.

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

Evaluate the following
a) −(−10)
b) −(2 − 6)
c) −(1 + 4 − 7)
d) −(−x) =
a) −(−10) = 10
d) −(−x) = x

What is the algebraic definition of the negative of a number
a + (−a) = −a + a = 0
5 + (−5) = 0.

What is the rule for "adding" a negative number?


What are the terms? 1 + (−2) + 3 + (−4) = 1 − 2 + 3 − 4
1 − 2 + 3 − 4

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.

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.

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

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.

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.

An even number of negative factors produces a
positive number.
(−2)(−2) = 4

While an odd number of negative factors produces a
negative number.
(−2)(−2)(−2) = −8

Multiplication is always simpler if factors will produce 10, or 100, or any power of 10.

